<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD Journal Publishing DTD v2.3 20070202//EN" "journalpublishing.dtd">
<article article-type="research-article" dtd-version="2.3" xml:lang="EN" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">
<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Genet.</journal-id>
<journal-title>Frontiers in Genetics</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Genet.</abbrev-journal-title>
<issn pub-type="epub">1664-8021</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="publisher-id">980437</article-id>
<article-id pub-id-type="doi">10.3389/fgene.2022.980437</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Genetics</subject>
<subj-group>
<subject>Original Research</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>Identifying potential microRNA biomarkers for colon cancer and colorectal cancer through bound nuclear norm regularization</article-title>
<alt-title alt-title-type="left-running-head">Zhai et al.</alt-title>
<alt-title alt-title-type="right-running-head">
<ext-link ext-link-type="uri" xlink:href="https://doi.org/10.3389/fgene.2022.980437">10.3389/fgene.2022.980437</ext-link>
</alt-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname>Zhai</surname>
<given-names>Shengyong</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="fn" rid="fn1">
<sup>&#x2020;</sup>
</xref>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Li</surname>
<given-names>Xiaoling</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
<xref ref-type="fn" rid="fn1">
<sup>&#x2020;</sup>
</xref>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Wu</surname>
<given-names>Yan</given-names>
</name>
<xref ref-type="aff" rid="aff4">
<sup>4</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/1541475/overview"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Shi</surname>
<given-names>Xiaoli</given-names>
</name>
<xref ref-type="aff" rid="aff4">
<sup>4</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/1382307/overview"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Ji</surname>
<given-names>Binbin</given-names>
</name>
<xref ref-type="aff" rid="aff4">
<sup>4</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/1190933/overview"/>
</contrib>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Qiu</surname>
<given-names>Chun</given-names>
</name>
<xref ref-type="aff" rid="aff5">
<sup>5</sup>
</xref>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
<uri xlink:href="https://loop.frontiersin.org/people/1888298/overview"/>
</contrib>
</contrib-group>
<aff id="aff1">
<sup>1</sup>
<institution>Department of General Surgery</institution>, <institution>Weifang People&#x2019;s Hospital</institution>, <addr-line>Shandong</addr-line>, <country>China</country>
</aff>
<aff id="aff2">
<sup>2</sup>
<institution>The Second Department of Oncology</institution>, <institution>Beidahuang Industry Group General Hospital</institution>, <addr-line>Harbin</addr-line>, <country>China</country>
</aff>
<aff id="aff3">
<sup>3</sup>
<institution>Heilongjiang Second Cancer Hospital</institution>, <addr-line>Harbin</addr-line>, <country>China</country>
</aff>
<aff id="aff4">
<sup>4</sup>
<institution>Geneis Beijing Co.</institution>, <institution>Ltd.</institution>, <addr-line>Beijing</addr-line>, <country>China</country>
</aff>
<aff id="aff5">
<sup>5</sup>
<institution>Department of Oncology</institution>, <institution>Hainan General Hospital</institution>, <addr-line>Haikou</addr-line>, <country>China</country>
</aff>
<author-notes>
<fn fn-type="edited-by">
<p>
<bold>Edited by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/857760/overview">Liqian Zhou</ext-link>, Hunan University of Technology, China</p>
</fn>
<fn fn-type="edited-by">
<p>
<bold>Reviewed by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/801622/overview">Guohua Huang</ext-link>, Shaoyang University, China</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/805132/overview">Ying Liang</ext-link>, Jiangxi Agricultural University, China</p>
</fn>
<corresp id="c001">&#x2a;Correspondence: Chun Qiu, <email>13976242127@139.com&#x200a;</email>
</corresp>
<fn fn-type="equal" id="fn1">
<label>
<sup>&#x2020;</sup>
</label>
<p>These authors have contributed equally to this work and share first authorship</p>
</fn>
<fn fn-type="other">
<p>This article was submitted to RNA, a section of the journal Frontiers in Genetics</p>
</fn>
</author-notes>
<pub-date pub-type="epub">
<day>22</day>
<month>09</month>
<year>2022</year>
</pub-date>
<pub-date pub-type="collection">
<year>2022</year>
</pub-date>
<volume>13</volume>
<elocation-id>980437</elocation-id>
<history>
<date date-type="received">
<day>28</day>
<month>06</month>
<year>2022</year>
</date>
<date date-type="accepted">
<day>01</day>
<month>08</month>
<year>2022</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2022 Zhai, Li, Wu, Shi, Ji and Qiu.</copyright-statement>
<copyright-year>2022</copyright-year>
<copyright-holder>Zhai, Li, Wu, Shi, Ji and Qiu</copyright-holder>
<license xlink:href="http://creativecommons.org/licenses/by/4.0/">
<p>This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</p>
</license>
</permissions>
<abstract>
<p>Colon cancer and colorectal cancer are two common cancer-related deaths worldwide. Identification of potential biomarkers for the two cancers can help us to evaluate their initiation, progression and therapeutic response. In this study, we propose a new microRNA-disease association identification method, BNNRMDA, to discover potential microRNA biomarkers for the two cancers. BNNRMDA better combines disease semantic similarity and Gaussian Association Profile Kernel (GAPK) similarity, microRNA function similarity and GAPK similarity, and the bound nuclear norm regularization model. Compared to other five classical microRNA-disease association identification methods (MIDPE, MIDP, RLSMDA, GRNMF, AND LPLNS), BNNRMDA obtains the highest AUC of 0.9071, demonstrating its strong microRNA-disease association identification performance. BNNRMDA is applied to discover possible microRNA biomarkers for colon cancer and colorectal cancer. The results show that all 73 known microRNAs associated with colon cancer in the HMDD database have the highest association scores with colon cancer and are ranked as top 73. Among 137 known microRNAs associated with colorectal cancer in the HMDD database, 129 microRNAs have the highest association scores with colorectal cancer and are ranked as top 129. In addition, we predict that hsa-miR-103a could be a potential biomarker of colon cancer and hsa-mir-193b and hsa-mir-7days could be potential biomarkers of colorectal cancer.</p>
</abstract>
<kwd-group>
<kwd>colon cancer</kwd>
<kwd>colorectal cancer</kwd>
<kwd>microRNA</kwd>
<kwd>biomarker</kwd>
<kwd>microRNA-disease association</kwd>
<kwd>bound nuclear norm regularization</kwd>
</kwd-group>
<contract-sponsor id="cn001">Medical and Health Science and Technology Development Project of Shandong Province<named-content content-type="fundref-id">10.13039/501100019446</named-content>
</contract-sponsor>
</article-meta>
</front>
<body>
<sec id="s1">
<title>1 Introduction</title>
<p>Cancers are seriously threatening and endangering human health (<xref ref-type="bibr" rid="B47">Yang et al., 2013</xref>; <xref ref-type="bibr" rid="B19">Liu et al., 2021</xref>; <xref ref-type="bibr" rid="B48">Yang et al., 2022</xref>). Colon cancer and colorectal cancer are two of leading causes of cancer-related deaths worldwide (<xref ref-type="bibr" rid="B12">Lee et al., 2018</xref>; <xref ref-type="bibr" rid="B34">Piawah and Venook, 2019</xref>). Patients with colon cancer only have a survival rate of 10% when diagnosed at late stage. More importantly, colon cancer shows a higher incidence rate in elder populations. The survival rate of patients with colon cancer is densely associated with the size, location, and stage of the tumor. Metastasis may be the leading cause of deaths for patients suffered from late-stage colon cancer. Thus, understanding the mechanisms of colon cancer could contribute to designing more strong therapeutic options (<xref ref-type="bibr" rid="B21">Ma et al., 2021</xref>).</p>
<p>Nowadays, patients with colorectal cancer show a younger trend. In the last decade, incidence rates and death rates of colorectal cancers separately increased by 22 and 13% among adults under 50 years in the United State. However, their precise aetiologic factors still remain unknown. Many evidence demonstrate that early screening of colorectal cancer can reduce their incidence and mortality. Thus, the identification of diagnosis or prognosis biomarkers can contribute to assessment of tumour initiation, progression and therapeutic response for colorectal cancer (<xref ref-type="bibr" rid="B36">Sampath et al., 2021</xref>).</p>
<p>Many researches show that numerous RNA data play important roles in the development and metastasis of various diseases including cancers and COVID-19 (<xref ref-type="bibr" rid="B10">Huang et al., 2017</xref>; <xref ref-type="bibr" rid="B29">Peng L. et al., 2020</xref>; <xref ref-type="bibr" rid="B46">Xu et al., 2020</xref>; <xref ref-type="bibr" rid="B49">Yang et al., 2020</xref>; <xref ref-type="bibr" rid="B53">Zhang et al., 2021</xref>; <xref ref-type="bibr" rid="B30">Peng L. et al., 2022</xref>; <xref ref-type="bibr" rid="B37">Shen et al., 2022</xref>; <xref ref-type="bibr" rid="B38">Tian et al., 2022</xref>). In particular, noncoding RNAs could be biomarkers to boost drug design (<xref ref-type="bibr" rid="B18">Liu et al., 2020</xref>; <xref ref-type="bibr" rid="B22">Meng et al., 2022</xref>). For example, lncRNAs and circRNAs have been used as biomarkers of cancers (<xref ref-type="bibr" rid="B33">Peng et al., 2021a</xref>; <xref ref-type="bibr" rid="B32">Peng et al., 2021b</xref>; <xref ref-type="bibr" rid="B4">Chen et al., 2021</xref>; <xref ref-type="bibr" rid="B15">Li et al., 2021</xref>; <xref ref-type="bibr" rid="B39">Verduci et al., 2021</xref>; <xref ref-type="bibr" rid="B42">Wang et al., 2021</xref>; <xref ref-type="bibr" rid="B31">Peng L. H. et al., 2022</xref>). MicroRNAs (miRNAs) are a class of small non-coding RNAs with 22&#x2013;24 nucleotides in length (<xref ref-type="bibr" rid="B14">Li et al., 2018</xref>; <xref ref-type="bibr" rid="B3">Chen et al., 2020</xref>). MicroRNAs can bind to mRNAs of target genes to inhibit expression of these genes. In addition, a few microRNAs may suppress tumors while other microRNAs may affect the progression and metastasis of tumors.</p>
<p>The dysfunction of microRNAs is densely linked to the inflammation of colon cancer. For example, Ma et al. (<xref ref-type="bibr" rid="B21">Ma et al., 2021</xref>) found that M2 macrophage-derived exosomal miR-155-5p may have an association with the immune escape of cells in colon cancer. Pagotto et al. (<xref ref-type="bibr" rid="B25">Pagotto et al., 2022</xref>) observed that the miR-483 gene could have a responsive to glucose availability for colon cancer. Miao et al. (<xref ref-type="bibr" rid="B23">Miao et al., 2021</xref>) identified that miR-4284 could be a therapeutic target in colon cancer. Dougherty et al. (<xref ref-type="bibr" rid="B6">Dougherty et al., 2021</xref>) inferred that the upregulations of microRNA-143 and microRNA-145 have close linkages with colonocytes suppresses colitis and inflammation-related colon cancer. Zhang et al. (<xref ref-type="bibr" rid="B53">Zhang et al., 2021</xref>) suggested that microRNA-24-3p could heighten the resistance of colon cancer cell to MTX. Yue et al. (<xref ref-type="bibr" rid="B52">Yue et al., 2021</xref>) reported that NEDD4 could trigger colon cancer progression through microRNA-340-5p suppression. In summary, the identification of microRNAs in the blood, tissues, and faecal matter will help us use these microRNA as biomarkers in early detection of colon cancer and thus design strong targeted therapeutic strategies for inflammation-mediated colon cancer (<xref ref-type="bibr" rid="B27">Peng et al., 2018</xref>; <xref ref-type="bibr" rid="B36">Sampath et al., 2021</xref>).</p>
<p>More importantly, microRNAs densely link to the carcinogenic process of colorectal cancer. For example, microRNA-143-3p can limit colorectal cancer metastases (Guo et al., 2019), microRNA-375-3p can boost chemosensitivity to 5-fluorouracil through targeting thymidylate synthase in colorectal cancer (<xref ref-type="bibr" rid="B46">Xu et al., 2020</xref>), microRNA-451a influences colorectal cancer proliferation (<xref ref-type="bibr" rid="B35">Ruhl et al., 2018</xref>), and microRNA-146a can inhibit tumorigenic inflammation of colorectal cancer (<xref ref-type="bibr" rid="B7">Garo et al., 2021</xref>). Biomarkers are an important strategy in early screening, prognostication, survival, and treatment response prediction for cancers. Therefore, microRNAs have been explored as biomarkers in colorectal cancer (<xref ref-type="bibr" rid="B28">Peng LH. et al., 2020</xref>; <xref ref-type="bibr" rid="B24">Ogunwobi et al., 2020</xref>).</p>
<p>Recently, many researchers have been devoted to microRNA biomarker identification for cancer including colon cancer and colorectal cancer by computational microRNA-disease association prediction (<xref ref-type="bibr" rid="B26">Peng et al., 2017</xref>; <xref ref-type="bibr" rid="B15">Li et al., 2021</xref>). Huang et al. (<xref ref-type="bibr" rid="B9">Huang et al., 2021</xref>) innovatively represented microRNA-disease-type triples as a tensor and further designed a tensor decomposition model to detect new microRNA-disease associations. Li et al. (<xref ref-type="bibr" rid="B15">Li et al., 2021</xref>) considered that the abnormal expression of microRNAs is densely associated with the evolution and progression of human diseases and inferred disease-related microRNAs as new biomarkers through a graph auto-encoder model. Chen et al. (<xref ref-type="bibr" rid="B4">Chen et al., 2021</xref>) designed a deep learning model for microRNA-disease association identification based on deep belief network. <xref ref-type="bibr" rid="B55">Wang et al. (2022)</xref>) pretrained a stacked autoencoder to predict potential microRNA-disease associations in an unsupervised manner. These methods effectively improved microRNA biomarker identification of human complex diseases.</p>
<p>In this study, we design a MicroRNA-Disease Association prediction algorithm (BNNRMDA) to find potential microRNA biomarkers for colon cancer and colorectal cancer based on disease semantic similarity, microRNA functional similarity, Gaussian association profile kernel (GAPK) similarity, and the Bound Nuclear Norm Regularization model.</p>
</sec>
<sec id="s2">
<title>2 Materials and methods</title>
<sec id="s2-1">
<title>2.1 Data</title>
<sec id="s2-1-1">
<title>2.1.1 Dataset</title>
<p>Experimentally confirmed microRNA-disease association data can be downloaded from the HMDD database provided by Li et al. (<xref ref-type="bibr" rid="B16">Li et al., 2014</xref>). The hierarchical structures between diseases can be downloaded from the MeSH database (<ext-link ext-link-type="uri" xlink:href="https://www.nlm.nih.gov/mesh/">https://www.nlm.nih.gov/mesh/</ext-link>). Experimentally supported microRNA-gene interactions can be downloaded from TarBase (<xref ref-type="bibr" rid="B40">Vergoulis et al., 2012</xref>), miRTarBase (<xref ref-type="bibr" rid="B8">Hsu et al., 2014</xref>), and miRecords (<xref ref-type="bibr" rid="B43">Xiao et al., 2009</xref>). We acquired microRNA-disease associations between 495 microRNAs and 378 diseases, hierarchical structures for 4,663 diseases, and 38,089 microRNA-gene interactions between 477 microRNAs and 12,422 genes. Finally, we obtained 4,791 associations between 353 microRNAs and 327 diseases after removing microRNAs without target genes and diseases without hierarchical structures.</p>
</sec>
<sec id="s2-1-2">
<title>2.1.2 Disease semantic similarity</title>
<p>For a known disease <inline-formula id="inf1">
<mml:math id="m1">
<mml:mi>d</mml:mi>
</mml:math>
</inline-formula>, it can be described as a directed acyclic graph (<inline-formula id="inf2">
<mml:math id="m2">
<mml:mrow>
<mml:mi>D</mml:mi>
<mml:mi>A</mml:mi>
<mml:mi>G</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>) based on the MeSH descriptor: <inline-formula id="inf3">
<mml:math id="m3">
<mml:mrow>
<mml:mi>D</mml:mi>
<mml:mi>A</mml:mi>
<mml:msub>
<mml:mi>G</mml:mi>
<mml:mi>d</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mi>d</mml:mi>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>T</mml:mi>
<mml:mi>d</mml:mi>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>E</mml:mi>
<mml:mi>d</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> where <inline-formula id="inf4">
<mml:math id="m4">
<mml:mrow>
<mml:msub>
<mml:mi>T</mml:mi>
<mml:mi>d</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> denotes the set of nodes that contains <inline-formula id="inf5">
<mml:math id="m5">
<mml:mi>d</mml:mi>
</mml:math>
</inline-formula> and all its ancestors, and <inline-formula id="inf6">
<mml:math id="m6">
<mml:mrow>
<mml:msub>
<mml:mi>E</mml:mi>
<mml:mi>d</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> represents corresponding direct edges. Given a disease <inline-formula id="inf7">
<mml:math id="m7">
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>&#x2208;</mml:mo>
<mml:msub>
<mml:mi>T</mml:mi>
<mml:mi>d</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, its semantic contribution to <inline-formula id="inf8">
<mml:math id="m8">
<mml:mi>d</mml:mi>
</mml:math>
</inline-formula> can be defined as <xref ref-type="disp-formula" rid="e1">Eq. 1</xref>:<disp-formula id="e1">
<mml:math id="m9">
<mml:mrow>
<mml:msub>
<mml:mi>D</mml:mi>
<mml:mi>d</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:mrow>
<mml:mo>{</mml:mo>
<mml:mrow>
<mml:mtable>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mi>i</mml:mi>
<mml:mi>f</mml:mi>
<mml:mo>&#xa0;</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#x2260;</mml:mo>
<mml:mi>d</mml:mi>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
</mml:mrow>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:mi>m</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>x</mml:mi>
<mml:mrow>
<mml:mo>{</mml:mo>
<mml:mrow>
<mml:mo>&#x394;</mml:mo>
<mml:mo>&#x2217;</mml:mo>
<mml:msub>
<mml:mi>D</mml:mi>
<mml:mi>d</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>&#x2032;</mml:mo>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mtext>&#x7c;</mml:mtext>
<mml:mi>t</mml:mi>
<mml:mo>&#x2032;</mml:mo>
<mml:mo>&#x2208;</mml:mo>
<mml:mi>c</mml:mi>
<mml:mi>h</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>l</mml:mi>
<mml:mi>d</mml:mi>
<mml:mi>r</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>n</mml:mi>
<mml:mo>&#xa0;</mml:mo>
<mml:mi>o</mml:mi>
<mml:mi>f</mml:mi>
<mml:mo>&#xa0;</mml:mo>
<mml:mi>t</mml:mi>
</mml:mrow>
<mml:mo>}</mml:mo>
</mml:mrow>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mi>i</mml:mi>
<mml:mi>f</mml:mi>
<mml:mo>&#xa0;</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#x2260;</mml:mo>
<mml:mi>d</mml:mi>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
</mml:mrow>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:mrow>
</mml:mrow>
</mml:math>
<label>(1)</label>
</disp-formula>where <inline-formula id="inf9">
<mml:math id="m10">
<mml:mo>&#x394;</mml:mo>
</mml:math>
</inline-formula> denotes the semantic contribution decay factor (<inline-formula id="inf10">
<mml:math id="m11">
<mml:mrow>
<mml:mo>&#x394;</mml:mo>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>0.5</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>) (<xref ref-type="bibr" rid="B41">Wang et al., 2010</xref>). In general, two diseases <inline-formula id="inf11">
<mml:math id="m12">
<mml:mrow>
<mml:msub>
<mml:mi>d</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf12">
<mml:math id="m13">
<mml:mrow>
<mml:msub>
<mml:mi>d</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> are more similar when they share more common ancestors. Thus, pairwise semantic similarity between <inline-formula id="inf13">
<mml:math id="m14">
<mml:mrow>
<mml:msub>
<mml:mi>d</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf14">
<mml:math id="m15">
<mml:mrow>
<mml:msub>
<mml:mi>d</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> can be defined as <xref ref-type="disp-formula" rid="e2">Eq. 2</xref>:<disp-formula id="e2">
<mml:math id="m16">
<mml:mrow>
<mml:msup>
<mml:mi>S</mml:mi>
<mml:mi>d</mml:mi>
</mml:msup>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>d</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>d</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mstyle displaystyle="true">
<mml:msub>
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>&#x2208;</mml:mo>
<mml:msub>
<mml:mi>T</mml:mi>
<mml:mrow>
<mml:msub>
<mml:mi>d</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2229;</mml:mo>
<mml:msub>
<mml:mi>T</mml:mi>
<mml:mrow>
<mml:msub>
<mml:mi>d</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>D</mml:mi>
<mml:mrow>
<mml:msub>
<mml:mi>d</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>D</mml:mi>
<mml:mrow>
<mml:msub>
<mml:mi>d</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:mstyle>
</mml:mrow>
<mml:mrow>
<mml:mstyle displaystyle="true">
<mml:msub>
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>&#x2208;</mml:mo>
<mml:msub>
<mml:mi>T</mml:mi>
<mml:mrow>
<mml:msub>
<mml:mi>d</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:msub>
<mml:mi>D</mml:mi>
<mml:mrow>
<mml:msub>
<mml:mi>d</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#x2b;</mml:mo>
<mml:mstyle displaystyle="true">
<mml:msub>
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>&#x2208;</mml:mo>
<mml:msub>
<mml:mi>T</mml:mi>
<mml:mrow>
<mml:msub>
<mml:mi>d</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:msub>
<mml:mi>D</mml:mi>
<mml:mrow>
<mml:msub>
<mml:mi>d</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>t</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:mstyle>
</mml:mrow>
</mml:mstyle>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
<label>(2)</label>
</disp-formula>
</p>
</sec>
<sec id="s2-1-3">
<title>2.1.3 MicroRNA functional similarity</title>
<p>MicroRNA similarity can be computed based on microRNA-gene associations and gene functional network. First, the associated log-likelihood scores <inline-formula id="inf15">
<mml:math id="m17">
<mml:mrow>
<mml:mi>L</mml:mi>
<mml:mi>L</mml:mi>
<mml:mi>S</mml:mi>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>g</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>g</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> between two genes <inline-formula id="inf16">
<mml:math id="m18">
<mml:mrow>
<mml:msub>
<mml:mi>g</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf17">
<mml:math id="m19">
<mml:mrow>
<mml:msub>
<mml:mi>g</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> can be calculated using HumanNet (<xref ref-type="bibr" rid="B13">Lee et al., 2011</xref>).</p>
<p>Second, <inline-formula id="inf18">
<mml:math id="m20">
<mml:mrow>
<mml:mi>L</mml:mi>
<mml:mi>L</mml:mi>
<mml:mi>S</mml:mi>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>g</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>g</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> is normalized by <xref ref-type="disp-formula" rid="e3">Eq. 3</xref>:<disp-formula id="e3">
<mml:math id="m21">
<mml:mrow>
<mml:mi>L</mml:mi>
<mml:mi>L</mml:mi>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mi>N</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>g</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>g</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mi>L</mml:mi>
<mml:mi>L</mml:mi>
<mml:mi>S</mml:mi>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>g</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>g</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>L</mml:mi>
<mml:mi>L</mml:mi>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mrow>
<mml:mi>m</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mi>L</mml:mi>
<mml:mi>L</mml:mi>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mrow>
<mml:mi>m</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>x</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>L</mml:mi>
<mml:mi>L</mml:mi>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mrow>
<mml:mi>m</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
<label>(3)</label>
</disp-formula>where <inline-formula id="inf19">
<mml:math id="m22">
<mml:mrow>
<mml:mi>L</mml:mi>
<mml:mi>L</mml:mi>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mrow>
<mml:mi>m</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf20">
<mml:math id="m23">
<mml:mrow>
<mml:mi>L</mml:mi>
<mml:mi>L</mml:mi>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mrow>
<mml:mi>m</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>x</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> represent the minimum and maximum associated log-likelihood scores computed by HumanNet, respectively.</p>
<p>Third, similarity between <inline-formula id="inf21">
<mml:math id="m24">
<mml:mrow>
<mml:msub>
<mml:mi>g</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf22">
<mml:math id="m25">
<mml:mrow>
<mml:msub>
<mml:mi>g</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> can be calculated by <xref ref-type="disp-formula" rid="e4">Eq. 4</xref>:<disp-formula id="e4">
<mml:math id="m26">
<mml:mrow>
<mml:msup>
<mml:mi>S</mml:mi>
<mml:mi>g</mml:mi>
</mml:msup>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>g</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>g</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:mrow>
<mml:mo>{</mml:mo>
<mml:mrow>
<mml:mtable>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:msub>
<mml:mi>g</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>g</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
</mml:mrow>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:mn>0</mml:mn>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mi>e</mml:mi>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>g</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>g</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#x2209;</mml:mo>
<mml:mi>H</mml:mi>
<mml:mi>u</mml:mi>
<mml:mi>m</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>N</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:mi>L</mml:mi>
<mml:mi>L</mml:mi>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mi>N</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>g</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>g</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mi>e</mml:mi>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>g</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>g</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#x2208;</mml:mo>
<mml:mi>H</mml:mi>
<mml:mi>u</mml:mi>
<mml:mi>m</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>N</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:mrow>
</mml:mrow>
</mml:math>
<label>(4)</label>
</disp-formula>where <inline-formula id="inf23">
<mml:math id="m27">
<mml:mrow>
<mml:mi>e</mml:mi>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>g</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>g</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> indicates interaction between <inline-formula id="inf24">
<mml:math id="m28">
<mml:mrow>
<mml:msub>
<mml:mi>g</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf25">
<mml:math id="m29">
<mml:mrow>
<mml:msub>
<mml:mi>g</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>.</p>
<p>Finally, the functional similarity between two microRNAs <inline-formula id="inf26">
<mml:math id="m30">
<mml:mrow>
<mml:msub>
<mml:mi>m</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf27">
<mml:math id="m31">
<mml:mrow>
<mml:msub>
<mml:mi>m</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> can be computed by <xref ref-type="disp-formula" rid="e5">Eq. 5</xref> based on their associated genes:<disp-formula id="e5">
<mml:math id="m32">
<mml:mrow>
<mml:msup>
<mml:mi>S</mml:mi>
<mml:mi>m</mml:mi>
</mml:msup>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>m</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>m</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mstyle displaystyle="true">
<mml:mo>&#x2211;</mml:mo>
</mml:mstyle>
<mml:mrow>
<mml:mi>g</mml:mi>
<mml:mo>&#x2208;</mml:mo>
<mml:msub>
<mml:mi>G</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:msub>
<mml:mi>S</mml:mi>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mi>g</mml:mi>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>G</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mstyle displaystyle="true">
<mml:mo>&#x2211;</mml:mo>
</mml:mstyle>
<mml:mrow>
<mml:mi>g</mml:mi>
<mml:mo>&#x2208;</mml:mo>
<mml:msub>
<mml:mi>G</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
</mml:msub>
<mml:mi>S</mml:mi>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mi>g</mml:mi>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>G</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:mrow>
<mml:mo>&#x7c;</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>G</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>&#x7c;</mml:mo>
</mml:mrow>
<mml:mo>&#x2b;</mml:mo>
<mml:mrow>
<mml:mo>&#x7c;</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>G</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>&#x7c;</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
<label>(5)</label>
</disp-formula>where <inline-formula id="inf28">
<mml:math id="m33">
<mml:mrow>
<mml:msub>
<mml:mi>G</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf29">
<mml:math id="m34">
<mml:mrow>
<mml:msub>
<mml:mi>G</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> denotes the gene sets associated with <inline-formula id="inf30">
<mml:math id="m35">
<mml:mrow>
<mml:msub>
<mml:mi>m</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf31">
<mml:math id="m36">
<mml:mrow>
<mml:msub>
<mml:mi>m</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, respectively, <inline-formula id="inf32">
<mml:math id="m37">
<mml:mrow>
<mml:mrow>
<mml:mo>&#x7c;</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>G</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>&#x7c;</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf33">
<mml:math id="m38">
<mml:mrow>
<mml:mrow>
<mml:mo>&#x7c;</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>G</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>&#x7c;</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> denote corresponding cardinalities, respectively, and <inline-formula id="inf34">
<mml:math id="m39">
<mml:mrow>
<mml:mi>S</mml:mi>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mi>g</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>G</mml:mi>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:mi>m</mml:mi>
<mml:mi>a</mml:mi>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mrow>
<mml:msub>
<mml:mi>g</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>&#x2208;</mml:mo>
<mml:mi>G</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo>{</mml:mo>
<mml:mrow>
<mml:msup>
<mml:mi>S</mml:mi>
<mml:mi>g</mml:mi>
</mml:msup>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mi>g</mml:mi>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>g</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mo>}</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>.</p>
</sec>
<sec id="s2-1-4">
<title>2.1.4 GAPK similarity</title>
<p>For a known disease <inline-formula id="inf35">
<mml:math id="m40">
<mml:mrow>
<mml:msub>
<mml:mi>d</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> in a microRNA-disease association matrix <inline-formula id="inf36">
<mml:math id="m41">
<mml:mrow>
<mml:msub>
<mml:mi>X</mml:mi>
<mml:mrow>
<mml:mi>a</mml:mi>
<mml:mo>&#xd7;</mml:mo>
<mml:mi>b</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, let the <inline-formula id="inf37">
<mml:math id="m42">
<mml:mi>i</mml:mi>
</mml:math>
</inline-formula> th row of <inline-formula id="inf38">
<mml:math id="m43">
<mml:mi>X</mml:mi>
</mml:math>
</inline-formula> denotes its Gaussian association profile <inline-formula id="inf39">
<mml:math id="m44">
<mml:mrow>
<mml:mi>G</mml:mi>
<mml:mi>A</mml:mi>
<mml:mi>P</mml:mi>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>d</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> to represent its association features with all diseases. GAPK similarity between diseases <inline-formula id="inf40">
<mml:math id="m45">
<mml:mrow>
<mml:msub>
<mml:mi>d</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf41">
<mml:math id="m46">
<mml:mrow>
<mml:msub>
<mml:mi>d</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> can be measured by <xref ref-type="disp-formula" rid="e6">Eq. 6</xref>.<disp-formula id="e6">
<mml:math id="m47">
<mml:mrow>
<mml:mtable>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:msub>
<mml:mi>G</mml:mi>
<mml:mi>D</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>d</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>d</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:mi>exp</mml:mi>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>&#x3b3;</mml:mi>
<mml:mi>d</mml:mi>
</mml:msub>
<mml:mo>&#x2016;</mml:mo>
<mml:mi>G</mml:mi>
<mml:mi>A</mml:mi>
<mml:mi>P</mml:mi>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>d</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>G</mml:mi>
<mml:mi>A</mml:mi>
<mml:mi>P</mml:mi>
<mml:msup>
<mml:mrow>
<mml:mrow>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>d</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mo>&#x2016;</mml:mo>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b3;</mml:mi>
<mml:mi>d</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mi>&#x3b3;</mml:mi>
<mml:msub>
<mml:mo>&#x2032;</mml:mo>
<mml:mi>d</mml:mi>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mfrac>
<mml:mn>1</mml:mn>
<mml:mi>a</mml:mi>
</mml:mfrac>
<mml:munderover>
<mml:mstyle displaystyle="true">
<mml:mo>&#x2211;</mml:mo>
</mml:mstyle>
<mml:mrow>
<mml:mi>k</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mi>a</mml:mi>
</mml:munderover>
<mml:mi mathvariant="italic">&#x2016;G</mml:mi>
<mml:mi>A</mml:mi>
<mml:mi>P</mml:mi>
<mml:msup>
<mml:mrow>
<mml:mrow>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>d</mml:mi>
<mml:mi>k</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mo>&#x2016;</mml:mo>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:mtd>
</mml:mtr>
</mml:mtable>
<mml:mo>&#xa0;</mml:mo>
</mml:mrow>
</mml:math>
<label>(6)</label>
</disp-formula>where <inline-formula id="inf42">
<mml:math id="m48">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b3;</mml:mi>
<mml:mi>d</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> indicates normalized kernel bandwidth according to parameter <inline-formula id="inf43">
<mml:math id="m49">
<mml:mrow>
<mml:mi>&#x3b3;</mml:mi>
<mml:msub>
<mml:mo>&#x2032;</mml:mo>
<mml:mi>d</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, and <inline-formula id="inf44">
<mml:math id="m50">
<mml:mi>a</mml:mi>
</mml:math>
</inline-formula> indicates the number of diseases.</p>
<p>Similarly, for a known microRNA <inline-formula id="inf45">
<mml:math id="m51">
<mml:mrow>
<mml:msub>
<mml:mi>m</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, let the <inline-formula id="inf46">
<mml:math id="m52">
<mml:mi>i</mml:mi>
</mml:math>
</inline-formula> th column of <inline-formula id="inf47">
<mml:math id="m53">
<mml:mi>X</mml:mi>
</mml:math>
</inline-formula> denotes its Gaussian association profile <inline-formula id="inf48">
<mml:math id="m54">
<mml:mrow>
<mml:mi>G</mml:mi>
<mml:mi>A</mml:mi>
<mml:mi>P</mml:mi>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>m</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> to describe its association features with all microRNAs. GAPK similarity between microRNAs <inline-formula id="inf49">
<mml:math id="m55">
<mml:mrow>
<mml:msub>
<mml:mi>m</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf50">
<mml:math id="m56">
<mml:mrow>
<mml:msub>
<mml:mi>m</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> can be measured by <xref ref-type="disp-formula" rid="e7">Eq. 7</xref>:<disp-formula id="e7">
<mml:math id="m57">
<mml:mrow>
<mml:mtable>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:msub>
<mml:mi>G</mml:mi>
<mml:mi>M</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>m</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>m</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:mi>exp</mml:mi>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>&#x3b3;</mml:mi>
<mml:mi>m</mml:mi>
</mml:msub>
<mml:mi mathvariant="italic">&#x2016;G</mml:mi>
<mml:mi>A</mml:mi>
<mml:mi>P</mml:mi>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>m</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>G</mml:mi>
<mml:mi>A</mml:mi>
<mml:mi>P</mml:mi>
<mml:msup>
<mml:mrow>
<mml:mrow>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>m</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mo>&#x2016;</mml:mo>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b3;</mml:mi>
<mml:mi>m</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mi>&#x3b3;</mml:mi>
<mml:msub>
<mml:mo>&#x2032;</mml:mo>
<mml:mi>m</mml:mi>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mfrac>
<mml:mn>1</mml:mn>
<mml:mi>b</mml:mi>
</mml:mfrac>
<mml:munderover>
<mml:mstyle displaystyle="true">
<mml:mo>&#x2211;</mml:mo>
</mml:mstyle>
<mml:mrow>
<mml:mi>k</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mi>b</mml:mi>
</mml:munderover>
<mml:mi mathvariant="italic">&#x2016;G</mml:mi>
<mml:mi>A</mml:mi>
<mml:mi>P</mml:mi>
<mml:msup>
<mml:mrow>
<mml:mrow>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>m</mml:mi>
<mml:mi>k</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mo>&#x2016;</mml:mo>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:math>
<label>(7)</label>
</disp-formula>where <inline-formula id="inf51">
<mml:math id="m58">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b3;</mml:mi>
<mml:mi>m</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> indicates normalized kernel bandwidth according to parameter <inline-formula id="inf52">
<mml:math id="m59">
<mml:mrow>
<mml:mi>&#x3b3;</mml:mi>
<mml:msub>
<mml:mo>&#x2032;</mml:mo>
<mml:mi>m</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, and <inline-formula id="inf53">
<mml:math id="m60">
<mml:mi>b</mml:mi>
</mml:math>
</inline-formula> indicates the number of microRNAs.</p>
</sec>
<sec id="s2-1-5">
<title>2.1.5 Similarity fusion</title>
<p>Disease semantic similarity <inline-formula id="inf54">
<mml:math id="m61">
<mml:mrow>
<mml:msup>
<mml:mi>S</mml:mi>
<mml:mi>d</mml:mi>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> and GAPK similarity <inline-formula id="inf55">
<mml:math id="m62">
<mml:mrow>
<mml:msub>
<mml:mi>G</mml:mi>
<mml:mi>d</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> are fused to calculate the final disease similarity matrix <inline-formula id="inf56">
<mml:math id="m63">
<mml:mrow>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mi>D</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> by <xref ref-type="disp-formula" rid="e8">Eq. 8</xref>:<disp-formula id="e8">
<mml:math id="m64">
<mml:mrow>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mi>D</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mi>w</mml:mi>
<mml:msub>
<mml:mi>G</mml:mi>
<mml:mi>D</mml:mi>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>w</mml:mi>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:msup>
<mml:mi>S</mml:mi>
<mml:mi>d</mml:mi>
</mml:msup>
</mml:mrow>
</mml:math>
<label>(8)</label>
</disp-formula>where the parameter <inline-formula id="inf57">
<mml:math id="m65">
<mml:mi>w</mml:mi>
</mml:math>
</inline-formula> is applied to measure the weight between disease semantic similarity and GAPK similarity.</p>
<p>MicroRNA functional similarity <inline-formula id="inf58">
<mml:math id="m66">
<mml:mrow>
<mml:msup>
<mml:mi>S</mml:mi>
<mml:mi>m</mml:mi>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> and GAPK similarity <inline-formula id="inf59">
<mml:math id="m67">
<mml:mrow>
<mml:msub>
<mml:mi>G</mml:mi>
<mml:mi>m</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> are fused to calculate the final microRNA similarity matrix by <xref ref-type="disp-formula" rid="e9">Eq. 9</xref>:<disp-formula id="e9">
<mml:math id="m68">
<mml:mrow>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mi>M</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mi>w</mml:mi>
<mml:msub>
<mml:mi>G</mml:mi>
<mml:mi>M</mml:mi>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>w</mml:mi>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:msup>
<mml:mi>S</mml:mi>
<mml:mi>m</mml:mi>
</mml:msup>
</mml:mrow>
</mml:math>
<label>(9)</label>
</disp-formula>where the parameter <inline-formula id="inf60">
<mml:math id="m69">
<mml:mi>w</mml:mi>
</mml:math>
</inline-formula> is applied to measure the weight between microRNA functional similarity and GAPK similarity.</p>
</sec>
</sec>
<sec id="s2-2">
<title>2.2 Heterogeneous microRNA-disease network construction</title>
<p>A heterogeneous microRNA-disease network is created by fusing microRNA similarity network, disease similarity network, and microRNA-disease association network. Each edge in similarity network is weighted based on the computed similarity. The heterogeneous microRNA-disease network can be described using a bipartite graph <inline-formula id="inf61">
<mml:math id="m70">
<mml:mrow>
<mml:mi>G</mml:mi>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>M</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>D</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>E</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>, where <inline-formula id="inf62">
<mml:math id="m71">
<mml:mi>M</mml:mi>
</mml:math>
</inline-formula> and <inline-formula id="inf63">
<mml:math id="m72">
<mml:mi>D</mml:mi>
</mml:math>
</inline-formula> separately represent microRNA set and disease set, <inline-formula id="inf64">
<mml:math id="m73">
<mml:mrow>
<mml:mi>E</mml:mi>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>G</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:mrow>
<mml:mo>{</mml:mo>
<mml:msub>
<mml:mi>e</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>}</mml:mo>
</mml:mrow>
<mml:mo>&#x2286;</mml:mo>
<mml:mi>M</mml:mi>
<mml:mo>&#xd7;</mml:mo>
<mml:mi>D</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> represents the microRNA-disease edge set. The adjacency matrix of <inline-formula id="inf65">
<mml:math id="m74">
<mml:mrow>
<mml:mi>G</mml:mi>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>M</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>D</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>E</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> is described as <xref ref-type="disp-formula" rid="e10">Eq. 10</xref>.<disp-formula id="e10">
<mml:math id="m75">
<mml:mrow>
<mml:mi>W</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mrow>
<mml:mo>[</mml:mo>
<mml:mrow>
<mml:mtable>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:msub>
<mml:mi>W</mml:mi>
<mml:mrow>
<mml:mi>m</mml:mi>
<mml:mi>m</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mtd>
<mml:mtd>
<mml:mrow>
<mml:msub>
<mml:mi>W</mml:mi>
<mml:mrow>
<mml:mi>m</mml:mi>
<mml:mi>d</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:mo>&#xa0;</mml:mo>
<mml:msubsup>
<mml:mi>W</mml:mi>
<mml:mrow>
<mml:mi>m</mml:mi>
<mml:mi>d</mml:mi>
</mml:mrow>
<mml:mi>T</mml:mi>
</mml:msubsup>
</mml:mrow>
</mml:mtd>
<mml:mtd>
<mml:mrow>
<mml:msub>
<mml:mi>W</mml:mi>
<mml:mrow>
<mml:mi>d</mml:mi>
<mml:mi>d</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
<mml:mo>]</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
<label>(10)</label>
</disp-formula>where <inline-formula id="inf66">
<mml:math id="m76">
<mml:mrow>
<mml:msub>
<mml:mi>W</mml:mi>
<mml:mrow>
<mml:mi>m</mml:mi>
<mml:mi>d</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> denotes known microRNA-disease association matrix, <inline-formula id="inf67">
<mml:math id="m77">
<mml:mrow>
<mml:msub>
<mml:mi>W</mml:mi>
<mml:mrow>
<mml:mi>m</mml:mi>
<mml:mi>m</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf68">
<mml:math id="m78">
<mml:mrow>
<mml:msub>
<mml:mi>W</mml:mi>
<mml:mrow>
<mml:mi>d</mml:mi>
<mml:mi>d</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> denotes the adjacency matrices about microRNA similarity network and disease similarity network, respectively. Hence, the adjacency matrix can be rewritten as <xref ref-type="disp-formula" rid="e11">Eq. 11</xref>.<disp-formula id="e11">
<mml:math id="m79">
<mml:mrow>
<mml:mi>W</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mrow>
<mml:mo>[</mml:mo>
<mml:mrow>
<mml:mtable>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mi>M</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mtd>
<mml:mtd>
<mml:mrow>
<mml:msub>
<mml:mi>X</mml:mi>
<mml:mrow>
<mml:mi>m</mml:mi>
<mml:mi>d</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:mo>&#xa0;</mml:mo>
<mml:msubsup>
<mml:mi>X</mml:mi>
<mml:mrow>
<mml:mi>m</mml:mi>
<mml:mi>d</mml:mi>
</mml:mrow>
<mml:mi>T</mml:mi>
</mml:msubsup>
</mml:mrow>
</mml:mtd>
<mml:mtd>
<mml:mrow>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mi>D</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
<mml:mo>]</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
<label>(11)</label>
</disp-formula>
</p>
</sec>
<sec id="s2-3">
<title>2.3 BNNRMDA model</title>
<p>In known microRNA-disease association dataset, majority of microRNA-disease pairs are unknown-associated. Inspired by the bound nuclear norm regularization model provided by Yang et al. (<xref ref-type="bibr" rid="B50">Yang et al., 2019</xref>), in this study, we design the bounded nuclear norm regularization-based MDA prediction method to score each unknown microRNA-disease pair. We describe microRNA-disease association inference as a matrix completion problem and construct model (12) to predict new microRNA-disease associations in microRNA-disease association matrix:<disp-formula id="e12">
<mml:math id="m80">
<mml:mrow>
<mml:mtable>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:munder>
<mml:mrow>
<mml:mi>min</mml:mi>
</mml:mrow>
<mml:mi>Y</mml:mi>
</mml:munder>
<mml:mi>r</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>k</mml:mi>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>Y</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>&#xa0;subject&#xa0;to&#xa0;&#x3a1;</mml:mtext>
</mml:mrow>
<mml:mtext>&#x3a9;</mml:mtext>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>Y</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mtext>&#x3a1;</mml:mtext>
<mml:mtext>&#x3a9;</mml:mtext>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>W</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:mtd>
</mml:mtr>
</mml:mtable>
<mml:mo>&#xa0;</mml:mo>
</mml:mrow>
</mml:math>
<label>(12)</label>
</disp-formula>where <inline-formula id="inf69">
<mml:math id="m81">
<mml:mi>Y</mml:mi>
</mml:math>
</inline-formula> denotes a matrix need to complete, <inline-formula id="inf70">
<mml:math id="m82">
<mml:mrow>
<mml:mi>r</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>k</mml:mi>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>Y</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> denotes the rank of <inline-formula id="inf71">
<mml:math id="m83">
<mml:mi>Y</mml:mi>
</mml:math>
</inline-formula>, <inline-formula id="inf72">
<mml:math id="m84">
<mml:mrow>
<mml:mi>W</mml:mi>
<mml:mo>&#x2208;</mml:mo>
<mml:msup>
<mml:mi mathvariant="normal">&#x211b;</mml:mi>
<mml:mrow>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>m</mml:mi>
<mml:mo>&#x2b;</mml:mo>
<mml:mi>n</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#xd7;</mml:mo>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>m</mml:mi>
<mml:mo>&#x2b;</mml:mo>
<mml:mi>n</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> denotes a known microRNA-disease association matrix, <inline-formula id="inf73">
<mml:math id="m85">
<mml:mtext>&#x3a9;</mml:mtext>
</mml:math>
</inline-formula> denotes a set containing all index pairs <inline-formula id="inf74">
<mml:math id="m86">
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mtext>i</mml:mtext>
<mml:mo>,</mml:mo>
<mml:mtext>j</mml:mtext>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> that correspond to known microRNA-disease associations in <inline-formula id="inf75">
<mml:math id="m87">
<mml:mtext>W</mml:mtext>
</mml:math>
</inline-formula>, and <inline-formula id="inf76">
<mml:math id="m88">
<mml:mrow>
<mml:msub>
<mml:mtext>&#x3a1;</mml:mtext>
<mml:mtext>&#x3a9;</mml:mtext>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> represents a projection operator on <inline-formula id="inf77">
<mml:math id="m89">
<mml:mtext>&#x3a9;</mml:mtext>
</mml:math>
</inline-formula> by <xref ref-type="disp-formula" rid="e13">Eq. 13</xref>:<disp-formula id="e13">
<mml:math id="m90">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mtext>&#x3a1;</mml:mtext>
<mml:mtext>&#x3a9;</mml:mtext>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>Y</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mrow>
<mml:mo>{</mml:mo>
<mml:mrow>
<mml:mtable>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:msub>
<mml:mi>Y</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>j</mml:mi>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#x2208;</mml:mo>
<mml:mtext>&#x3a9;</mml:mtext>
</mml:mrow>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mn>0</mml:mn>
<mml:mo>,</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>j</mml:mi>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#x2209;</mml:mo>
<mml:mtext>&#x3a9;</mml:mtext>
</mml:mrow>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:mrow>
<mml:mo>&#xa0;</mml:mo>
</mml:mrow>
</mml:math>
<label>(13)</label>
</disp-formula>
</p>
<p>Model (12) is a non-convex model and difficult to solve. Thus, we transform it to a nuclear norm model through the nuclear norm optimization method proposed by <xref ref-type="bibr" rid="B56">Candes et al. (2013)</xref> by <xref ref-type="disp-formula" rid="e14">Eq. 14</xref>:<disp-formula id="e14">
<mml:math id="m91">
<mml:mrow>
<mml:mtable>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:munder>
<mml:mrow>
<mml:mi>min</mml:mi>
</mml:mrow>
<mml:mi>A</mml:mi>
</mml:munder>
<mml:mo>&#xa0;</mml:mo>
<mml:mi mathvariant="italic">&#x2016;Y</mml:mi>
<mml:msub>
<mml:mi>&#x2016;</mml:mi>
<mml:mo>&#x2217;</mml:mo>
</mml:msub>
</mml:mrow>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>subject&#xa0;to&#xa0;&#x3a1;</mml:mtext>
</mml:mrow>
<mml:mtext>&#x3a9;</mml:mtext>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>Y</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mtext>&#x3a1;</mml:mtext>
<mml:mtext>&#x3a9;</mml:mtext>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>W</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:mtd>
</mml:mtr>
</mml:mtable>
<mml:mo>&#xa0;</mml:mo>
</mml:mrow>
</mml:math>
<label>(14)</label>
</disp-formula>where <inline-formula id="inf78">
<mml:math id="m92">
<mml:mrow>
<mml:msub>
<mml:mi>Y</mml:mi>
<mml:mo>&#x2217;</mml:mo>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> represents the nuclear norm of <inline-formula id="inf79">
<mml:math id="m93">
<mml:mi>Y</mml:mi>
</mml:math>
</inline-formula>.</p>
<p>Because the value of each element in microRNA and disease similarity matrices <inline-formula id="inf80">
<mml:math id="m94">
<mml:mrow>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mi>m</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf81">
<mml:math id="m95">
<mml:mrow>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mi>d</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is in the range of [0,1] and the value of each element in microRNA-disease association matrix <inline-formula id="inf82">
<mml:math id="m96">
<mml:mrow>
<mml:msub>
<mml:mi>X</mml:mi>
<mml:mrow>
<mml:mi>m</mml:mi>
<mml:mi>d</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is 1 or 0, the computed microRNA-disease association scores are restricted to [0,1]. Higher score indicates bigger association probability for one microRNA-disease pair. But the elements in <inline-formula id="inf83">
<mml:math id="m97">
<mml:mtext>Y</mml:mtext>
</mml:math>
</inline-formula> are in the range of <inline-formula id="inf84">
<mml:math id="m98">
<mml:mrow>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>&#x221e;</mml:mi>
<mml:mo>,</mml:mo>
<mml:mo>&#x2b;</mml:mo>
<mml:mi>&#x221e;</mml:mi>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>. Therefore, we add a bounded constraint to <xref ref-type="disp-formula" rid="e14">Eq. 14</xref> to make the computed scores in [0, 1]. Considering the affect of data noise on the prediction performance, in addition, we develop a rank minimization-based matrix completion model by <xref ref-type="disp-formula" rid="e15">Eq. 15</xref>:<disp-formula id="e15">
<mml:math id="m99">
<mml:mrow>
<mml:mtable>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:munder>
<mml:mrow>
<mml:mi>min</mml:mi>
</mml:mrow>
<mml:mi>A</mml:mi>
</mml:munder>
<mml:mi mathvariant="italic">&#x2016;Y</mml:mi>
<mml:msub>
<mml:mi>&#x2016;</mml:mi>
<mml:mo>&#x2217;</mml:mo>
</mml:msub>
</mml:mrow>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:mtext>subject&#xa0;to</mml:mtext>
<mml:mo>&#xa0;</mml:mo>
<mml:mi>&#x2016;</mml:mi>
<mml:msub>
<mml:mtext>P</mml:mtext>
<mml:mtext>&#x3a9;</mml:mtext>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>Y</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mtext>&#x3a1;</mml:mtext>
<mml:mtext>&#x3a9;</mml:mtext>
</mml:msub>
<mml:msub>
<mml:mrow>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>W</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mi>&#x2016;</mml:mi>
</mml:mrow>
<mml:mi>F</mml:mi>
</mml:msub>
<mml:mo>&#x2264;</mml:mo>
<mml:mi mathvariant="italic">&#x3f5;</mml:mi>
</mml:mrow>
</mml:mtd>
</mml:mtr>
</mml:mtable>
<mml:mo>&#xa0;</mml:mo>
</mml:mrow>
</mml:math>
<label>(15)</label>
</disp-formula>where <inline-formula id="inf85">
<mml:math id="m100">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mrow>
<mml:mo>&#x2016;</mml:mo>
<mml:mo>.</mml:mo>
<mml:mo>&#x2016;</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mi>F</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> indicates Frobenius norm and <inline-formula id="inf86">
<mml:math id="m101">
<mml:mi mathvariant="italic">&#x3f5;</mml:mi>
</mml:math>
</inline-formula> represents the noise level.</p>
<p>We introduce a soft regularization term to tolerate data noise considering the difficulty in selecting an appropriate parameter in <xref ref-type="disp-formula" rid="e15">Eq. 15</xref>. Consequently, a bound nuclear norm regularization model is built to infer potential microRNA-disease associations by <xref ref-type="disp-formula" rid="e16">Eq. 16</xref>:<disp-formula id="e16">
<mml:math id="m102">
<mml:mrow>
<mml:mtable>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:munder>
<mml:mrow>
<mml:mi>min</mml:mi>
</mml:mrow>
<mml:mi>Y</mml:mi>
</mml:munder>
<mml:mi mathvariant="italic">&#x2016;Y</mml:mi>
<mml:msub>
<mml:mi>&#x2016;</mml:mi>
<mml:mo>&#x2217;</mml:mo>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:mfrac>
<mml:mi>&#x3b1;</mml:mi>
<mml:mn>2</mml:mn>
</mml:mfrac>
<mml:mi>&#x2016;</mml:mi>
<mml:msub>
<mml:mtext>&#x3a1;</mml:mtext>
<mml:mtext>&#x3a9;</mml:mtext>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>Y</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mtext>&#x3a1;</mml:mtext>
<mml:mtext>&#x3a9;</mml:mtext>
</mml:msub>
<mml:msubsup>
<mml:mrow>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>W</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mi>&#x2016;</mml:mi>
</mml:mrow>
<mml:mi>F</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
</mml:mrow>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:mtext>subject&#xa0;to</mml:mtext>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mn>0</mml:mn>
<mml:mo>&#x2264;</mml:mo>
<mml:mi>Y</mml:mi>
<mml:mo>&#x2264;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:math>
<label>(16)</label>
</disp-formula>where the parameter <inline-formula id="inf87">
<mml:math id="m103">
<mml:mi>&#x3b1;</mml:mi>
</mml:math>
</inline-formula> is applied to weigh the importance between the nuclear norm and the error term.</p>
<p>Consequently, we introduce an auxiliary matrix <inline-formula id="inf88">
<mml:math id="m104">
<mml:mi>Z</mml:mi>
</mml:math>
</inline-formula> and define model 17) to optimize model (16):<disp-formula id="e17">
<mml:math id="m105">
<mml:mrow>
<mml:mtable>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:munder>
<mml:mrow>
<mml:mi>min</mml:mi>
</mml:mrow>
<mml:mi>Y</mml:mi>
</mml:munder>
<mml:mi mathvariant="italic">&#x2016;Y</mml:mi>
<mml:msub>
<mml:mi>&#x2016;</mml:mi>
<mml:mo>&#x2217;</mml:mo>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:mfrac>
<mml:mi>&#x3b1;</mml:mi>
<mml:mn>2</mml:mn>
</mml:mfrac>
<mml:mi>&#x2016;</mml:mi>
<mml:msub>
<mml:mtext>&#x3a1;</mml:mtext>
<mml:mtext>&#x3a9;</mml:mtext>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>Z</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mtext>&#x3a1;</mml:mtext>
<mml:mtext>&#x3a9;</mml:mtext>
</mml:msub>
<mml:msubsup>
<mml:mrow>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>W</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mi>&#x2016;</mml:mi>
</mml:mrow>
<mml:mi>F</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
</mml:mrow>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:mtext>subject&#xa0;to</mml:mtext>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mi>Y</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mi>Z</mml:mi>
</mml:mrow>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:mn>0</mml:mn>
<mml:mo>&#x2264;</mml:mo>
<mml:mi>W</mml:mi>
<mml:mo>&#x2264;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:math>
<label>(17)</label>
</disp-formula>where <inline-formula id="inf89">
<mml:math id="m106">
<mml:mrow>
<mml:msub>
<mml:mi>Y</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mtext>&#x3a1;</mml:mtext>
<mml:mtext>&#x3a9;</mml:mtext>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>W</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>.</p>
<p>Thus, the corresponding augmented Lagrange function is written as <xref ref-type="disp-formula" rid="e18">Eq. 18</xref>:<disp-formula id="e18">
<mml:math id="m107">
<mml:mrow>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mi>Z</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>Y</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>L</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>&#x3b1;</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>&#x3b2;</mml:mi>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:mi mathvariant="italic">&#x2016;Y</mml:mi>
<mml:msub>
<mml:mi>&#x2016;</mml:mi>
<mml:mo>&#x2217;</mml:mo>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:mfrac>
<mml:mi>&#x3b1;</mml:mi>
<mml:mn>2</mml:mn>
</mml:mfrac>
<mml:mi>&#x2016;</mml:mi>
<mml:msub>
<mml:mtext>&#x3a1;</mml:mtext>
<mml:mtext>&#x3a9;</mml:mtext>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>Z</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mtext>&#x3a1;</mml:mtext>
<mml:mtext>&#x3a9;</mml:mtext>
</mml:msub>
<mml:msubsup>
<mml:mrow>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>W</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mi>&#x2016;</mml:mi>
</mml:mrow>
<mml:mi>F</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>T</mml:mi>
<mml:mi>r</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msup>
<mml:mi>L</mml:mi>
<mml:mi>T</mml:mi>
</mml:msup>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mi>Y</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>Z</mml:mi>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#x2b;</mml:mo>
<mml:mfrac>
<mml:mi>&#x3b2;</mml:mi>
<mml:mn>2</mml:mn>
</mml:mfrac>
<mml:mi>&#x2016;</mml:mi>
<mml:mi>Y</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:msubsup>
<mml:mi>Z&#x2016;</mml:mi>
<mml:mi>F</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
</mml:mrow>
</mml:math>
<label>(18)</label>
</disp-formula>where <inline-formula id="inf90">
<mml:math id="m108">
<mml:mi>L</mml:mi>
</mml:math>
</inline-formula> and <inline-formula id="inf91">
<mml:math id="m109">
<mml:mi>&#x3b2;</mml:mi>
</mml:math>
</inline-formula> represent the Lagrange multiplier and penalty parameter, respectively.</p>
<p>At the <inline-formula id="inf92">
<mml:math id="m110">
<mml:mi>t</mml:mi>
</mml:math>
</inline-formula> -th iteration, we alternatively compute one of <inline-formula id="inf93">
<mml:math id="m111">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="bold-italic">Y</mml:mi>
<mml:mrow>
<mml:mi>k</mml:mi>
<mml:mo>&#x2b;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula id="inf94">
<mml:math id="m112">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="bold-italic">Z</mml:mi>
<mml:mrow>
<mml:mi>k</mml:mi>
<mml:mo>&#x2b;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf95">
<mml:math id="m113">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="bold-italic">L</mml:mi>
<mml:mrow>
<mml:mi>k</mml:mi>
<mml:mo>&#x2b;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> by fixing other two values according to the solution from Yang et al. (<xref ref-type="bibr" rid="B50">Yang et al., 2019</xref>). Finally, microRNA-disease association matrix <inline-formula id="inf96">
<mml:math id="m114">
<mml:mrow>
<mml:msubsup>
<mml:mi mathvariant="bold-italic">Z</mml:mi>
<mml:mrow>
<mml:mi>m</mml:mi>
<mml:mi>d</mml:mi>
</mml:mrow>
<mml:mo>&#x2217;</mml:mo>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula> is updated through completing the unlabeled elements in <inline-formula id="inf97">
<mml:math id="m115">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="bold-italic">Z</mml:mi>
<mml:mrow>
<mml:mi>m</mml:mi>
<mml:mi>d</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>.</p>
</sec>
</sec>
<sec id="s3">
<title>3 Experiments</title>
<sec id="s3-1">
<title>3.1 Experimental settings and evaluation</title>
<p>In this study, we perform five-fold cross validation for 10 times to investigate the microRNA-disease association inference ability of BNNRMDA. During five-fold cross validation, 80% of elements in microRNA-disease association matrix <inline-formula id="inf98">
<mml:math id="m116">
<mml:mi>X</mml:mi>
</mml:math>
</inline-formula> are randomly chosen as the training set and the remaining are taken as the test set. Parameters <inline-formula id="inf99">
<mml:math id="m117">
<mml:mi>&#x3b1;</mml:mi>
</mml:math>
</inline-formula>, <inline-formula id="inf100">
<mml:math id="m118">
<mml:mtext>&#x3b2;</mml:mtext>
</mml:math>
</inline-formula>, <inline-formula id="inf101">
<mml:math id="m119">
<mml:mrow>
<mml:mo>&#xa0;</mml:mo>
<mml:mi>w</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> , and <inline-formula id="inf102">
<mml:math id="m120">
<mml:mrow>
<mml:mi>&#x3b3;</mml:mi>
<mml:mo>&#x2032;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> are set by grid search. We find that BNNRMDA obtain the best AUC when the four parameters are set as <inline-formula id="inf103">
<mml:math id="m121">
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula id="inf104">
<mml:math id="m122">
<mml:mrow>
<mml:mtext>&#x3b2;</mml:mtext>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>10</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula id="inf105">
<mml:math id="m123">
<mml:mrow>
<mml:mo>&#xa0;</mml:mo>
<mml:mi>w</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>0.3</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula> , and <inline-formula id="inf106">
<mml:math id="m124">
<mml:mrow>
<mml:mi>&#x3b3;</mml:mi>
<mml:mo>&#x2032;</mml:mo>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>0.5</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>, respectively. Therefore, we set the four parameters as corresponding values. In addition, AUC is widely used to measure the performance of association prediction methods, and thus we use it to measure the performance of BNNRMDA.</p>
</sec>
<sec id="s3-2">
<title>3.2 Performance measurement</title>
<p>To measure the microRNA-disease association prediction performance of BNNRMDA, we compare it with MIDPE (<xref ref-type="bibr" rid="B57">Xuan et al., 2015</xref>), MIDP (<xref ref-type="bibr" rid="B57">Xuan et al., 2015</xref>), RLSMDA (<xref ref-type="bibr" rid="B58">Chen and Yan, 2014</xref>), GRNMF (<xref ref-type="bibr" rid="B59">Xiao et al., 2018</xref>), and LPLNS (<xref ref-type="bibr" rid="B14">Li et al., 2018</xref>). MIDP (<xref ref-type="bibr" rid="B57">Xuan et al., 2015</xref>) and MIDPE (<xref ref-type="bibr" rid="B57">Xuan et al., 2015</xref>) are two random walk-based microRNA-disease association prediction methods. MIDP is used to detect association information for microRNAs related to diseases. MIDPE is used to detect association information through the bilayer network. RLSMDA (<xref ref-type="bibr" rid="B58">Chen and Yan, 2014</xref>) is a semi-supervised learning-based microRNA-disease association inference framework. GRNMF (<xref ref-type="bibr" rid="B59">Xiao et al., 2018</xref>) is a graph regularized non-negative matrix factorization-based microRNA-disease association prediction model. In addition, GRNMF built an association probability profile for each disease or miRNA based on a weighted nearest <inline-formula id="inf107">
<mml:math id="m125">
<mml:mi>K</mml:mi>
</mml:math>
</inline-formula> neighbor profiles. LPLNS (<xref ref-type="bibr" rid="B14">Li et al., 2018</xref>) combined label propagation and linear neighborhood similarity for microRNA-disease association prediction. MIDP, MIDPE, RLSMDA, GRNMF, and LPLNS obtained better AUCs for microRNA-disease association prediction. <xref ref-type="table" rid="T1">Table 1</xref> shows the AUC values of six microRNA-disease association prediction methods under cross validation.</p>
<table-wrap id="T1" position="float">
<label>TABLE 1</label>
<caption>
<p>AUCs of microRNA-disease association prediction methods under cross validation.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th rowspan="2" align="left">Method</th>
<th rowspan="2" align="left">MIDPE</th>
<th rowspan="2" align="left">MIDP</th>
<th rowspan="2" align="left">RLSMDA</th>
<th rowspan="2" align="left">GRNMF</th>
<th rowspan="2" align="left">LPLNS</th>
<th rowspan="2" align="left">BNNRMDA</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td rowspan="2" align="left">AUC</td>
<td rowspan="2" align="char" char=".">0.7820</td>
<td rowspan="2" align="char" char=".">0.8256</td>
<td rowspan="2" align="char" char=".">0.8555</td>
<td rowspan="2" align="char" char=".">0.8963</td>
<td align="left">0.9034</td>
<td rowspan="2" align="char" char=".">0.9071</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>From <xref ref-type="table" rid="T1">Table 1</xref>, we can find that BNNRMDA obtains better AUC of 0.9071 than MIDPE, MIDP, RLSMDA, GRNMF, and LPLNS. Compared to MIDPE, MIDP, RLSMDA, GRNMF, and LPLNS, BNNRMDA increases the performance of 13.79, 8.98, 5.69, 1.19, and 0.41% based on the AUC value, respectively. The results show that our proposed BNNRMDA method can effectively predict new microRNA-disease associations.</p>
</sec>
<sec id="s3-3">
<title>3.3 Case study</title>
<p>In the above section, we have computed the performance of BNNRMDA. The results show that BNNRMDA obtains better AUC and outperforms other five microRNA-disease association prediction methods. We continue to implement case analyses to identify possible microRNA biomarkers for colon cancer and colorectal cancer.</p>
<sec id="s3-3-1">
<title>3.3.1 Inferring possible microRNA biomarkers for colon cancer</title>
<p>Colon cancer is a common malignant tumor and has a very high incidence rate in adult with age of 40&#x2013;50 (<xref ref-type="bibr" rid="B54">Zhu et al., 2020</xref>; <xref ref-type="bibr" rid="B19">Liu et al., 2021</xref>). More importantly, it has no any symptoms in the early stage. Therefore, it is important to infer possible biomarkers to boost the diagnosis and treatment for colon cancer (<xref ref-type="bibr" rid="B19">Liu et al., 2021</xref>). Among the HMDD dataset, there are 73 known microRNAs associated with colon cancer among 353 microRNAs. Based on the proposed BNNRMDA method, we compute the association score for each microRNA-disease pair. The results show that all 73 known microRNAs associated with colon cancer in the HMDD database have the highest association scores with colon cancer and are ranked as top 73. We continue to investigate the following 30 miRNAs that have higher association scores with colon cancer and are ranked as 74&#x2013;103. The results are shown in <xref ref-type="table" rid="T2">Table 2</xref> and <xref ref-type="fig" rid="F1">Figure 1</xref>. From <xref ref-type="table" rid="T2">Table 2</xref> and <xref ref-type="fig" rid="F1">Figure 1</xref>, we can find that 18 microRNAs are confirmed to associate with colon cancer by literature retrieval. In addition, 12 microRNAs are inferred to associate with colon cancer and are potential biomarkers of colon cancer.</p>
<table-wrap id="T2" position="float">
<label>TABLE 2</label>
<caption>
<p>The inferred top 30 microRNAs associated with colon cancer except for 73 known microRNAs.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left">Rank</th>
<th align="left">MicroRNA</th>
<th align="left">Evidence</th>
<th align="left">Rank</th>
<th align="left">MicroRNA</th>
<th align="left">Evidence</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">1</td>
<td align="left">hsa-mir-200a</td>
<td align="left">25371200</td>
<td align="left">16</td>
<td align="left">hsa-mir-99a</td>
<td align="left">Unconfirmed</td>
</tr>
<tr>
<td align="left">2</td>
<td align="left">hsa-mir-375</td>
<td align="left">29930763</td>
<td align="left">17</td>
<td align="left">hsa-mir-195</td>
<td align="left">26064276</td>
</tr>
<tr>
<td align="left">3</td>
<td align="left">hsa-mir-222</td>
<td align="left">27855613</td>
<td align="left">18</td>
<td align="left">hsa-mir-96</td>
<td align="left">Unconfirmed</td>
</tr>
<tr>
<td align="left">4</td>
<td align="left">hsa-mir-30d</td>
<td align="left">28651493</td>
<td align="left">19</td>
<td align="left">hsa-mir-148a</td>
<td align="left">Unconfirmed</td>
</tr>
<tr>
<td align="left">5</td>
<td align="left">hsa-mir-103a</td>
<td align="left">Unconfirmed</td>
<td align="left">20</td>
<td align="left">hsa-mir-98</td>
<td align="left">28025745</td>
</tr>
<tr>
<td align="left">6</td>
<td align="left">hsa-mir-100</td>
<td align="left">28032929</td>
<td align="left">21</td>
<td align="left">hsa-mir-34c</td>
<td align="left">https://doi.org/10.1166/jbt. 2018.1859</td>
</tr>
<tr>
<td align="left">7</td>
<td align="left">hsa-mir-181a</td>
<td align="left">25977338</td>
<td align="left">22</td>
<td align="left">hsa-mir-182</td>
<td align="left">Unconfirmed</td>
</tr>
<tr>
<td align="left">8</td>
<td align="left">hsa-mir-133a</td>
<td align="left">29930763</td>
<td align="left">23</td>
<td align="left">hsa-mir-20b</td>
<td align="left">33044899</td>
</tr>
<tr>
<td align="left">9</td>
<td align="left">hsa-mir-429</td>
<td align="left">Unconfirmed</td>
<td align="left">24</td>
<td align="left">hsa-mir-124</td>
<td align="left">30980700</td>
</tr>
<tr>
<td align="left">10</td>
<td align="left">hsa-mir-224</td>
<td align="left">Unconfirmed</td>
<td align="left">25</td>
<td align="left">hsa-mir-7</td>
<td align="left">26648422</td>
</tr>
<tr>
<td align="left">11</td>
<td align="left">hsa-mir-93</td>
<td align="left">22180714</td>
<td align="left">26</td>
<td align="left">hsa-mir-193b</td>
<td align="left">31007734</td>
</tr>
<tr>
<td align="left">12</td>
<td align="left">hsa-mir-25</td>
<td align="left">23435373</td>
<td align="left">27</td>
<td align="left">hsa-mir-210</td>
<td align="left">27611932</td>
</tr>
<tr>
<td align="left">13</td>
<td align="left">hsa-mir-181b</td>
<td align="left">18172508</td>
<td align="left">28</td>
<td align="left">hsa-mir-10a</td>
<td align="left">Unconfirmed</td>
</tr>
<tr>
<td align="left">14</td>
<td align="left">hsa-mir-183</td>
<td align="left">Unconfirmed</td>
<td align="left">29</td>
<td align="left">hsa-mir-138</td>
<td align="left">Unconfirmed</td>
</tr>
<tr>
<td align="left">15</td>
<td align="left">hsa-mir-153</td>
<td align="left">Unconfirmed</td>
<td align="left">30</td>
<td align="left">hsa-mir-196a</td>
<td align="left">Unconfirmed</td>
</tr>
</tbody>
</table>
</table-wrap>
<fig id="F1" position="float">
<label>FIGURE 1</label>
<caption>
<p>Associations between the predicted top 30 microRNAs and colon cancer except for known 73 microRNA-colon cancer associations in the HMDD database that are predicted to have the highest association scores with colon cancer. Black dot lines denote associations between microRNAs and colon cancer and these associations have been reported by publications. Blue dot lines denote associations between microRNAs and colon cancer and these associations are unknown and need to experimental validation.</p>
</caption>
<graphic xlink:href="fgene-13-980437-g001.tif"/>
</fig>
<p>In addition, we infer that microRNA hsa-mir-103a may associate with colon cancer. Wnt signaling pathway is hyper-activated in many human cancers. Therefore, Wnt pathway demonstrates promising diagnostic and therapeutic effect in cancer medicine. <xref ref-type="bibr" rid="B60">Fasihi et al. (2018)</xref> found that hsa-miR-103a may be a possible regulator of Wnt signaling pathway by detecting its effect on Wnt pathway components in colorectal cancer-originated cell lines and its expression in colorectal cancer tissues. They also found that hsa-miR-103a has an upregulation function in colorectal cancer tissues through RT-qPCR and its overexpression could cause elevated Wnt activity. Therefore, we infer that hsa-miR-103a could be a potential biomarker of colon cancer (<xref ref-type="bibr" rid="B60">Fasihi et al., 2017</xref>).</p>
</sec>
<sec id="s3-3-2">
<title>3.3.2 Inferring possible microRNA biomarkers for colorectal cancer</title>
<p>Colorectal cancer is the third leading cause of cancer-related deaths in the United States. In the United State, there are about 1.85 million cases and 850 thousand deaths annually. In 2020, there are 53,200 colorectal cancer deaths in the United State. Among new colorectal cancer diagnoses, approximately 20% of patients suffered from metastatic disease and approximately 25% of patients suffered from localized disease that may later develop metastases. Of patients who are diagnosed as metastatic colorectal cancer, about 70&#x2013;75% of patients survive more than 1&#xa0;year, about 30&#x2013;35% patients survive more than 3 years, and less than 20% patients survive more than 5&#xa0;years (<xref ref-type="bibr" rid="B44">Xie et al., 2020</xref>; <xref ref-type="bibr" rid="B1">Biller and Schrag, 2021</xref>).</p>
<p>Among the HMDD dataset, there are 137 known microRNAs associated with colorectal cancer among 353 microRNAs. Based on the proposed BNNRMDA method, we compute the association score for each microRNA-colorectal cancer pair. The results show that 129 known microRNAs associated with colorectal cancer in the HMDD database have the highest association scores with colorectal cancer and are ranked as top 129. We continue to investigate the following 30 miRNAs that have higher association scores with colorectal cancer and are ranked as 130&#x2013;159. The results are shown in <xref ref-type="table" rid="T3">Table 3</xref> and <xref ref-type="fig" rid="F2">Figure 2</xref>. From <xref ref-type="table" rid="T3">Table 3</xref> and <xref ref-type="fig" rid="F2">Figure 2</xref>, we can find that 8 microRNAs are known to associate with colorectal cancer in the HMDD database. In addition, the remaining 22 microRNAs are inferred to associate with colorectal cancer and are reported by publications. The results confirm the strong microRNA identification performance of BNNRMDA for colorectal cancer. In addition, we predict that hsa-mir-193b and hsa-mir-7&#xa0;days may associate with colorectal cancer and need validation.</p>
<table-wrap id="T3" position="float">
<label>TABLE 3</label>
<caption>
<p>The inferred top 30 microRNAs associated with colorectal cancer except for 129 known microRNAs.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left">Rank</th>
<th align="left">MicroRNA</th>
<th align="left">Evidence</th>
<th align="left">Rank</th>
<th align="left">MicroRNA</th>
<th align="left">Evidence</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">1</td>
<td align="left">hsa-mir-191</td>
<td align="left">18079988</td>
<td align="left">16</td>
<td align="left">hsa-mir-223</td>
<td align="left">27759076</td>
</tr>
<tr>
<td align="left">2</td>
<td align="left">hsa-mir-760</td>
<td align="left">the HMDD database</td>
<td align="left">17</td>
<td align="left">hsa-mir-100</td>
<td align="left">25973296</td>
</tr>
<tr>
<td align="left">3</td>
<td align="left">hsa-mir-337</td>
<td align="left">the HMDD database</td>
<td align="left">18</td>
<td align="left">hsa-mir-204</td>
<td align="left">25209181</td>
</tr>
<tr>
<td align="left">4</td>
<td align="left">hsa-mir-1915</td>
<td align="left">the HMDD database</td>
<td align="left">19</td>
<td align="left">hsa-let-7g</td>
<td align="left">18172508</td>
</tr>
<tr>
<td align="left">5</td>
<td align="left">hsa-mir-24</td>
<td align="left">30375302</td>
<td align="left">20</td>
<td align="left">hsa-mir-106b</td>
<td align="left">34070923</td>
</tr>
<tr>
<td align="left">6</td>
<td align="left">hsa-mir-520a</td>
<td align="left">the HMDD database</td>
<td align="left">21</td>
<td align="left">hsa-mir-296</td>
<td align="left">28209128</td>
</tr>
<tr>
<td align="left">7</td>
<td align="left">hsa-mir-101</td>
<td align="left">30797148</td>
<td align="left">22</td>
<td align="left">hsa-let-7f</td>
<td align="left">29805607</td>
</tr>
<tr>
<td align="left">8</td>
<td align="left">hsa-mir-138</td>
<td align="left">27248318</td>
<td align="left">23</td>
<td align="left">hsa-mir-29c</td>
<td align="left">29262657</td>
</tr>
<tr>
<td align="left">9</td>
<td align="left">hsa-mir-608</td>
<td align="left">the HMDD database</td>
<td align="left">24</td>
<td align="left">hsa-mir-30c</td>
<td align="left">25799050</td>
</tr>
<tr>
<td align="left">10</td>
<td align="left">hsa-mir-1303</td>
<td align="left">the HMDD database</td>
<td align="left">25</td>
<td align="left">hsa-mir-30b</td>
<td align="left">32112903</td>
</tr>
<tr>
<td align="left">11</td>
<td align="left">hsa-mir-629</td>
<td align="left">30042169</td>
<td align="left">26</td>
<td align="left">hsa-mir-302a</td>
<td align="left">31754405</td>
</tr>
<tr>
<td align="left">12</td>
<td align="left">hsa-mir-2110</td>
<td align="left">the HMDD database</td>
<td align="left">27</td>
<td align="left">hsa-mir-326</td>
<td align="left">25760058</td>
</tr>
<tr>
<td align="left">13</td>
<td align="left">hsa-mir-147b</td>
<td align="left">the HMDD database</td>
<td align="left">28</td>
<td align="left">hsa-mir-98</td>
<td align="left">34370878</td>
</tr>
<tr>
<td align="left">14</td>
<td align="left">hsa-mir-205</td>
<td align="left">29488611</td>
<td align="left">29</td>
<td align="left">hsa-mir-128</td>
<td align="left">30257253</td>
</tr>
<tr>
<td align="left">15</td>
<td align="left">hsa-mir-197</td>
<td align="left">30106114</td>
<td align="left">30</td>
<td align="left">hsa-mir-30d</td>
<td align="left">28651493</td>
</tr>
</tbody>
</table>
</table-wrap>
<fig id="F2" position="float">
<label>FIGURE 2</label>
<caption>
<p>Associations between the predicted top 30 microRNAs and colorectal cancer except for known 129 microRNA-colorectal cancer associations in the HMDD database. Black dot lines denote associations between microRNAs and colorectal cancer and these associations have been reported by publications. Orange solid lines denote associations between microRNAs and colorectal cancer and these associations are unknown and need to experimental validation.</p>
</caption>
<graphic xlink:href="fgene-13-980437-g002.tif"/>
</fig>
</sec>
</sec>
</sec>
<sec id="s4">
<title>4 Conclusion</title>
<p>Colon cancer and colorectal cancer are two of leading causes of cancer-related deaths worldwide and are seriously threatening human health. Inference of diagnosis or prognosis biomarkers for colon cancer and colorectal cancer can help to evaluate their initiation, progression and therapeutic response. In this study, we developed a new microRNA-disease association prediction method, BNNRMDA, to find possible microRNA biomarkers for colon cancer and colorectal cancer. BNNRMDA effectively integrated disease semantic similarity and GAPK similarity, microRNA function similarity and GAPK similarity, and bound nuclear norm regularization.</p>
<p>Compared to other five classical microRNA-disease association prediction methods, BNNRMDA obtains the best AUC of 0.9071, demonstrating its powerful microRNA-disease association prediction performance. We continue to use the proposed BNNRMDA method for finding possible microRNA biomarkers for colon cancer and colorectal cancer. The results show that hsa-miR-103a could be a potential biomarker of colon cancer and hsa-mir-193b and hsa-mir-7&#xa0;days could be potential biomarkers of colorectal cancer.</p>
<p>Our proposed BNNRMDA method fully considers the affect of Gaussian association profile similarity on the prediction performance. In addition, the bound nuclear norm regularization approach can effectively learn the intrinsic distribution of data. Therefore, BNNRMDA significantly outperform other MDA prediction methods. Although BNNRMDA obtains better AUC, its performance including AUC, precision, recall, and accuracy need to further improve. In the future, we will improve the bound nuclear norm regularization model to discover possible biomarkers for colon cancer and colorectal cancer.</p>
</sec>
</body>
<back>
<sec sec-type="data-availability" id="s5">
<title>Data availability statement</title>
<p>The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.</p>
</sec>
<sec id="s6">
<title>Author contributions</title>
<p>Conceptualization: S-YZ and CQ; Methodology: S-YZ, X-LL and CQ; Project administration: CQ, YW, X-LS and B-BJ; Software: S-YZ, X-LL and CQ; Writing-original draft: S-YZ, X-LL and CQ; Writing-review and editing: S-YZ, and CQ.</p>
</sec>
<sec id="s7">
<title>Funding</title>
<p>This work was supported by the Medical and Health Science Technology Development Program in Shandong Province (202104080159) and Science Technology Development Program in Weifang City (2021YX007).</p>
</sec>
<sec sec-type="COI-statement" id="s8">
<title>Conflict of interest</title>
<p>Authors YW, XS, and BJ were employed by the company Geneis (Beijing) Co. Ltd. In addition, this manuscript was conducted by a multicenter study initiated by the corresponding author (CQ). Geneis Beijing Co., Ltd. Contacted the doctors in hospitals around the country.</p>
<p>The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
</sec>
<sec sec-type="disclaimer" id="s9">
<title>Publisher&#x2019;s note</title>
<p>All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.</p>
</sec>
<ref-list>
<title>References</title>
<ref id="B1">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Biller</surname>
<given-names>L. H.</given-names>
</name>
<name>
<surname>Schrag</surname>
<given-names>D.</given-names>
</name>
</person-group> (<year>2021</year>). <article-title>Diagnosis and treatment of metastatic colorectal cancer: A review.</article-title> <source>Jama</source> <volume>325</volume> (<issue>7</issue>), <fpage>669</fpage>&#x2013;<lpage>685</lpage>. <pub-id pub-id-type="doi">10.1001/jama.2021.0106</pub-id> </citation>
</ref>
<ref id="B56">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Candes</surname>
<given-names>E.</given-names>
</name>
<name>
<surname>Recht</surname>
<given-names>B.</given-names>
</name>
</person-group> (<year>2013</year>). <article-title>Simple bounds for recovering low-complexity models[J]</article-title>. <source>Mathematical Programming</source> <volume>141</volume> (<issue>1</issue>), <fpage>577</fpage>&#x2013;<lpage>589</lpage>. </citation>
</ref>
<ref id="B58">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Chen</surname>
<given-names>X.</given-names>
</name>
<name>
<surname>Yan</surname>
<given-names>G. Y.</given-names>
</name>
</person-group> (<year>2014</year>). <article-title>Semi-supervised learning for potential human microRNA-disease associations inference[J]</article-title>. <source>Scientific reports</source> <volume>4</volume> (<issue>1</issue>), <fpage>1</fpage>&#x2013;<lpage>10</lpage>. </citation>
</ref>
<ref id="B2">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Chen</surname>
<given-names>B.</given-names>
</name>
<name>
<surname>Xia</surname>
<given-names>Z.</given-names>
</name>
<name>
<surname>Deng</surname>
<given-names>Y. N.</given-names>
</name>
<name>
<surname>Yang</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Zhang</surname>
<given-names>P.</given-names>
</name>
<name>
<surname>Zhu</surname>
<given-names>H.</given-names>
</name>
<etal/>
</person-group>(<year>2019</year>). <article-title>Emerging microRNA biomarkers for colorectal cancer diagnosis and prognosis.</article-title> <source>Open Biol.</source> <volume>9</volume> (<issue>1</issue>), <fpage>180212</fpage>. <pub-id pub-id-type="doi">10.1098/rsob.180212</pub-id> </citation>
</ref>
<ref id="B3">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Chen</surname>
<given-names>H.</given-names>
</name>
<name>
<surname>Guo</surname>
<given-names>R.</given-names>
</name>
<name>
<surname>Li</surname>
<given-names>G.</given-names>
</name>
<name>
<surname>Zhang</surname>
<given-names>W.</given-names>
</name>
<name>
<surname>Zhang</surname>
<given-names>Z.</given-names>
</name>
</person-group> (<year>2020</year>). <article-title>Comparative analysis of similarity measurements in miRNAs with applications to miRNA-disease association predictions.</article-title> <source>BMC Bioinforma.</source> <volume>21</volume> (<issue>1</issue>), <fpage>176</fpage>&#x2013;<lpage>214</lpage>. <pub-id pub-id-type="doi">10.1186/s12859-020-3515-9</pub-id> </citation>
</ref>
<ref id="B4">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Chen</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Yang</surname>
<given-names>X.</given-names>
</name>
<name>
<surname>Yu</surname>
<given-names>C.</given-names>
</name>
<name>
<surname>Zhou</surname>
<given-names>W.</given-names>
</name>
<name>
<surname>Xia</surname>
<given-names>Q.</given-names>
</name>
<name>
<surname>Liu</surname>
<given-names>Y.</given-names>
</name>
<etal/>
</person-group>(<year>2021</year>). <article-title>The potential of circRNA as a novel diagnostic biomarker in cervical cancer</article-title>. <source>J. Oncol.</source> <volume>2021</volume>, <fpage>2021</fpage>&#x2013;<lpage>2026</lpage>. <pub-id pub-id-type="doi">10.1155/2021/5529486</pub-id> </citation>
</ref>
<ref id="B5">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Chen</surname>
<given-names>X.</given-names>
</name>
<name>
<surname>Li</surname>
<given-names>T. H.</given-names>
</name>
<name>
<surname>Zhao</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Wang</surname>
<given-names>C. C.</given-names>
</name>
<name>
<surname>Zhu</surname>
<given-names>C. C.</given-names>
</name>
</person-group> (<year>2021</year>). <article-title>Deep-belief network for predicting potential miRNA-disease associations</article-title>. <source>Brief. Bioinform.</source> <volume>22</volume> (<issue>3</issue>), <fpage>bbaa186</fpage>. <pub-id pub-id-type="doi">10.1093/bib/bbaa186</pub-id> </citation>
</ref>
<ref id="B6">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Dougherty</surname>
<given-names>U.</given-names>
</name>
<name>
<surname>Mustafi</surname>
<given-names>R.</given-names>
</name>
<name>
<surname>Zhu</surname>
<given-names>H.</given-names>
</name>
<name>
<surname>Zhu</surname>
<given-names>X.</given-names>
</name>
<name>
<surname>Deb</surname>
<given-names>D.</given-names>
</name>
<name>
<surname>Meredith</surname>
<given-names>S. C.</given-names>
</name>
<etal/>
</person-group> (<year>2021</year>). <article-title>Upregulation of polycistronic microRNA-143 and microRNA-145 in colonocytes suppresses colitis and inflammation-associated colon cancer.</article-title> <source>Epigenetics</source> <volume>16</volume> (<issue>12</issue>), <fpage>1317</fpage>&#x2013;<lpage>1334</lpage>. <pub-id pub-id-type="doi">10.1080/15592294.2020.1863117</pub-id> </citation>
</ref>
<ref id="B60">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Fasihi</surname>
<given-names>A. M.</given-names>
</name>
<name>
<surname>Soltani</surname>
<given-names>B.</given-names>
</name>
<name>
<surname>Atashi</surname>
<given-names>A.</given-names>
</name>
</person-group> (<year>2018</year>). <article-title>Introduction of hsa&#x2013;miR&#x2013;103a and hsa&#x2013;miR&#x2013;1827 and hsa&#x2013;miR&#x2013;137 as new regulators of Wnt signaling pathway and their relation to colorectal carcinoma[J]</article-title>. <source>J. cellular biochemistry</source> <volume>119</volume> (<issue>7</issue>), <fpage>5104</fpage>&#x2013;<lpage>5117</lpage>. </citation>
</ref>
<ref id="B7">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Garo</surname>
<given-names>L. P.</given-names>
</name>
<name>
<surname>Ajay</surname>
<given-names>A. K.</given-names>
</name>
<name>
<surname>Fujiwara</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Gabriely</surname>
<given-names>G.</given-names>
</name>
<name>
<surname>Raheja</surname>
<given-names>R.</given-names>
</name>
<name>
<surname>Kuhn</surname>
<given-names>C.</given-names>
</name>
<etal/>
</person-group> (<year>2021</year>). <article-title>MicroRNA-146a limits tumorigenic inflammation in colorectal cancer</article-title>. <source>Nat. Commun.</source> <volume>12</volume> (<issue>1</issue>), <fpage>2419</fpage>&#x2013;<lpage>2516</lpage>. <pub-id pub-id-type="doi">10.1038/s41467-021-22641-y</pub-id> </citation>
</ref>
<ref id="B8">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Hsu</surname>
<given-names>S. D.</given-names>
</name>
<name>
<surname>Tseng</surname>
<given-names>Y. T.</given-names>
</name>
<name>
<surname>Shrestha</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Lin</surname>
<given-names>Y. L.</given-names>
</name>
<name>
<surname>Khaleel</surname>
<given-names>A.</given-names>
</name>
<name>
<surname>Chou</surname>
<given-names>C. H.</given-names>
</name>
<etal/>
</person-group> (<year>2014</year>). <article-title>miRTarBase update 2014: an information resource for experimentally validated miRNA-target interactions.</article-title> <source>Nucleic Acids Res.</source> <volume>42</volume> (<issue>D1</issue>), <fpage>D78</fpage>&#x2013;<lpage>D85</lpage>. <pub-id pub-id-type="doi">10.1093/nar/gkt1266</pub-id> </citation>
</ref>
<ref id="B9">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Huang</surname>
<given-names>F.</given-names>
</name>
<name>
<surname>Yue</surname>
<given-names>X.</given-names>
</name>
<name>
<surname>Xiong</surname>
<given-names>Z.</given-names>
</name>
<name>
<surname>Yu</surname>
<given-names>Z.</given-names>
</name>
<name>
<surname>Liu</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Zhang</surname>
<given-names>W.</given-names>
</name>
</person-group> (<year>2021</year>). <article-title>Tensor decomposition with relational constraints for predicting multiple types of microRNA-disease associations.</article-title> <source>Brief. Bioinform.</source> <volume>22</volume> (<issue>3</issue>), <fpage>bbaa140</fpage>. <pub-id pub-id-type="doi">10.1093/bib/bbaa140</pub-id> </citation>
</ref>
<ref id="B10">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Huang</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Li</surname>
<given-names>X.</given-names>
</name>
<name>
<surname>Guo</surname>
<given-names>P.</given-names>
</name>
<name>
<surname>Yao</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Liao</surname>
<given-names>B.</given-names>
</name>
<name>
<surname>Zhang</surname>
<given-names>W.</given-names>
</name>
<etal/>
</person-group> (<year>2017</year>). <article-title>Matrix completion with side information and its applications in predicting the antigenicity of influenza viruses.</article-title> <source>Bioinformatics</source> <volume>33</volume> (<issue>20</issue>), <fpage>3195</fpage>&#x2013;<lpage>3201</lpage>. <pub-id pub-id-type="doi">10.1093/bioinformatics/btx390</pub-id> </citation>
</ref>
<ref id="B12">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Lee</surname>
<given-names>C. H.</given-names>
</name>
<name>
<surname>Im</surname>
<given-names>E. J.</given-names>
</name>
<name>
<surname>Moon</surname>
<given-names>P. G.</given-names>
</name>
<name>
<surname>Baek</surname>
<given-names>M. C.</given-names>
</name>
</person-group> (<year>2018</year>). <article-title>Discovery of a diagnostic biomarker for colon cancer through proteomic profiling of small extracellular vesicles.</article-title> <source>BMC cancer</source> <volume>18</volume> (<issue>1</issue>), <fpage>1058</fpage>&#x2013;<lpage>1111</lpage>. <pub-id pub-id-type="doi">10.1186/s12885-018-4952-y</pub-id> </citation>
</ref>
<ref id="B13">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Lee</surname>
<given-names>I.</given-names>
</name>
<name>
<surname>Blom</surname>
<given-names>U. M.</given-names>
</name>
<name>
<surname>Wang</surname>
<given-names>P. I.</given-names>
</name>
<name>
<surname>Shim</surname>
<given-names>J. E.</given-names>
</name>
<name>
<surname>Marcotte</surname>
<given-names>E. M.</given-names>
</name>
</person-group> (<year>2011</year>). <article-title>Prioritizing candidate disease genes by network-based boosting of genome-wide association data.</article-title> <source>Genome Res.</source> <volume>21</volume> (<issue>7</issue>), <fpage>1109</fpage>&#x2013;<lpage>1121</lpage>. <pub-id pub-id-type="doi">10.1101/gr.118992.110</pub-id> </citation>
</ref>
<ref id="B14">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Li</surname>
<given-names>G.</given-names>
</name>
<name>
<surname>Luo</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Xiao</surname>
<given-names>Q.</given-names>
</name>
<name>
<surname>Liang</surname>
<given-names>C.</given-names>
</name>
<name>
<surname>Ding</surname>
<given-names>P.</given-names>
</name>
</person-group> (<year>2018</year>). <article-title>Predicting microRNA-disease associations using label propagation based on linear neighborhood similarity.</article-title> <source>J. Biomed. Inf.</source> <volume>82</volume>, <fpage>169</fpage>&#x2013;<lpage>177</lpage>. <pub-id pub-id-type="doi">10.1016/j.jbi.2018.05.005</pub-id> </citation>
</ref>
<ref id="B15">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Li</surname>
<given-names>T.</given-names>
</name>
<name>
<surname>Huang</surname>
<given-names>T.</given-names>
</name>
<name>
<surname>Guo</surname>
<given-names>C.</given-names>
</name>
<name>
<surname>Wang</surname>
<given-names>A.</given-names>
</name>
<name>
<surname>Shi</surname>
<given-names>X.</given-names>
</name>
<name>
<surname>Mo</surname>
<given-names>X.</given-names>
</name>
<etal/>
</person-group> (<year>2021</year>). <article-title>Genomic variation, origin tracing, and vaccine development of SARS-CoV-2: A systematic review.</article-title> <source>Innovation.</source> <volume>2</volume> (<issue>2</issue>), <fpage>100116</fpage>. <pub-id pub-id-type="doi">10.1016/j.xinn.2021.100116</pub-id> </citation>
</ref>
<ref id="B16">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Li</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Qiu</surname>
<given-names>C.</given-names>
</name>
<name>
<surname>Tu</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Geng</surname>
<given-names>B.</given-names>
</name>
<name>
<surname>Yang</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Jiang</surname>
<given-names>T.</given-names>
</name>
<etal/>
</person-group> (<year>2014</year>). <article-title>HMDD v2.0: A database for experimentally supported human microRNA and disease associations.</article-title> <source>Nucleic Acids Res.</source> <volume>42</volume> (<issue>D1</issue>), <fpage>D1070</fpage>&#x2013;<lpage>D1074</lpage>. <pub-id pub-id-type="doi">10.1093/nar/gkt1023</pub-id> </citation>
</ref>
<ref id="B17">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Li</surname>
<given-names>Z.</given-names>
</name>
<name>
<surname>Li</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Nie</surname>
<given-names>R.</given-names>
</name>
<etal/>
</person-group> (<year>2021</year>). <article-title>A graph auto-encoder model for miRNA-disease associations prediction[J]</article-title>. <source>Briefings Bioinforma.</source> (<issue>4</issue>), <volume>22</volume>, <fpage>bbaa240</fpage>. <pub-id pub-id-type="doi">10.1093/bib/bbaa240</pub-id> </citation>
</ref>
<ref id="B18">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Liu</surname>
<given-names>C.</given-names>
</name>
<name>
<surname>Wei</surname>
<given-names>D.</given-names>
</name>
<name>
<surname>Xiang</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Ren</surname>
<given-names>F.</given-names>
</name>
<name>
<surname>Huang</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Lang</surname>
<given-names>J.</given-names>
</name>
<etal/>
</person-group> (<year>2020</year>). <article-title>An improved anticancer drug-response prediction based on an ensemble method integrating matrix completion and ridge regression.</article-title> <source>Mol. Ther. Nucleic Acids</source> <volume>21</volume>, <fpage>676</fpage>&#x2013;<lpage>686</lpage>. <pub-id pub-id-type="doi">10.1016/j.omtn.2020.07.003</pub-id> </citation>
</ref>
<ref id="B19">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Liu</surname>
<given-names>D.</given-names>
</name>
<name>
<surname>Huang</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Nie</surname>
<given-names>W.</given-names>
</name>
<name>
<surname>Zhang</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Deng</surname>
<given-names>L.</given-names>
</name>
</person-group> (<year>2021</year>). <article-title>Smalf: miRNA-disease associations prediction based on stacked autoencoder and XGBoost</article-title>. <source>BMC Bioinforma.</source> <volume>22</volume> (<issue>1</issue>), <fpage>219</fpage>&#x2013;<lpage>318</lpage>. <pub-id pub-id-type="doi">10.1186/s12859-021-04135-2</pub-id> </citation>
</ref>
<ref id="B20">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Liu</surname>
<given-names>H.</given-names>
</name>
<name>
<surname>Qiu</surname>
<given-names>C.</given-names>
</name>
<name>
<surname>Wang</surname>
<given-names>B.</given-names>
</name>
<name>
<surname>Bing</surname>
<given-names>P.</given-names>
</name>
<name>
<surname>Tian</surname>
<given-names>G.</given-names>
</name>
<name>
<surname>Zhang</surname>
<given-names>X.</given-names>
</name>
<etal/>
</person-group> (<year>2021</year>). <article-title>Evaluating DNA methylation, gene expression, somatic mutation, and their combinations in inferring tumor tissue-of-origin</article-title>. <source>Front. Cell Dev. Biol.</source> <volume>9</volume>, <fpage>886</fpage>. <pub-id pub-id-type="doi">10.3389/fcell.2021.619330</pub-id> </citation>
</ref>
<ref id="B21">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Ma</surname>
<given-names>Y. S.</given-names>
</name>
<name>
<surname>Wu</surname>
<given-names>T. M.</given-names>
</name>
<name>
<surname>Ling</surname>
<given-names>C. C.</given-names>
</name>
<name>
<surname>Yu</surname>
<given-names>F.</given-names>
</name>
<name>
<surname>Zhang</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Cao</surname>
<given-names>P. S.</given-names>
</name>
<etal/>
</person-group> (<year>2021</year>). <article-title>M2 macrophage-derived exosomal microRNA-155-5p promotes the immune escape of colon cancer by downregulating ZC3H12B.</article-title> <source>Mol. Ther. Oncolytics</source> <volume>20</volume>, <fpage>484</fpage>&#x2013;<lpage>498</lpage>. <pub-id pub-id-type="doi">10.1016/j.omto.2021.02.005</pub-id> </citation>
</ref>
<ref id="B22">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Meng</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Lu</surname>
<given-names>C.</given-names>
</name>
<name>
<surname>Jin</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Xu</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Zeng</surname>
<given-names>X.</given-names>
</name>
<name>
<surname>Yang</surname>
<given-names>J.</given-names>
</name>
</person-group> (<year>2022</year>). <article-title>A weighted bilinear neural collaborative filtering approach for drug repositioning</article-title>. <source>Brief. Bioinform.</source> <volume>23</volume>, <fpage>bbab581</fpage>. <pub-id pub-id-type="doi">10.1093/bib/bbab581</pub-id> </citation>
</ref>
<ref id="B23">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Miao</surname>
<given-names>X.</given-names>
</name>
<name>
<surname>Li</surname>
<given-names>Z.</given-names>
</name>
<name>
<surname>Zhang</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Wang</surname>
<given-names>T.</given-names>
</name>
</person-group> (<year>2021</year>). <article-title>MicroRNA-4284 inhibits colon cancer epithelial-mesenchymal transition by down-regulating Perilipin 5</article-title>. <source>STEMedicine</source> <volume>2</volume> (<issue>6</issue>), <fpage>e85</fpage>. <pub-id pub-id-type="doi">10.37175/stemedicine.v2i6.85</pub-id> </citation>
</ref>
<ref id="B24">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Ogunwobi</surname>
<given-names>O. O.</given-names>
</name>
<name>
<surname>Mahmood</surname>
<given-names>F.</given-names>
</name>
<name>
<surname>Akingboye</surname>
<given-names>A.</given-names>
</name>
</person-group> (<year>2020</year>). <article-title>Biomarkers in colorectal cancer: Current research and future prospects.</article-title> <source>Int. J. Mol. Sci.</source> <volume>21</volume> (<issue>15</issue>), <fpage>5311</fpage>. <pub-id pub-id-type="doi">10.3390/ijms21155311</pub-id> </citation>
</ref>
<ref id="B25">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Pagotto</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Colorito</surname>
<given-names>M. L.</given-names>
</name>
<name>
<surname>Nicotra</surname>
<given-names>A.</given-names>
</name>
<name>
<surname>Apuzzo</surname>
<given-names>T.</given-names>
</name>
<name>
<surname>Tinari</surname>
<given-names>N.</given-names>
</name>
<name>
<surname>Protasi</surname>
<given-names>F.</given-names>
</name>
<etal/>
</person-group> (<year>2022</year>). <article-title>A perspective analysis: microRNAs, glucose metabolism, and drug resistance in colon cancer stem cells.</article-title> <source>Cancer Gene Ther.</source> <volume>29</volume> (<issue>1</issue>), <fpage>4</fpage>&#x2013;<lpage>9</lpage>. <pub-id pub-id-type="doi">10.1038/s41417-021-00298-5</pub-id> </citation>
</ref>
<ref id="B26">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Peng</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Chen</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Ma</surname>
<given-names>N.</given-names>
</name>
<name>
<surname>Chen</surname>
<given-names>X.</given-names>
</name>
</person-group> (<year>2017</year>). <article-title>Narrmda: Negative-aware and rating-based recommendation algorithm for miRNA-disease association prediction.</article-title> <source>Mol. Biosyst.</source> <volume>13</volume> (<issue>12</issue>), <fpage>2650</fpage>&#x2013;<lpage>2659</lpage>. <pub-id pub-id-type="doi">10.1039/c7mb00499k</pub-id> </citation>
</ref>
<ref id="B27">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Peng</surname>
<given-names>L. H.</given-names>
</name>
<name>
<surname>Sun</surname>
<given-names>C. N.</given-names>
</name>
<name>
<surname>Guan</surname>
<given-names>N. N.</given-names>
</name>
<name>
<surname>Li</surname>
<given-names>J. Q.</given-names>
</name>
<name>
<surname>Chen</surname>
<given-names>X.</given-names>
</name>
</person-group> (<year>2018</year>). <article-title>Hnmda: Heterogeneous network-based miRNA-disease association prediction.</article-title> <source>Mol. Genet. Genomics</source> <volume>293</volume> (<issue>4</issue>), <fpage>983</fpage>&#x2013;<lpage>995</lpage>. <pub-id pub-id-type="doi">10.1007/s00438-018-1438-1</pub-id> </citation>
</ref>
<ref id="B28">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Peng</surname>
<given-names>L. H.</given-names>
</name>
<name>
<surname>Zhou</surname>
<given-names>L. Q.</given-names>
</name>
<name>
<surname>Chen</surname>
<given-names>X.</given-names>
</name>
<name>
<surname>Piao</surname>
<given-names>X.</given-names>
</name>
</person-group> (<year>2020b</year>). <article-title>A computational study of potential miRNA-disease association inference based on ensemble learning and kernel ridge regression</article-title>. <source>Front. Bioeng. Biotechnol.</source> <volume>8</volume>, <fpage>40</fpage>. <pub-id pub-id-type="doi">10.3389/fbioe.2020.00040</pub-id> </citation>
</ref>
<ref id="B29">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Peng</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Tian</surname>
<given-names>X.</given-names>
</name>
<name>
<surname>Shen</surname>
<given-names>L.</given-names>
</name>
<etal/>
</person-group> (<year>2020a</year>). <article-title>Drug designing and repositioning against severe acute respiratory coronavirus 2 (SARS-Cov-2) through computational simulation: Current progress and hopes</article-title>. <source>Front. Genet.</source> <volume>5</volume>, <fpage>1</fpage>&#x2013;<lpage>5</lpage>. <pub-id pub-id-type="doi">10.23880/oajmb-16000168</pub-id> </citation>
</ref>
<ref id="B30">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Peng</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Wang</surname>
<given-names>F.</given-names>
</name>
<name>
<surname>Wang</surname>
<given-names>Z.</given-names>
</name>
<name>
<surname>Tan</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Huang</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Tian</surname>
<given-names>X.</given-names>
</name>
<etal/>
</person-group> (<year>2022a</year>). <article-title>Cell-cell communication inference and analysis in the tumour microenvironments from single-cell transcriptomics: Data resources and computational strategies.</article-title> <source>Brief. Bioinform.</source> <volume>23</volume> (<issue>4</issue>), <fpage>bbac234</fpage>. <pub-id pub-id-type="doi">10.1093/bib/bbac234</pub-id> </citation>
</ref>
<ref id="B31">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Peng</surname>
<given-names>L. H.</given-names>
</name>
<name>
<surname>Tan</surname>
<given-names>J. W.</given-names>
</name>
<name>
<surname>Tian</surname>
<given-names>X. F.</given-names>
</name>
<etal/>
</person-group> (<year>2022b</year>). <article-title>EnANNDeep: An ensemble-based lncRNA&#x2013;protein interaction prediction framework with adaptive k-nearest neighbor classifier and deep models[J]</article-title>. <source>Interdiscip. Sci. Comput. Life Sci.</source> <volume>14</volume>, <fpage>1</fpage>&#x2013;<lpage>24</lpage>. </citation>
</ref>
<ref id="B32">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Peng</surname>
<given-names>L. H.</given-names>
</name>
<name>
<surname>Wang</surname>
<given-names>C.</given-names>
</name>
<name>
<surname>Tian</surname>
<given-names>X. F.</given-names>
</name>
<name>
<surname>Zhou</surname>
<given-names>L. Q.</given-names>
</name>
<name>
<surname>Li</surname>
<given-names>K. Q.</given-names>
</name>
</person-group> (<year>2021b</year>). <article-title>Finding lncRNA-protein interactions based on deep learning with dual-net neural architecture</article-title>. <source>IEEE/ACM Trans. Comput. Biol. Bioinform.</source> <volume>29</volume>, <fpage>1</fpage>. <pub-id pub-id-type="doi">10.1109/TCBB.2021.3116232</pub-id> </citation>
</ref>
<ref id="B33">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Peng</surname>
<given-names>L. H.</given-names>
</name>
<name>
<surname>Yuan</surname>
<given-names>R. Y.</given-names>
</name>
<name>
<surname>Shen</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Gao</surname>
<given-names>P. F.</given-names>
</name>
<name>
<surname>Zhou</surname>
<given-names>L. Q.</given-names>
</name>
</person-group> (<year>2021a</year>). <article-title>LPI-EnEDT: An ensemble framework with extra tree and decision tree classifiers for imbalanced lncRNA-protein interaction data classification[J]</article-title>. <source>BioData Min.</source> <volume>14</volume> (<issue>1</issue>), <fpage>1</fpage>&#x2013;<lpage>22</lpage>. </citation>
</ref>
<ref id="B34">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Piawah</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Venook</surname>
<given-names>A. P.</given-names>
</name>
</person-group> (<year>2019</year>). <article-title>Targeted therapy for colorectal cancer metastases: A review of current methods of molecularly targeted therapy and the use of tumor biomarkers in the treatment of metastatic colorectal cancer.</article-title> <source>Cancer</source> <volume>125</volume> (<issue>23</issue>), <fpage>4139</fpage>&#x2013;<lpage>4147</lpage>. <pub-id pub-id-type="doi">10.1002/cncr.32163</pub-id> </citation>
</ref>
<ref id="B35">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Ruhl</surname>
<given-names>R.</given-names>
</name>
<name>
<surname>Rana</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Kelley</surname>
<given-names>K.</given-names>
</name>
<name>
<surname>Espinosa-Diez</surname>
<given-names>C.</given-names>
</name>
<name>
<surname>Hudson</surname>
<given-names>C.</given-names>
</name>
<name>
<surname>Lanciault</surname>
<given-names>C.</given-names>
</name>
<etal/>
</person-group> (<year>2018</year>). <article-title>microRNA-451a regulates colorectal cancer proliferation in response to radiation.</article-title> <source>BMC cancer</source> <volume>18</volume> (<issue>1</issue>), <fpage>517</fpage>&#x2013;<lpage>519</lpage>. <pub-id pub-id-type="doi">10.1186/s12885-018-4370-1</pub-id> </citation>
</ref>
<ref id="B36">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Sampath</surname>
<given-names>S. S.</given-names>
</name>
<name>
<surname>Venkatabalasubramanian</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Ramalingam</surname>
<given-names>S.</given-names>
</name>
</person-group> (<year>2021</year>). <article-title>Role of MicroRNAs in the progression and metastasis of colon cancer.</article-title> <source>Endocr. Metab. Immune Disord. Drug Targets</source> <volume>21</volume> (<issue>1</issue>), <fpage>35</fpage>&#x2013;<lpage>46</lpage>. <pub-id pub-id-type="doi">10.2174/1871530320666200825184924</pub-id> </citation>
</ref>
<ref id="B37">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Shen</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Liu</surname>
<given-names>F.</given-names>
</name>
<name>
<surname>Huang</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Liu</surname>
<given-names>G.</given-names>
</name>
<name>
<surname>Zhou</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Peng</surname>
<given-names>L.</given-names>
</name>
</person-group> (<year>2022</year>). <article-title>VDA-RWLRLS: An anti-SARS-CoV-2 drug prioritizing framework combining an unbalanced bi-random walk and Laplacian regularized least squares</article-title>. <source>Comput. Biol. Med.</source> <volume>140</volume>, <fpage>105119</fpage>. <pub-id pub-id-type="doi">10.1016/j.compbiomed.2021.105119</pub-id> </citation>
</ref>
<ref id="B38">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Tian</surname>
<given-names>X.</given-names>
</name>
<name>
<surname>Shen</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Gao</surname>
<given-names>P.</given-names>
</name>
<name>
<surname>Huang</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Liu</surname>
<given-names>G.</given-names>
</name>
<name>
<surname>Zhou</surname>
<given-names>L.</given-names>
</name>
<etal/>
</person-group> (<year>2022</year>). <article-title>Discovery of potential therapeutic drugs for COVID-19 through logistic matrix factorization with kernel diffusion.</article-title> <source>Front. Microbiol.</source>, <volume>13</volume>, <fpage>740382</fpage>. <pub-id pub-id-type="doi">10.3389/fmicb.2022.740382</pub-id> </citation>
</ref>
<ref id="B39">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Verduci</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Tarcitano</surname>
<given-names>E.</given-names>
</name>
<name>
<surname>Strano</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Yarden</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Blandino</surname>
<given-names>G.</given-names>
</name>
</person-group> (<year>2021</year>). <article-title>CircRNAs: Role in human diseases and potential use as biomarkers.</article-title> <source>Cell Death Dis.</source> <volume>12</volume> (<issue>5</issue>), <fpage>468</fpage>&#x2013;<lpage>512</lpage>. <pub-id pub-id-type="doi">10.1038/s41419-021-03743-3</pub-id> </citation>
</ref>
<ref id="B40">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Vergoulis</surname>
<given-names>T.</given-names>
</name>
<name>
<surname>Vlachos</surname>
<given-names>I. S.</given-names>
</name>
<name>
<surname>Alexiou</surname>
<given-names>P.</given-names>
</name>
<name>
<surname>Georgakilas</surname>
<given-names>G.</given-names>
</name>
<name>
<surname>Maragkakis</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Reczko</surname>
<given-names>M.</given-names>
</name>
<etal/>
</person-group> (<year>2012</year>). <article-title>TarBase 6.0: Capturing the exponential growth of miRNA targets with experimental support.</article-title> <source>Nucleic Acids Res.</source> <volume>40</volume> (<issue>D1</issue>), <fpage>D222</fpage>&#x2013;<lpage>D229</lpage>. <pub-id pub-id-type="doi">10.1093/nar/gkr1161</pub-id> </citation>
</ref>
<ref id="B41">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Wang</surname>
<given-names>D.</given-names>
</name>
<name>
<surname>Wang</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Lu</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Song</surname>
<given-names>F.</given-names>
</name>
<name>
<surname>Cui</surname>
<given-names>Q.</given-names>
</name>
</person-group> (<year>2010</year>). <article-title>Inferring the human microRNA functional similarity and functional network based on microRNA-associated diseases.</article-title> <source>Bioinformatics</source> <volume>26</volume> (<issue>13</issue>), <fpage>1644</fpage>&#x2013;<lpage>1650</lpage>. <pub-id pub-id-type="doi">10.1093/bioinformatics/btq241</pub-id> </citation>
</ref>
<ref id="B42">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Wang</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Dong</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Gong</surname>
<given-names>A.</given-names>
</name>
<name>
<surname>Kong</surname>
<given-names>H.</given-names>
</name>
<name>
<surname>Gao</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Hao</surname>
<given-names>X.</given-names>
</name>
<etal/>
</person-group> (<year>2021</year>). <article-title>Exosomal circRNAs as novel cancer biomarkers: Challenges and opportunities.</article-title> <source>Int. J. Biol. Sci.</source> <volume>17</volume> (<issue>2</issue>), <fpage>562</fpage>&#x2013;<lpage>573</lpage>. <pub-id pub-id-type="doi">10.7150/ijbs.48782</pub-id> </citation>
</ref>
<ref id="B55">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Wang</surname>
<given-names>C. C.</given-names>
</name>
<name>
<surname>Li</surname>
<given-names>T. H.</given-names>
</name>
<name>
<surname>Huang</surname>
<given-names>L.</given-names>
</name>
</person-group> (<year>2022</year>). <article-title>Prediction of potential miRNA&#x2013;disease associations based on stacked autoencoder[J]</article-title>. <source>Briefings in Bioinformatics</source> <volume>23</volume> (<issue>2</issue>), <fpage>1</fpage>&#x2013;<lpage>11</lpage>. </citation>
</ref>
<ref id="B43">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Xiao</surname>
<given-names>F.</given-names>
</name>
<name>
<surname>Zuo</surname>
<given-names>Z.</given-names>
</name>
<name>
<surname>Cai</surname>
<given-names>G.</given-names>
</name>
<name>
<surname>Kang</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Gao</surname>
<given-names>X.</given-names>
</name>
<name>
<surname>Li</surname>
<given-names>T.</given-names>
</name>
</person-group> (<year>2009</year>). <article-title>miRecords: an integrated resource for microRNA-target interactions.</article-title> <source>Nucleic Acids Res.</source> <volume>37</volume> (<issue>1</issue>), <fpage>D105</fpage>&#x2013;<lpage>D110</lpage>. <pub-id pub-id-type="doi">10.1093/nar/gkn851</pub-id> </citation>
</ref>
<ref id="B59">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Xiao</surname>
<given-names>Q.</given-names>
</name>
<name>
<surname>Luo</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Liang</surname>
<given-names>C.</given-names>
</name>
</person-group> (<year>2018</year>). <article-title>A graph regularized non-negative matrix factorization method for identifying microRNA-disease associations[J]</article-title>. <source>Bioinformatics</source> <volume>34</volume> (<issue>2</issue>), <fpage>239</fpage>&#x2013;<lpage>248</lpage>. </citation>
</ref>
<ref id="B44">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Xie</surname>
<given-names>Y. H.</given-names>
</name>
<name>
<surname>Chen</surname>
<given-names>Y. X.</given-names>
</name>
<name>
<surname>Fang</surname>
<given-names>J. Y.</given-names>
</name>
</person-group> (<year>2020</year>). <article-title>Comprehensive review of targeted therapy for colorectal cancer[J]</article-title>. <source>Signal Transduct. Target. Ther.</source> <volume>5</volume> (<issue>1</issue>), <fpage>1</fpage>&#x2013;<lpage>30</lpage>. <pub-id pub-id-type="doi">10.1038/s41392-020-0116</pub-id> </citation>
</ref>
<ref id="B45">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Xu</surname>
<given-names>F.</given-names>
</name>
<name>
<surname>Ye</surname>
<given-names>M. L.</given-names>
</name>
<name>
<surname>Zhang</surname>
<given-names>Y. P.</given-names>
</name>
<name>
<surname>Li</surname>
<given-names>W. J.</given-names>
</name>
<name>
<surname>Li</surname>
<given-names>M. T.</given-names>
</name>
<name>
<surname>Wang</surname>
<given-names>H. Z.</given-names>
</name>
<etal/>
</person-group> (<year>2020</year>). <article-title>MicroRNA-375-3p enhances chemosensitivity to 5-fluorouracil by targeting thymidylate synthase in colorectal cancer.</article-title> <source>Cancer Sci.</source> <volume>111</volume> (<issue>5</issue>), <fpage>1528</fpage>&#x2013;<lpage>1541</lpage>. <pub-id pub-id-type="doi">10.1111/cas.14356</pub-id> </citation>
</ref>
<ref id="B46">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Xu</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Cai</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Liao</surname>
<given-names>B.</given-names>
</name>
<name>
<surname>Zhu</surname>
<given-names>W.</given-names>
</name>
<name>
<surname>Yang</surname>
<given-names>J.</given-names>
</name>
</person-group> (<year>2020</year>). <article-title>CMF-impute: An accurate imputation tool for single-cell RNA-seq data.</article-title> <source>Bioinformatics</source> <volume>36</volume> (<issue>10</issue>), <fpage>3139</fpage>&#x2013;<lpage>3147</lpage>. <pub-id pub-id-type="doi">10.1093/bioinformatics/btaa109</pub-id> </citation>
</ref>
<ref id="B57">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Xuan</surname>
<given-names>P.</given-names>
</name>
<name>
<surname>Han</surname>
<given-names>K.</given-names>
</name>
<name>
<surname>Guo</surname>
<given-names>Y.</given-names>
</name>
</person-group> (<year>2015</year>). <article-title>Prediction of potential disease-associated microRNAs based on random walk[J]</article-title>. <source>Bioinformatics</source> <volume>31</volume> (<issue>11</issue>), <fpage>1805</fpage>&#x2013;<lpage>1815</lpage>. </citation>
</ref>
<ref id="B47">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Yang</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Gr&#xfc;newald</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Wan</surname>
<given-names>X. F.</given-names>
</name>
</person-group> (<year>2013</year>). <article-title>Quartet-net: A quartet-based method to reconstruct phylogenetic networks.</article-title> <source>Mol. Biol. Evol.</source> <volume>30</volume> (<issue>5</issue>), <fpage>1206</fpage>&#x2013;<lpage>1217</lpage>. <pub-id pub-id-type="doi">10.1093/molbev/mst040</pub-id> </citation>
</ref>
<ref id="B48">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Yang</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Ju</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Guo</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Ji</surname>
<given-names>B.</given-names>
</name>
<name>
<surname>Shi</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Yang</surname>
<given-names>Z.</given-names>
</name>
<etal/>
</person-group> (<year>2022</year>). <article-title>Prediction of HER2-positive breast cancer recurrence and metastasis risk from histopathological images and clinical information via multimodal deep learning.</article-title> <source>Comput. Struct. Biotechnol. J.</source> <volume>20</volume>, <fpage>333</fpage>&#x2013;<lpage>342</lpage>. <pub-id pub-id-type="doi">10.1016/j.csbj.2021.12.028</pub-id> </citation>
</ref>
<ref id="B49">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Yang</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Peng</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Zhang</surname>
<given-names>B.</given-names>
</name>
<name>
<surname>Houten</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Schadt</surname>
<given-names>E.</given-names>
</name>
<name>
<surname>Zhu</surname>
<given-names>J.</given-names>
</name>
<etal/>
</person-group> (<year>2020</year>). <article-title>Human geroprotector discovery by targeting the converging subnetworks of aging and age-related diseases.</article-title> <source>Geroscience</source> <volume>42</volume> (<issue>1</issue>), <fpage>353</fpage>&#x2013;<lpage>372</lpage>. <pub-id pub-id-type="doi">10.1007/s11357-019-00106-x</pub-id> </citation>
</ref>
<ref id="B50">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Yang</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Luo</surname>
<given-names>H.</given-names>
</name>
<name>
<surname>Li</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Wang</surname>
<given-names>J.</given-names>
</name>
</person-group> (<year>2019</year>). <article-title>Drug repositioning based on bounded nuclear norm regularization.</article-title> <source>Bioinformatics</source> <volume>35</volume> (<issue>14</issue>), <fpage>i455</fpage>&#x2013;<lpage>i463</lpage>. <pub-id pub-id-type="doi">10.1093/bioinformatics/btz331</pub-id> </citation>
</ref>
<ref id="B51">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Yuan</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Liu</surname>
<given-names>W.</given-names>
</name>
<name>
<surname>Zhang</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Sun</surname>
<given-names>S.</given-names>
</name>
</person-group> (<year>2018</year>). <article-title>CircRNA circ_0026344 as a prognostic biomarker suppresses colorectal cancer progression via microRNA-21 and microRNA-31.</article-title> <source>Biochem. Biophys. Res. Commun.</source> <volume>503</volume> (<issue>2</issue>), <fpage>870</fpage>&#x2013;<lpage>875</lpage>. <pub-id pub-id-type="doi">10.1016/j.bbrc.2018.06.089</pub-id> </citation>
</ref>
<ref id="B52">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Yue</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Yun</surname>
<given-names>Z.</given-names>
</name>
<name>
<surname>Li</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Yan</surname>
<given-names>G.</given-names>
</name>
<name>
<surname>Kang</surname>
<given-names>Z.</given-names>
</name>
</person-group> (<year>2021</year>). <article-title>NEDD4 triggers FOXA1 ubiquitination and promotes colon cancer progression under microRNA-340-5p suppression and ATF1 upregulation.</article-title> <source>RNA Biol.</source> <volume>18</volume> (<issue>11</issue>), <fpage>1981</fpage>&#x2013;<lpage>1995</lpage>. <pub-id pub-id-type="doi">10.1080/15476286.2021.1885232</pub-id> </citation>
</ref>
<ref id="B53">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Zhang</surname>
<given-names>H. W.</given-names>
</name>
<name>
<surname>Shi</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Liu</surname>
<given-names>J. B.</given-names>
</name>
<name>
<surname>Wang</surname>
<given-names>H. M.</given-names>
</name>
<name>
<surname>Wang</surname>
<given-names>P. Y.</given-names>
</name>
<name>
<surname>Wu</surname>
<given-names>Z. J.</given-names>
</name>
<etal/>
</person-group> (<year>2021</year>). <article-title>Cancer-associated fibroblast-derived exosomal microRNA-24-3p enhances colon cancer cell resistance to MTX by down-regulating CDX2/HEPH axis.</article-title> <source>J. Cell. Mol. Med.</source> <volume>25</volume> (<issue>8</issue>), <fpage>3699</fpage>&#x2013;<lpage>3713</lpage>. <pub-id pub-id-type="doi">10.1111/jcmm.15765</pub-id> </citation>
</ref>
<ref id="B54">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Zhu</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Xu</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Liu</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Qiao</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Sun</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Zhao</surname>
<given-names>Q.</given-names>
</name>
</person-group> (<year>2020</year>). <article-title>MicroRNAs associated with colon cancer: New potential prognostic markers and targets for therapy.</article-title> <source>Front. Bioeng. Biotechnol.</source> <volume>8</volume>, <fpage>176</fpage>. <pub-id pub-id-type="doi">10.3389/fbioe.2020.00176</pub-id> </citation>
</ref>
</ref-list>
</back>
</article>