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<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">1238095</article-id>
<article-id pub-id-type="doi">10.3389/fgene.2023.1238095</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>Predicting potential lncRNA biomarkers for lung cancer and neuroblastoma based on an ensemble of a deep neural network and LightGBM</article-title>
<alt-title alt-title-type="left-running-head">Su 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.2023.1238095">10.3389/fgene.2023.1238095</ext-link>
</alt-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname>Su</surname>
<given-names>Zhenguo</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>Lu</surname>
<given-names>Huihui</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</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="aff3">
<sup>3</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/1541475/overview"/>
</contrib>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Li</surname>
<given-names>Zejun</given-names>
</name>
<xref ref-type="aff" rid="aff4">
<sup>4</sup>
</xref>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
<uri xlink:href="https://loop.frontiersin.org/people/1973522/overview"/>
</contrib>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Duan</surname>
<given-names>Lian</given-names>
</name>
<xref ref-type="aff" rid="aff5">
<sup>5</sup>
</xref>
<xref ref-type="aff" rid="aff6">
<sup>6</sup>
</xref>
<xref ref-type="aff" rid="aff7">
<sup>7</sup>
</xref>
<xref ref-type="aff" rid="aff8">
<sup>8</sup>
</xref>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
<uri xlink:href="https://loop.frontiersin.org/people/2343727/overview"/>
</contrib>
</contrib-group>
<aff id="aff1">
<sup>1</sup>
<institution>Clinical Lab</institution>, <institution>Yantai Affiliated Hospital of Binzhou Medical University</institution>, <addr-line>Yantai</addr-line>, <country>China</country>
</aff>
<aff id="aff2">
<sup>2</sup>
<institution>Department of Thoracic Cardiovascular Surgery</institution>, <institution>Hunan Province Directly Affiliated TCM Hospital</institution>, <addr-line>Zhuzhou</addr-line>, <country>China</country>
</aff>
<aff id="aff3">
<sup>3</sup>
<institution>Geneis (Beijing) Co., Ltd.</institution>, <addr-line>Beijing</addr-line>, <country>China</country>
</aff>
<aff id="aff4">
<sup>4</sup>
<institution>School of Computer Science</institution>, <institution>Hunan Institute of Technology</institution>, <addr-line>Hengyang</addr-line>, <country>China</country>
</aff>
<aff id="aff5">
<sup>5</sup>
<institution>Faculty of Pediatrics</institution>, <institution>The Chinese PLA General Hospital</institution>, <addr-line>Beijing</addr-line>, <country>China</country>
</aff>
<aff id="aff6">
<sup>6</sup>
<institution>Department of Pediatric Surgery</institution>, <institution>The Seventh Medical Center of PLA General Hospital</institution>, <addr-line>Beijing</addr-line>, <country>China</country>
</aff>
<aff id="aff7">
<sup>7</sup>
<institution>National Engineering Laboratory for Birth Defects Prevention and Control of Key Technology</institution>, <addr-line>Beijing</addr-line>, <country>China</country>
</aff>
<aff id="aff8">
<sup>8</sup>
<institution>Beijing Key Laboratory of Pediatric Organ Failure</institution>, <addr-line>Beijing</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/1472367/overview">Junlin Xu</ext-link>, Hunan University, 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/1080094/overview">XianFang Tang</ext-link>, Wuhan Textile University, China</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1794066/overview">Wenyan Wang</ext-link>, Anhui University of Technology, China</p>
</fn>
<corresp id="c001">&#x2a;Correspondence: Zejun Li, <email>lzjfox@hnit.edu.cn</email>; Lian Duan, <email>duanlian301@163.com</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>
</author-notes>
<pub-date pub-type="epub">
<day>16</day>
<month>08</month>
<year>2023</year>
</pub-date>
<pub-date pub-type="collection">
<year>2023</year>
</pub-date>
<volume>14</volume>
<elocation-id>1238095</elocation-id>
<history>
<date date-type="received">
<day>10</day>
<month>06</month>
<year>2023</year>
</date>
<date date-type="accepted">
<day>19</day>
<month>07</month>
<year>2023</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2023 Su, Lu, Wu, Li and Duan.</copyright-statement>
<copyright-year>2023</copyright-year>
<copyright-holder>Su, Lu, Wu, Li and Duan</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>
<bold>Introduction:</bold> Lung cancer is one of the most frequent neoplasms worldwide with approximately 2.2 million new cases and 1.8 million deaths each year. The expression levels of programmed death ligand-1 (PDL1) demonstrate a complex association with lung cancer. Neuroblastoma is a high-risk malignant tumor and is mainly involved in childhood patients. Identification of new biomarkers for these two diseases can significantly promote their diagnosis and therapy. However, <italic>in vivo</italic> experiments to discover potential biomarkers are costly and laborious. Consequently, artificial intelligence technologies, especially machine learning methods, provide a powerful avenue to find new biomarkers for various diseases.</p>
<p>
<bold>Methods:</bold> We developed a machine learning-based method named LDAenDL to detect potential long noncoding RNA (lncRNA) biomarkers for lung cancer and neuroblastoma using an ensemble of a deep neural network and LightGBM. LDAenDL first computes the Gaussian kernel similarity and functional similarity of lncRNAs and the Gaussian kernel similarity and semantic similarity of diseases to obtain their similar networks. Next, LDAenDL combines a graph convolutional network, graph attention network, and convolutional neural network to learn the biological features of the lncRNAs and diseases based on their similarity networks. Third, these features are concatenated and fed to an ensemble model composed of a deep neural network and LightGBM to find new lncRNA&#x2013;disease associations (LDAs). Finally, the proposed LDAenDL method is applied to identify possible lncRNA biomarkers associated with lung cancer and neuroblastoma.</p>
<p>
<bold>Results:</bold> The experimental results show that LDAenDL computed the best AUCs of 0.8701, 107 0.8953, and 0.9110 under cross-validation on lncRNAs, diseases, and lncRNA&#x2010;disease pairs on Dataset 1, respectively, and 0.9490, 0.9157, and 0.9708 on Dataset 2, respectively. Furthermore, AUPRs of 0.8903, 0.9061, and 0.9166 under three cross&#x2010;validations were obtained on Dataset 1, and 0.9582, 0.9122, and 0.9743 on Dataset 2. The results demonstrate that LDAenDL significantly outperformed the other four classical LDA prediction methods (i.e., SDLDA, LDNFSGB, IPCAF, and LDASR). Case studies demonstrate that CCDC26 and IFNG-AS1 may be new biomarkers of lung cancer, SNHG3 may associate with PDL1 for lung cancer, and HOTAIR and BDNF-AS may be potential biomarkers of neuroblastoma.</p>
<p>
<bold>Conclusion:</bold> We hope that the proposed LDAenDL method can help the development of targeted therapies for these two diseases.</p>
</abstract>
<kwd-group>
<kwd>lncRNA</kwd>
<kwd>biomarker</kwd>
<kwd>lung cancer</kwd>
<kwd>neuroblastoma</kwd>
<kwd>deep neural network</kwd>
<kwd>LightGBM</kwd>
</kwd-group>
<custom-meta-wrap>
<custom-meta>
<meta-name>section-at-acceptance</meta-name>
<meta-value>RNA</meta-value>
</custom-meta>
</custom-meta-wrap>
</article-meta>
</front>
<body>
<sec id="s1">
<title>1 Introduction</title>
<p>Long non-coding RNAs (lncRNAs) are non-coding RNAs with more than 200 nucleotides (<xref ref-type="bibr" rid="B1">Bertone et al., 2004</xref>; <xref ref-type="bibr" rid="B28">Peng et al., 2022a</xref>; <xref ref-type="bibr" rid="B29">Peng et al., 2022b</xref>). LncRNAs play an important role in the development and progression of various diseases (<xref ref-type="bibr" rid="B14">Lanjanian et al., 2021</xref>; <xref ref-type="bibr" rid="B26">Meng et al., 2021</xref>; <xref ref-type="bibr" rid="B51">Yang and Li 2021</xref>; <xref ref-type="bibr" rid="B30">Peng et al., 2022c</xref>). LncRNAs have dense associations with many diseases, for example, lung cancer, colorectal cancer, prostate cancer, and Alzheimer&#x2019;s disease (<xref ref-type="bibr" rid="B12">Klattenhoff et al., 2013</xref>; <xref ref-type="bibr" rid="B40">Tan et al., 2013</xref>; <xref ref-type="bibr" rid="B4">Chakravarty et al., 2014</xref>; <xref ref-type="bibr" rid="B9">He et al., 2014</xref>; <xref ref-type="bibr" rid="B55">Zhang et al., 2014</xref>). LncRNA H19 is associated with the under-regulation of renal carcinoma cells (<xref ref-type="bibr" rid="B43">Wang et al., 2015</xref>). The expression of EGOT in breast cancer is much lower than one in adjacent noncancerous tissues (<xref ref-type="bibr" rid="B2">Broadbent et al., 2008</xref>). NEAT1 is overexpressed in prostate cancer cells (<xref ref-type="bibr" rid="B27">Pasmant et al., 2011</xref>). The identification of lncRNA-disease associations (LDAs) helps us to further understand the biological processes and the molecular mechanisms of various complex diseases. However, the number of known and experimentally validated LDAs is very small. Thus, it is important to identify potential LDAs. Determining LDAs through <italic>in vivo</italic> experiments is costly and time-consuming, therefore, it is necessary to design efficient computational approaches for identifying potential LDAs (<xref ref-type="bibr" rid="B26">Meng et al., 2021</xref>; <xref ref-type="bibr" rid="B31">Peng et al., 2022d</xref>). Computational LDA prediction methods are categorized as biological network-based methods and machine learning-based methods.</p>
<p>Biological network-based methods use network algorithms for association prediction (<xref ref-type="bibr" rid="B22">Liu et al., 2023a</xref>). This type of method first constructs heterogeneous networks of lncRNAs and diseases and then identifies LDAs via matrix decomposition, random walk, and so on. To predict potential LDAs, LRWRHLDA combined Laplace normalized random walk with restart (<xref ref-type="bibr" rid="B45">Wang et al., 2022</xref>), LDGRNMF used graph regularized nonnegative matrix factorization (<xref ref-type="bibr" rid="B44">Wang et al., 2021</xref>), DSCMF developed a dual sparse collaborative matrix factorization approach (<xref ref-type="bibr" rid="B19">Liu et al., 2021a</xref>), RWSF-BLP added random walk-based multi-similarity fusion to bidirectional label propagation (<xref ref-type="bibr" rid="B47">Xie et al., 2021</xref>), HBRWRLDA utilized bi-random walk on hypergraphs (<xref ref-type="bibr" rid="B48">Xie et al., 2022</xref>), and MHRWRLDA exploited a random walk model with restart through multiplex and heterogeneous networks (<xref ref-type="bibr" rid="B53">Yao et al., 2021</xref>).</p>
<p>With the fast advance of RNA sequencing technologies, artificial intelligence has obtained wide applications in biomedical data analysis (<xref ref-type="bibr" rid="B32">Peng et al., 2023a</xref>; <xref ref-type="bibr" rid="B33">Peng et al., 2023b</xref>; <xref ref-type="bibr" rid="B49">Xu et al., 2023</xref>). Notably, artificial intelligence technologies, especially machine learning methods, have been widely applied to predict miRNA-disease associations (<xref ref-type="bibr" rid="B21">Liu et al., 2022</xref>) and circRNA-disease associations (<xref ref-type="bibr" rid="B23">Liu et al., 2023b</xref>). To find new LDAs, HGATLDA developed a novel heterogeneous graph attention network model (<xref ref-type="bibr" rid="B57">Zhao et al., 2022</xref>), DeepMNE extracted multi-omics data and designed a deep multi-network embedding model (<xref ref-type="bibr" rid="B25">Ma, 2022</xref>), iLncDA-LTR is a rank-based method (<xref ref-type="bibr" rid="B46">Wu et al., 2022</xref>), MAGCNSE utilized a graph convolutional network (<xref ref-type="bibr" rid="B17">Liang et al., 2022</xref>), LDAformer extracted topological features and used a transformer encoder for LDA classification (<xref ref-type="bibr" rid="B59">Zhou et al., 2022</xref>), BiGAN explored a bidirectional generative adversarial network (<xref ref-type="bibr" rid="B52">Yang et al., 2021</xref>), and SVDNVLDA extracted linear and non-linear features and used an XGBoost for LDA prediction (<xref ref-type="bibr" rid="B16">Li et al., 2021</xref>).</p>
<p>Computational methods have found many potential LDAs, however, network-based methods were more likely to favor well-investigated lncRNAs or diseases and can not predict LDAs for new lncRNAs or new diseases. Machine learning-based methods failed to effectively integrate different kernels from multiple data sources. Thus, in this study, we developed a machine learning-based method named LDAenDL to detect potential lncRNA biomarkers for lung cancer and neuroblastoma based on an ensemble of a deep neural network and LightGBM.</p>
</sec>
<sec sec-type="materials|methods" id="s2">
<title>2 Materials and methods</title>
<p>As shown in <xref ref-type="fig" rid="F1">Figure 1</xref>, LDAenDL first computes the Gaussian kernel similarity and functional similarity of lncRNAs and the Gaussian kernel similarity and semantic similarity of diseases to obtain their similar networks. Next, LDAenDL combines a graph convolutional network (GCN) (<xref ref-type="bibr" rid="B11">Kipf and Welling, 2016</xref>), graph attention network (GAT) (<xref ref-type="bibr" rid="B42">Velickovic et al., 2017</xref>), and convolutional neural network (<xref ref-type="bibr" rid="B8">Gu et al., 2018</xref>) to learn the biological features of lncRNAs and diseases based on their similarity networks. Third, these features are concatenated and fed to an ensemble model composed of a deep neural network (DNN) and LightGBM to find new LDAs. Finally, LDAenDL was applied to identify possible lncRNA biomarkers associated with lung cancer and neuroblastoma.</p>
<fig id="F1" position="float">
<label>FIGURE 1</label>
<caption>
<p>The pipeline of LDAenDL.</p>
</caption>
<graphic xlink:href="fgene-14-1238095-g001.tif"/>
</fig>
<sec id="s2-1">
<title>2.1 Data preparation</title>
<p>We used two human LDA datasets that were provided by <xref ref-type="bibr" rid="B5">Chen et al. (2012)</xref> and <xref ref-type="bibr" rid="B6">Cui et al. (2018)</xref>. Dataset 1 contains 605 LDAs between 157 diseases and 82 lncRNAs. Dataset 2 contains 1,529 LDAs between 190 diseases and 89 lncRNAs. An LDA network can be denoted as <inline-formula id="inf1">
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</sec>
<sec id="s2-2">
<title>2.2 Similarity computation</title>
<p>Inspired by the LDA-DLPU method (<xref ref-type="bibr" rid="B28">Peng et al., 2022a</xref>), we computed the Gaussian kernel similarity and functional similarity of lncRNAs and the Gaussian kernel similarity and semantic similarity of diseases. Based on the computed lncRNA similarity and disease similarity matrices, we learned the features of lncRNAs and diseases by combining a GCN, GAT, and CNN.</p>
</sec>
<sec id="s2-3">
<title>2.3 Feature learning</title>
<p>
<xref ref-type="bibr" rid="B60">Dai et al. (2022)</xref> designed a hybrid graph representation learning model (GraphCDA) to represent the features of circRNAs and diseases and obtained better circRNA-disease association prediction performance. Inspired by GraphCDA proposed by <xref ref-type="bibr" rid="B60">Dai et al. (2022)</xref>, we exploit a GraphCDA-based LDA feature learning model.</p>
<sec id="s2-3-1">
<title>2.3.1 Graph convolutional network</title>
<p>A GCN was applied to obtain the feature representations of lncRNAs and diseases based on their similarity networks. For a GCN G, it is denoted as an adjacency matrix <inline-formula id="inf5">
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<mml:msub>
<mml:mo>&#x2211;</mml:mo>
<mml:mi>j</mml:mi>
</mml:msub>
<mml:msubsup>
<mml:mi mathvariant="normal">S</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>j</mml:mi>
</mml:mrow>
<mml:mo>&#x2032;</mml:mo>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf11">
<mml:math id="m13">
<mml:mrow>
<mml:mi>Q</mml:mi>
<mml:mo>&#x2208;</mml:mo>
<mml:msup>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mi>F</mml:mi>
<mml:mo>&#xd7;</mml:mo>
<mml:mi>F</mml:mi>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> denote degree matrix and trainable weight matrix, and &#x3c3;(&#xb7;) denotes a ReLU activation function.</p>
</sec>
<sec id="s2-3-2">
<title>2.3.2 Graph attention network</title>
<p>A GAT (<xref ref-type="bibr" rid="B41">Veli&#x10d;kovi&#x107; et al., 2017</xref>) uses multi-head attention to set weights for all adjacent nodes based on their importance. LDAenDL introduces a GAT layer between two GCN layers to help the GCN to extract high-level features of lncRNAs and diseases.</p>
<p>For the GCN G, a GAT layer outputs node representations <inline-formula id="inf12">
<mml:math id="m14">
<mml:mrow>
<mml:msup>
<mml:mi>H</mml:mi>
<mml:mrow>
<mml:mi>n</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>w</mml:mi>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> in Eq. <xref ref-type="disp-formula" rid="e3">3</xref>:<disp-formula id="e3">
<mml:math id="m15">
<mml:mrow>
<mml:msup>
<mml:mi>H</mml:mi>
<mml:mrow>
<mml:mi>n</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>w</mml:mi>
</mml:mrow>
</mml:msup>
<mml:mo>&#x3d;</mml:mo>
<mml:mi>G</mml:mi>
<mml:mi>A</mml:mi>
<mml:mi>T</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>S</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>H</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
<label>(3)</label>
</disp-formula>
</p>
<p>For <inline-formula id="inf13">
<mml:math id="m16">
<mml:mrow>
<mml:mi>K</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> attention mechanisms in multi-head attention and its weight matrix <inline-formula id="inf14">
<mml:math id="m17">
<mml:mrow>
<mml:msub>
<mml:mi>W</mml:mi>
<mml:mi>k</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, let <inline-formula id="inf15">
<mml:math id="m18">
<mml:mrow>
<mml:mover accent="true">
<mml:msub>
<mml:mi>H</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>&#x2192;</mml:mo>
</mml:mover>
</mml:mrow>
</mml:math>
</inline-formula> denote the input feature vector of the <inline-formula id="inf16">
<mml:math id="m19">
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>-th lncRNA, its feature representation <inline-formula id="inf17">
<mml:math id="m20">
<mml:mrow>
<mml:msubsup>
<mml:mover accent="true">
<mml:mi>H</mml:mi>
<mml:mo>&#x2192;</mml:mo>
</mml:mover>
<mml:mi>i</mml:mi>
<mml:mrow>
<mml:mi>n</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>w</mml:mi>
</mml:mrow>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula> in <inline-formula id="inf18">
<mml:math id="m21">
<mml:mrow>
<mml:msup>
<mml:mi>H</mml:mi>
<mml:mrow>
<mml:mi>n</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>w</mml:mi>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> can be denoted as Eq. <xref ref-type="disp-formula" rid="e4">4</xref>:<disp-formula id="e4">
<mml:math id="m22">
<mml:mrow>
<mml:msubsup>
<mml:mover accent="true">
<mml:mi>H</mml:mi>
<mml:mo>&#x2192;</mml:mo>
</mml:mover>
<mml:mi>i</mml:mi>
<mml:mrow>
<mml:mi>n</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>w</mml:mi>
</mml:mrow>
</mml:msubsup>
<mml:mo>&#x3d;</mml:mo>
<mml:mi>&#x3c3;</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mi>K</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mrow>
<mml:mstyle displaystyle="true">
<mml:munderover>
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:mi>k</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mi>K</mml:mi>
</mml:munderover>
</mml:mstyle>
<mml:mrow>
<mml:mstyle displaystyle="true">
<mml:munderover>
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:mi>j</mml:mi>
<mml:mo>&#x2260;</mml:mo>
<mml:mi>i</mml:mi>
</mml:mrow>
<mml:mi>n</mml:mi>
</mml:munderover>
</mml:mstyle>
<mml:mrow>
<mml:msubsup>
<mml:mi>&#x3d5;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>j</mml:mi>
</mml:mrow>
<mml:mi>k</mml:mi>
</mml:msubsup>
<mml:msub>
<mml:mi>W</mml:mi>
<mml:mi>k</mml:mi>
</mml:msub>
<mml:msub>
<mml:mover accent="true">
<mml:mi>H</mml:mi>
<mml:mo>&#x2192;</mml:mo>
</mml:mover>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mrow>
</mml:mrow>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
<label>(4)</label>
</disp-formula>where <inline-formula id="inf19">
<mml:math id="m23">
<mml:mrow>
<mml:msubsup>
<mml:mi>&#x3d5;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
<mml:mi>k</mml:mi>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula> denotes the <inline-formula id="inf20">
<mml:math id="m24">
<mml:mrow>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>-th attention coefficients between two lncRNA nodes <inline-formula id="inf21">
<mml:math id="m25">
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf22">
<mml:math id="m26">
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>:<disp-formula id="e5">
<mml:math id="m27">
<mml:mrow>
<mml:msubsup>
<mml:mi>&#x3d5;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>j</mml:mi>
</mml:mrow>
<mml:mi>k</mml:mi>
</mml:msubsup>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mi>exp</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi mathvariant="normal">f</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msubsup>
<mml:mi>a</mml:mi>
<mml:mi>k</mml:mi>
<mml:mi>T</mml:mi>
</mml:msubsup>
<mml:mrow>
<mml:mfenced open="[" close="]" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>W</mml:mi>
<mml:mi>k</mml:mi>
</mml:msub>
<mml:msub>
<mml:mover accent="true">
<mml:mi>H</mml:mi>
<mml:mo>&#x2192;</mml:mo>
</mml:mover>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>&#x2225;</mml:mo>
<mml:msub>
<mml:mi>W</mml:mi>
<mml:mi>k</mml:mi>
</mml:msub>
<mml:msub>
<mml:mover accent="true">
<mml:mi>H</mml:mi>
<mml:mo>&#x2192;</mml:mo>
</mml:mover>
<mml:mi>j</mml:mi>
</mml:msub>
<mml:mo>&#x2225;</mml:mo>
<mml:msub>
<mml:mi>B</mml:mi>
<mml:mi>k</mml:mi>
</mml:msub>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:mstyle displaystyle="true">
<mml:munder>
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>&#x2260;</mml:mo>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:munder>
</mml:mstyle>
<mml:mrow>
<mml:mi>exp</mml:mi>
<mml:mo>&#x2061;</mml:mo>
<mml:mo>&#x2061;</mml:mo>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi mathvariant="normal">f</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msubsup>
<mml:mi>a</mml:mi>
<mml:mi>k</mml:mi>
<mml:mi>T</mml:mi>
</mml:msubsup>
<mml:mrow>
<mml:mfenced open="[" close="]" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>W</mml:mi>
<mml:mi>k</mml:mi>
</mml:msub>
<mml:msub>
<mml:mover accent="true">
<mml:mi>H</mml:mi>
<mml:mo>&#x2192;</mml:mo>
</mml:mover>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>&#x2225;</mml:mo>
<mml:msub>
<mml:mi>W</mml:mi>
<mml:mi>k</mml:mi>
</mml:msub>
<mml:msub>
<mml:mover accent="true">
<mml:mi>H</mml:mi>
<mml:mo>&#x2192;</mml:mo>
</mml:mover>
<mml:mi>t</mml:mi>
</mml:msub>
<mml:mo>&#x2225;</mml:mo>
<mml:msub>
<mml:mi>B</mml:mi>
<mml:mi>k</mml:mi>
</mml:msub>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
<label>(5)</label>
</disp-formula>where &#x7c;&#x7c; denotes a concatenation operation, <inline-formula id="inf23">
<mml:math id="m28">
<mml:mrow>
<mml:mi>f</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> denotes the LeaklyReLU activation function, <inline-formula id="inf24">
<mml:math id="m29">
<mml:mrow>
<mml:msub>
<mml:mi>a</mml:mi>
<mml:mi>k</mml:mi>
</mml:msub>
<mml:mo>&#x2208;</mml:mo>
<mml:msup>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mi>F</mml:mi>
<mml:mo>&#x2b;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> denotes a weight vector related to the <inline-formula id="inf25">
<mml:math id="m30">
<mml:mrow>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>-th attention mechanism, and <inline-formula id="inf26">
<mml:math id="m31">
<mml:mrow>
<mml:msub>
<mml:mi>B</mml:mi>
<mml:mi>k</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> denotes the weight of an edge <inline-formula id="inf27">
<mml:math id="m32">
<mml:mrow>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>.</p>
</sec>
<sec id="s2-3-3">
<title>2.3.3 Feature representation of lncRNAs and diseases</title>
<p>For a lncRNA similarity network <inline-formula id="inf28">
<mml:math id="m33">
<mml:mrow>
<mml:msub>
<mml:mi>G</mml:mi>
<mml:mi>c</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, its adjacency matrix <inline-formula id="inf29">
<mml:math id="m34">
<mml:mrow>
<mml:mi mathvariant="normal">C</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>, and node feature matrix <inline-formula id="inf30">
<mml:math id="m35">
<mml:mrow>
<mml:msubsup>
<mml:mi>H</mml:mi>
<mml:mi>c</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:msubsup>
<mml:mo>&#x2208;</mml:mo>
<mml:msup>
<mml:mi mathvariant="normal">R</mml:mi>
<mml:mrow>
<mml:msub>
<mml:mi>N</mml:mi>
<mml:mi>c</mml:mi>
</mml:msub>
<mml:mo>&#xd7;</mml:mo>
<mml:msub>
<mml:mi>F</mml:mi>
<mml:mi>c</mml:mi>
</mml:msub>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula>, we alternately use GCN and GAT layers to obtain the graph feature representation of lncRNAs at different levels in Eq. <xref ref-type="disp-formula" rid="e6">6</xref>:<disp-formula id="e6">
<mml:math id="m36">
<mml:mrow>
<mml:mfenced open="{" close="" separators="|">
<mml:mrow>
<mml:mtable columnalign="center">
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:msubsup>
<mml:mi>H</mml:mi>
<mml:mi>c</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:msubsup>
<mml:mo>&#x3d;</mml:mo>
<mml:mi>G</mml:mi>
<mml:mi>C</mml:mi>
<mml:mi>N</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mo>,</mml:mo>
<mml:msubsup>
<mml:mi>H</mml:mi>
<mml:mi>c</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:msubsup>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:msubsup>
<mml:mi>H</mml:mi>
<mml:mi>c</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:msubsup>
<mml:mo>&#x3d;</mml:mo>
<mml:mi>G</mml:mi>
<mml:mi>A</mml:mi>
<mml:mi>T</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mo>,</mml:mo>
<mml:msubsup>
<mml:mi>H</mml:mi>
<mml:mi>c</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:msubsup>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:msubsup>
<mml:mi>H</mml:mi>
<mml:mi>c</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>3</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:msubsup>
<mml:mo>&#x3d;</mml:mo>
<mml:mi>G</mml:mi>
<mml:mi>C</mml:mi>
<mml:mi>N</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mo>,</mml:mo>
<mml:msubsup>
<mml:mi>H</mml:mi>
<mml:mi>c</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:msubsup>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:math>
<label>(6)</label>
</disp-formula>
</p>
<p>Thus, a 1D CNN is used to produce the lncRNA feature representation matrix <inline-formula id="inf31">
<mml:math id="m37">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">X</mml:mi>
<mml:mi>c</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> by combining the output features <inline-formula id="inf32">
<mml:math id="m38">
<mml:mrow>
<mml:msubsup>
<mml:mi>H</mml:mi>
<mml:mi>c</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf33">
<mml:math id="m39">
<mml:mrow>
<mml:msubsup>
<mml:mi>H</mml:mi>
<mml:mi>c</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>3</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula> in the different GCN layers.</p>
<p>Similarly, the graph feature representations of diseases at different levels are denoted by Eq. <xref ref-type="disp-formula" rid="e7">7</xref>:<disp-formula id="e7">
<mml:math id="m40">
<mml:mrow>
<mml:mfenced open="{" close="" separators="|">
<mml:mrow>
<mml:mtable columnalign="center">
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:msubsup>
<mml:mi mathvariant="normal">H</mml:mi>
<mml:mi>d</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:msubsup>
<mml:mo>&#x3d;</mml:mo>
<mml:mi mathvariant="normal">G</mml:mi>
<mml:mi mathvariant="normal">C</mml:mi>
<mml:mi mathvariant="normal">N</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>D</mml:mi>
<mml:mo>,</mml:mo>
<mml:msubsup>
<mml:mi>H</mml:mi>
<mml:mi>d</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:msubsup>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:msubsup>
<mml:mi mathvariant="normal">H</mml:mi>
<mml:mi>d</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:msubsup>
<mml:mo>&#x3d;</mml:mo>
<mml:mi mathvariant="normal">G</mml:mi>
<mml:mi mathvariant="normal">A</mml:mi>
<mml:mi mathvariant="normal">T</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>D</mml:mi>
<mml:mo>,</mml:mo>
<mml:msubsup>
<mml:mi>H</mml:mi>
<mml:mi>d</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:msubsup>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:msubsup>
<mml:mi mathvariant="normal">H</mml:mi>
<mml:mi>d</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>3</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:msubsup>
<mml:mo>&#x3d;</mml:mo>
<mml:mi mathvariant="normal">G</mml:mi>
<mml:mi mathvariant="normal">C</mml:mi>
<mml:mi mathvariant="normal">N</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>D</mml:mi>
<mml:mo>,</mml:mo>
<mml:msubsup>
<mml:mi>H</mml:mi>
<mml:mi>d</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:msubsup>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:math>
<label>(7)</label>
</disp-formula>
</p>
<p>A 1D CNN is used to produce the disease feature representation matrix <inline-formula id="inf34">
<mml:math id="m41">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">X</mml:mi>
<mml:mi>c</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> by combining the output features <inline-formula id="inf35">
<mml:math id="m42">
<mml:mrow>
<mml:msubsup>
<mml:mi>H</mml:mi>
<mml:mi mathvariant="normal">d</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf36">
<mml:math id="m43">
<mml:mrow>
<mml:msubsup>
<mml:mi>H</mml:mi>
<mml:mi mathvariant="normal">d</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>3</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula> in the different GCN layers.</p>
</sec>
<sec id="s2-3-4">
<title>2.3.4 Preference matrix construction</title>
<p>The preference matrix <inline-formula id="inf37">
<mml:math id="m44">
<mml:mrow>
<mml:mi>U</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> that describes all lncRNA-disease pairs can be represented as Eq. <xref ref-type="disp-formula" rid="e8">8</xref> based on <inline-formula id="inf38">
<mml:math id="m45">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">X</mml:mi>
<mml:mi>c</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf39">
<mml:math id="m46">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">X</mml:mi>
<mml:mi>d</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>:<disp-formula id="e8">
<mml:math id="m47">
<mml:mrow>
<mml:mi mathvariant="normal">U</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:msup>
<mml:msub>
<mml:mi>X</mml:mi>
<mml:mi>c</mml:mi>
</mml:msub>
<mml:mi mathvariant="normal">T</mml:mi>
</mml:msup>
<mml:msub>
<mml:mi>X</mml:mi>
<mml:mi>d</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
<label>(8)</label>
</disp-formula>
</p>
<p>We used binary cross-entropy as the activation function to evaluate the difference between the preference matrix <inline-formula id="inf40">
<mml:math id="m48">
<mml:mrow>
<mml:mi mathvariant="normal">U</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> and the known adjacency matrix <inline-formula id="inf41">
<mml:math id="m49">
<mml:mrow>
<mml:mi mathvariant="normal">R</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>. By minimizing the loss function on two LDA datasets, the feature representation matrices <inline-formula id="inf42">
<mml:math id="m50">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">X</mml:mi>
<mml:mi>c</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf43">
<mml:math id="m51">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">X</mml:mi>
<mml:mi>d</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> of lncRNAs and diseases are learned.</p>
</sec>
</sec>
<sec id="s2-4">
<title>2.4 LDA prediction</title>
<sec id="s2-4-1">
<title>2.4.1 DNN</title>
<p>We built a DNN to predict new LDAs based on known LDAs and the learned LDA features. The DNN contains an input layer, an output layer, and multiple hidden layers. In the input layer, there are F neurons that are the same as the number of LDA features.</p>
<p>Given an LDA sample <inline-formula id="inf44">
<mml:math id="m52">
<mml:mrow>
<mml:mi>x</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>, the input layer with <inline-formula id="inf45">
<mml:math id="m53">
<mml:mrow>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> inputs is represented by Eq. <xref ref-type="disp-formula" rid="e9">9</xref>:<disp-formula id="e9">
<mml:math id="m54">
<mml:mrow>
<mml:mfenced open="" close="]" separators="|">
<mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>x</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mo>[</mml:mo>
<mml:mi>x</mml:mi>
</mml:mrow>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:mo>&#x2026;</mml:mo>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mi>k</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:math>
<label>(9)</label>
</disp-formula>where <inline-formula id="inf46">
<mml:math id="m55">
<mml:mrow>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mn>i</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> denotes the <inline-formula id="inf47">
<mml:math id="m56">
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>-th feature in a sample <inline-formula id="inf48">
<mml:math id="m57">
<mml:mrow>
<mml:mi>x</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>.</p>
<p>The hidden layer is represented by Eq. <xref ref-type="disp-formula" rid="e10">10</xref>:<disp-formula id="e10">
<mml:math id="m58">
<mml:mrow>
<mml:msub>
<mml:mi>h</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msubsup>
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mi>k</mml:mi>
</mml:msubsup>
<mml:mtext>&#x200a;</mml:mtext>
<mml:msub>
<mml:mi>w</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>b</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
<label>(10)</label>
</disp-formula>where <inline-formula id="inf49">
<mml:math id="m59">
<mml:mrow>
<mml:msub>
<mml:mi>w</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf50">
<mml:math id="m60">
<mml:mrow>
<mml:msub>
<mml:mi>b</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> denote the weight of <inline-formula id="inf51">
<mml:math id="m61">
<mml:mrow>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and the bias in the <inline-formula id="inf52">
<mml:math id="m62">
<mml:mrow>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>-th hidden layer, respectively.</p>
<p>The output in the <inline-formula id="inf53">
<mml:math id="m63">
<mml:mrow>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>-th hidden layer is denoted by Eq. <xref ref-type="disp-formula" rid="e11">11</xref>:<disp-formula id="e11">
<mml:math id="m64">
<mml:mrow>
<mml:mi>h</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mi>f</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>h</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
<label>(11)</label>
</disp-formula>where <inline-formula id="inf54">
<mml:math id="m65">
<mml:mrow>
<mml:mi>f</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> denotes a ReLU activation function. Finally, the output layer with the sigmoid function outputs the LDA prediction results in Eq. <xref ref-type="disp-formula" rid="e12">12</xref>:<disp-formula id="e12">
<mml:math id="m66">
<mml:mrow>
<mml:mi>&#x3c3;</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>h</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mn>1</mml:mn>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2b;</mml:mo>
<mml:msup>
<mml:mi>e</mml:mi>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>h</mml:mi>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
<label>(12)</label>
</disp-formula>
</p>
</sec>
<sec id="s2-4-2">
<title>2.4.2 LightGBM</title>
<p>In this section, we built a LightGBM (<xref ref-type="bibr" rid="B10">Ke et al., 2017</xref>) to identify new LDAs. For a training set <inline-formula id="inf55">
<mml:math id="m67">
<mml:mrow>
<mml:mi>X</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:msubsup>
<mml:mrow>
<mml:mfenced open="{" close="}" separators="|">
<mml:mrow>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>y</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mi>n</mml:mi>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula> with <inline-formula id="inf56">
<mml:math id="m68">
<mml:mrow>
<mml:mi>n</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> lncRNA-disease pair, LightGBM intends to build an approximation of <inline-formula id="inf57">
<mml:math id="m69">
<mml:mrow>
<mml:mover accent="true">
<mml:mi>f</mml:mi>
<mml:mo>&#x5e;</mml:mo>
</mml:mover>
</mml:mrow>
</mml:math>
</inline-formula> to a certain function <inline-formula id="inf58">
<mml:math id="m70">
<mml:mrow>
<mml:mi>f</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>x</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> by minimizing the expected value of loss function <inline-formula id="inf59">
<mml:math id="m71">
<mml:mrow>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>y</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>f</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>x</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> by Eq. <xref ref-type="disp-formula" rid="e13">13</xref>:<disp-formula id="e13">
<mml:math id="m72">
<mml:mrow>
<mml:mover accent="true">
<mml:mi>f</mml:mi>
<mml:mo>&#x5e;</mml:mo>
</mml:mover>
<mml:mo>&#x3d;</mml:mo>
<mml:mi>arg</mml:mi>
<mml:munder>
<mml:mi>min</mml:mi>
<mml:mi>f</mml:mi>
</mml:munder>
<mml:mtext>&#x200a;</mml:mtext>
<mml:msub>
<mml:mi>E</mml:mi>
<mml:mrow>
<mml:mi>x</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>y</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mfenced open="[" close="]" separators="|">
<mml:mrow>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>y</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>f</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>x</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
<label>(13)</label>
</disp-formula>
</p>
<p>LightGBM integrates <inline-formula id="inf60">
<mml:math id="m73">
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> regression trees <inline-formula id="inf61">
<mml:math id="m74">
<mml:mrow>
<mml:msubsup>
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mi>T</mml:mi>
</mml:msubsup>
<mml:mtext>&#x200a;</mml:mtext>
<mml:msub>
<mml:mi>f</mml:mi>
<mml:mi>t</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>X</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> to approximate the final model by Eq. <xref ref-type="disp-formula" rid="e14">14</xref>:<disp-formula id="e14">
<mml:math id="m75">
<mml:mrow>
<mml:msub>
<mml:mi>f</mml:mi>
<mml:mi>T</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>X</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:msubsup>
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mi>T</mml:mi>
</mml:msubsup>
<mml:msub>
<mml:mi>f</mml:mi>
<mml:mi>t</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>X</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
<label>(14)</label>
</disp-formula>
</p>
<p>The regression trees are expressed as <inline-formula id="inf62">
<mml:math id="m76">
<mml:mrow>
<mml:msub>
<mml:mi>w</mml:mi>
<mml:mrow>
<mml:mi>q</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>x</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:mi>q</mml:mi>
<mml:mo>&#x2208;</mml:mo>
<mml:mrow>
<mml:mfenced open="{" close="}" separators="|">
<mml:mrow>
<mml:mn>1,2</mml:mn>
<mml:mo>,</mml:mo>
<mml:mo>&#x2026;</mml:mo>
<mml:mo>,</mml:mo>
<mml:mi>J</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>, where <inline-formula id="inf63">
<mml:math id="m77">
<mml:mrow>
<mml:mi>J</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula id="inf64">
<mml:math id="m78">
<mml:mrow>
<mml:mi>q</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>, and <inline-formula id="inf65">
<mml:math id="m79">
<mml:mrow>
<mml:mi mathvariant="normal">w</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> denote the number of leaves, the decision rules of the tree, and the sample weight of leaf nodes, respectively.</p>
<p>At step <inline-formula id="inf66">
<mml:math id="m80">
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>, LightGBM is trained in an additive form:<disp-formula id="e15">
<mml:math id="m81">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">&#x393;</mml:mi>
<mml:mi>t</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mrow>
<mml:mstyle displaystyle="true">
<mml:munderover>
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mi>n</mml:mi>
</mml:munderover>
</mml:mstyle>
<mml:mrow>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>y</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>F</mml:mi>
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>f</mml:mi>
<mml:mi>t</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mrow>
</mml:mrow>
</mml:math>
<label>(15)</label>
</disp-formula>
</p>
<p>The objective function (15) is rapidly approximated with Newton&#x2019;s method (<xref ref-type="bibr" rid="B39">Sun et al., 2020</xref>).</p>
<p>To solve the objective function of LightGBM, we removed the constant term for simplicity, and model (15) can be represented as Eq. <xref ref-type="disp-formula" rid="e16">16</xref>:<disp-formula id="e16">
<mml:math id="m82">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">&#x393;</mml:mi>
<mml:mi>t</mml:mi>
</mml:msub>
<mml:mo>&#x2245;</mml:mo>
<mml:mrow>
<mml:mstyle displaystyle="true">
<mml:munderover>
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mi>n</mml:mi>
</mml:munderover>
</mml:mstyle>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>g</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:msub>
<mml:mi>f</mml:mi>
<mml:mi>t</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x2b;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mfrac>
<mml:msub>
<mml:mi>h</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:msubsup>
<mml:mi>f</mml:mi>
<mml:mi>t</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mrow>
</mml:math>
<label>(16)</label>
</disp-formula>where <inline-formula id="inf67">
<mml:math id="m83">
<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="inf68">
<mml:math id="m84">
<mml:mrow>
<mml:msub>
<mml:mi>h</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> are the first-order and second-order gradients related to the loss function. Given the sample set <inline-formula id="inf69">
<mml:math id="m85">
<mml:mrow>
<mml:msub>
<mml:mi>I</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> related to leaf <inline-formula id="inf70">
<mml:math id="m86">
<mml:mrow>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>, Eq. <xref ref-type="disp-formula" rid="e16">16</xref> is transformed to Eq. <xref ref-type="disp-formula" rid="e17">17</xref>:<disp-formula id="e17">
<mml:math id="m87">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">&#x393;</mml:mi>
<mml:mi>t</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mrow>
<mml:mstyle displaystyle="true">
<mml:munderover>
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:mi>j</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mi>J</mml:mi>
</mml:munderover>
</mml:mstyle>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mstyle displaystyle="true">
<mml:munder>
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>&#x2208;</mml:mo>
<mml:msub>
<mml:mi>I</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
</mml:munder>
</mml:mstyle>
<mml:msub>
<mml:mi>g</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:msub>
<mml:mi>w</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mfrac>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mstyle displaystyle="true">
<mml:munder>
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>&#x2208;</mml:mo>
<mml:msub>
<mml:mi>I</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
</mml:munder>
</mml:mstyle>
<mml:mrow>
<mml:msub>
<mml:mi>h</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:mi>&#x3bb;</mml:mi>
</mml:mrow>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:msubsup>
<mml:mi>w</mml:mi>
<mml:mi>j</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mrow>
</mml:math>
<label>(17)</label>
</disp-formula>
</p>
<p>Given a certain tree structure <inline-formula id="inf71">
<mml:math id="m88">
<mml:mrow>
<mml:mi>q</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>x</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>, for each leaf node <inline-formula id="inf72">
<mml:math id="m89">
<mml:mrow>
<mml:msubsup>
<mml:mi>w</mml:mi>
<mml:mi>j</mml:mi>
<mml:mo>&#x2a;</mml:mo>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula>, its optimal leaf weight and the extreme value of <inline-formula id="inf73">
<mml:math id="m90">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">&#x393;</mml:mi>
<mml:mi>k</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> could be computed by Eq. <xref ref-type="disp-formula" rid="e18">18</xref>:<disp-formula id="e18">
<mml:math id="m91">
<mml:mrow>
<mml:mtable columnalign="center">
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:msubsup>
<mml:mi>w</mml:mi>
<mml:mi>j</mml:mi>
<mml:mo>&#x2a;</mml:mo>
</mml:msubsup>
<mml:mo>&#x3d;</mml:mo>
<mml:mo>&#x2212;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mstyle displaystyle="true">
<mml:munder>
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>&#x2208;</mml:mo>
<mml:msub>
<mml:mi>I</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
</mml:munder>
</mml:mstyle>
<mml:msub>
<mml:mi>g</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mstyle displaystyle="true">
<mml:munder>
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>&#x2208;</mml:mo>
<mml:msub>
<mml:mi>I</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
</mml:munder>
</mml:mstyle>
<mml:mrow>
<mml:msub>
<mml:mi>h</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:mi>&#x3bb;</mml:mi>
</mml:mrow>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:msubsup>
<mml:mi mathvariant="normal">&#x393;</mml:mi>
<mml:mi>T</mml:mi>
<mml:mo>&#x2a;</mml:mo>
</mml:msubsup>
<mml:mo>&#x3d;</mml:mo>
<mml:mo>&#x2212;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mfrac>
<mml:mrow>
<mml:mstyle displaystyle="true">
<mml:munderover>
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:mi>j</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mi>J</mml:mi>
</mml:munderover>
</mml:mstyle>
<mml:mfrac>
<mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mstyle displaystyle="true">
<mml:munder>
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>&#x2208;</mml:mo>
<mml:msub>
<mml:mi>I</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
</mml:munder>
</mml:mstyle>
<mml:msub>
<mml:mi>g</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msup>
<mml:mrow>
<mml:mstyle displaystyle="true">
<mml:munder>
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>&#x2208;</mml:mo>
<mml:msub>
<mml:mi>I</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
</mml:munder>
</mml:mstyle>
<mml:mrow>
<mml:msub>
<mml:mi>h</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:mi>&#x3bb;</mml:mi>
</mml:mrow>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mrow>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:math>
<label>(18)</label>
</disp-formula>where <inline-formula id="inf74">
<mml:math id="m92">
<mml:mrow>
<mml:msubsup>
<mml:mi mathvariant="normal">&#x393;</mml:mi>
<mml:mi>T</mml:mi>
<mml:mo>&#x2a;</mml:mo>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula> is a scoring function used to evaluate the quality of a tree structure <inline-formula id="inf75">
<mml:math id="m93">
<mml:mrow>
<mml:mi>q</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>. Finally, Model (15) can be denoted as:<disp-formula id="e19">
<mml:math id="m94">
<mml:mrow>
<mml:mi>G</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mfrac>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mfrac>
<mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mstyle displaystyle="true">
<mml:munder>
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>&#x2208;</mml:mo>
<mml:msub>
<mml:mi>I</mml:mi>
<mml:mi>L</mml:mi>
</mml:msub>
</mml:mrow>
</mml:munder>
</mml:mstyle>
<mml:msub>
<mml:mi>g</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msup>
<mml:mrow>
<mml:mstyle displaystyle="true">
<mml:munder>
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>&#x2208;</mml:mo>
<mml:msub>
<mml:mi>I</mml:mi>
<mml:mi>L</mml:mi>
</mml:msub>
</mml:mrow>
</mml:munder>
</mml:mstyle>
<mml:mrow>
<mml:msub>
<mml:mi>h</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:mi>&#x3bb;</mml:mi>
</mml:mrow>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x2b;</mml:mo>
<mml:mfrac>
<mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mstyle displaystyle="true">
<mml:munder>
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>&#x2208;</mml:mo>
<mml:msub>
<mml:mi>I</mml:mi>
<mml:mi>R</mml:mi>
</mml:msub>
</mml:mrow>
</mml:munder>
</mml:mstyle>
<mml:msub>
<mml:mi>g</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
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<label>(19)</label>
</disp-formula>where <inline-formula id="inf76">
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</inline-formula>, respectively.</p>
</sec>
<sec id="s2-4-3">
<title>2.4.3 Ensemble learning</title>
<p>Through the solution of models (12) and (15), we can identify potential LDAs based on a DNN and LightGBM. Ensemble learning has better prediction accuracy than a single model. To further improve LDA prediction accuracy, we combined a DNN and LightGBM and developed an ensemble model for LDA identification through soft voting in Eq. <xref ref-type="disp-formula" rid="e16">16</xref>:<disp-formula id="e20">
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<label>(20)</label>
</disp-formula>where <inline-formula id="inf79">
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<mml:mi>C</mml:mi>
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</inline-formula> are their weights with values of 0.4 and 0.6, respectively. In particular, a lncRNA&#x2013;disease pair is taken as an LDA if its association probability is greater than 0.5; otherwise, the pair is taken as a negative LDA.</p>
</sec>
</sec>
</sec>
<sec sec-type="results" id="s3">
<title>3 Results</title>
<sec id="s3-1">
<title>3.1 Evaluation metrics</title>
<p>In this article, we compared our proposed LDAenDL method with four LDA prediction methods, SDLDA, LDNFSGB, IPCAF, and LDASR. Precision, recall, accuracy, F1-score, AUC, and AUPR were used to compare the performance of LDAenDL with the four methods. The six metrics have been defined by <xref ref-type="bibr" rid="B29">Peng et al. (2022b)</xref> (<xref ref-type="bibr" rid="B36">Shen et al., 2022</xref>).</p>
</sec>
<sec id="s3-2">
<title>3.2 Comparison of LDAenDL with the other four methods</title>
<p>To implement the performance evaluation, inspired by the three cross-validations proposed by <xref ref-type="bibr" rid="B58">Zhou et al. (2021)</xref>, we conducted cross-validations on lncRNAs (CV1), diseases (CV2), and lncRNA-disease pairs (CV3). <xref ref-type="table" rid="T1">Tables 1</xref>&#x2013;<xref ref-type="table" rid="T3">3</xref> give the precision, recall, accuracy, F1-score, AUC, and AUPR under CV1, CV2, and CV3 on two LDA datasets. In <xref ref-type="table" rid="T1">Tables 1</xref>&#x2013;<xref ref-type="table" rid="T6">6</xref>, the bold font in each row denotes the best performance.</p>
<table-wrap id="T1" position="float">
<label>TABLE 1</label>
<caption>
<p>Comparison of LDAenDL with the other four methods under CV1.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center"/>
<th align="left"/>
<th align="center">SDLDA</th>
<th align="center">LDNFSGB</th>
<th align="center">IPCARF</th>
<th align="center">LDASR</th>
<th align="center">LDAenDL</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td rowspan="2" align="left">Precision</td>
<td align="left">Dataset 1</td>
<td align="center">0.8514 &#xb1; 0.0509</td>
<td align="center">0.7004 &#xb1; 0.0639</td>
<td align="center">0.4878 &#xb1; 0.1309</td>
<td align="center">0.6726 &#xb1; 0.1200</td>
<td align="center">
<bold>0.8764 &#xb1; 0.0493</bold>
</td>
</tr>
<tr>
<td align="left">Dataset 2</td>
<td align="center">
<bold>0.9399 &#xb1; 0.0154</bold>
</td>
<td align="center">0.8552 &#xb1; 0.0393</td>
<td align="center">0.6615 &#xb1; 0.0966</td>
<td align="center">0.8405 &#xb1; 0.0300</td>
<td align="center">0.9391 &#xb1; 0.0290</td>
</tr>
<tr>
<td rowspan="2" align="left">Recall</td>
<td align="left">Dataset 1</td>
<td align="center">0.6521 &#xb1; 0.0732</td>
<td align="center">0.6092 &#xb1; 0.0790</td>
<td align="center">0.5721 &#xb1; 0.1580</td>
<td align="center">0.5129 &#xb1; 0.0946</td>
<td align="center">
<bold>0.7019 &#xb1; 0.0639</bold>
</td>
</tr>
<tr>
<td align="left">Dataset 2</td>
<td align="center">0.8239 &#xb1; 0.0437</td>
<td align="center">0.8021 &#xb1; 0.0498</td>
<td align="center">0.6434 &#xb1; 0.1545</td>
<td align="center">0.7358 &#xb1; 0.0562</td>
<td align="center">
<bold>0.8304 &#xb1; 0.0523</bold>
</td>
</tr>
<tr>
<td rowspan="2" align="left">Accuracy</td>
<td align="left">Dataset 1</td>
<td align="center">0.7799 &#xb1; 0.0341</td>
<td align="center">0.6769 &#xb1; 0.0423</td>
<td align="center">0.4906 &#xb1; 0.0951</td>
<td align="center">0.6417 &#xb1; 0.0597</td>
<td align="center">
<bold>0.7996 &#xb1; 0.0312</bold>
</td>
</tr>
<tr>
<td align="left">Dataset 2</td>
<td align="center">0.8857 &#xb1; 0.0283</td>
<td align="center">0.8323 &#xb1; 0.0230</td>
<td align="center">0.6526 &#xb1; 0.0775</td>
<td align="center">0.7972 &#xb1; 0.0268</td>
<td align="center">
<bold>0.8879 &#xb1; 0.0289</bold>
</td>
</tr>
<tr>
<td rowspan="2" align="left">F1-score</td>
<td align="left">Dataset 1</td>
<td align="center">0.7365 &#xb1; 0.0563</td>
<td align="center">0.6462 &#xb1; 0.0451</td>
<td align="center">0.5125 &#xb1; 0.1100</td>
<td align="center">0.5668 &#xb1; 0.0536</td>
<td align="center">
<bold>0.7768 &#xb1; 0.0399</bold>
</td>
</tr>
<tr>
<td align="left">Dataset 2</td>
<td align="center">0.8775 &#xb1; 0.0278</td>
<td align="center">0.8260 &#xb1; 0.0230</td>
<td align="center">0.6401 &#xb1; 0.1017</td>
<td align="center">0.7827 &#xb1; 0.0260</td>
<td align="center">
<bold>0.8804 &#xb1; 0.0334</bold>
</td>
</tr>
<tr>
<td rowspan="2" align="left">AUC</td>
<td align="left">Dataset 1</td>
<td align="center">0.8023 &#xb1; 0.0477</td>
<td align="center">0.7346 &#xb1; 0.0465</td>
<td align="center">0.5096 &#xb1; 0.1432</td>
<td align="center">0.7057 &#xb1; 0.0420</td>
<td align="center">
<bold>0.8701 &#xb1; 0.0339</bold>
</td>
</tr>
<tr>
<td align="left">Dataset 2</td>
<td align="center">0.9366 &#xb1; 0.0195</td>
<td align="center">0.8839 &#xb1; 0.0270</td>
<td align="center">0.7104 &#xb1; 0.0997</td>
<td align="center">0.8641 &#xb1; 0.0256</td>
<td align="center">
<bold>0.9490 &#xb1; 0.0220</bold>
</td>
</tr>
<tr>
<td rowspan="2" align="left">AUPR</td>
<td align="left">Dataset 1</td>
<td align="center">0.8461 &#xb1; 0.0553</td>
<td align="center">0.7239 &#xb1; 0.0626</td>
<td align="center">0.5336 &#xb1; 0.1423</td>
<td align="center">0.6775 &#xb1; 0.0971</td>
<td align="center">
<bold>0.8903 &#xb1; 0.0273</bold>
</td>
</tr>
<tr>
<td align="left">Dataset 2</td>
<td align="center">0.9533 &#xb1; 0.0129</td>
<td align="center">0.8832 &#xb1; 0.0307</td>
<td align="center">0.7128 &#xb1; 0.1012</td>
<td align="center">0.8671 &#xb1; 0.0252</td>
<td align="center">
<bold>0.9582 &#xb1; 0.0167</bold>
</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>The bold value denotes the best performance.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<table-wrap id="T2" position="float">
<label>TABLE 2</label>
<caption>
<p>Comparison of LDAenDL with the other four methods under CV2.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center"/>
<th align="left"/>
<th align="center">SDLDA</th>
<th align="center">LDNFSGB</th>
<th align="center">IPCARF</th>
<th align="center">LDASR</th>
<th align="center">LDAenDL</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td rowspan="2" align="left">Precision</td>
<td align="left">Dataset 1</td>
<td align="center">0.8854 &#xb1; 0.0377</td>
<td align="center">0.7548 &#xb1; 0.0639</td>
<td align="center">0.5583 &#xb1; 0.0910</td>
<td align="center">0.7462 &#xb1; 0.0613</td>
<td align="center">
<bold>0.9135 &#xb1; 0.0317</bold>
</td>
</tr>
<tr>
<td align="left">Dataset 2</td>
<td align="center">0.9232 &#xb1; 0.0331</td>
<td align="center">0.8005 &#xb1; 0.0625</td>
<td align="center">0.5557 &#xb1; 0.1473</td>
<td align="center">0.7625 &#xb1; 0.0749</td>
<td align="center">
<bold>0.9528 &#xb1; 0.0225</bold>
</td>
</tr>
<tr>
<td rowspan="2" align="left">Recall</td>
<td align="left">Dataset 1</td>
<td align="center">
<bold>0.7182 &#xb1; 0.0694</bold>
</td>
<td align="center">0.7309 &#xb1; 0.0646</td>
<td align="center">0.7538 &#xb1; 0.1067</td>
<td align="center">0.6431 &#xb1; 0.0757</td>
<td align="center">0.6649 &#xb1; 0.0814</td>
</tr>
<tr>
<td align="left">Dataset 2</td>
<td align="center">
<bold>0.8579 &#xb1; 0.0655</bold>
</td>
<td align="center">0.6936 &#xb1; 0.0794</td>
<td align="center">0.5279 &#xb1; 0.1969</td>
<td align="center">0.5758 &#xb1; 0.0894</td>
<td align="center">0.4616 &#xb1; 0.1702</td>
</tr>
<tr>
<td rowspan="2" align="left">Accuracy</td>
<td align="left">Dataset 1</td>
<td align="center">
<bold>0.8187 &#xb1; 0.0282</bold>
</td>
<td align="center">0.7552 &#xb1; 0.0291</td>
<td align="center">0.5766 &#xb1; 0.0740</td>
<td align="center">0.7165 &#xb1; 0.0339</td>
<td align="center">0.8005 &#xb1; 0.0381</td>
</tr>
<tr>
<td align="left">Dataset 2</td>
<td align="center">
<bold>0.9043 &#xb1; 0.0174</bold>
</td>
<td align="center">0.7670 &#xb1; 0.0432</td>
<td align="center">0.5593 &#xb1; 0.1159</td>
<td align="center">0.7010 &#xb1; 0.0463</td>
<td align="center">0.7196 &#xb1; 0.0821</td>
</tr>
<tr>
<td rowspan="2" align="left">F1-score</td>
<td align="left">Dataset 1</td>
<td align="center">
<bold>0.7917 &#xb1; 0.0519</bold>
</td>
<td align="center">0.7407 &#xb1; 0.0526</td>
<td align="center">0.6339 &#xb1; 0.0715</td>
<td align="center">0.6873 &#xb1; 0.0512</td>
<td align="center">0.7664 &#xb1; 0.0593</td>
</tr>
<tr>
<td align="left">Dataset 2</td>
<td align="center">
<bold>0.8886 &#xb1; 0.0475</bold>
</td>
<td align="center">0.7402 &#xb1; 0.0577</td>
<td align="center">0.5190 &#xb1; 0.1434</td>
<td align="center">0.6485 &#xb1; 0.0555</td>
<td align="center">0.6032 &#xb1; 0.1612</td>
</tr>
<tr>
<td rowspan="2" align="left">AUC</td>
<td align="left">Dataset 1</td>
<td align="center">0.8788 &#xb1; 0.0274</td>
<td align="center">0.8329 &#xb1; 0.0273</td>
<td align="center">0.6402 &#xb1; 0.1004</td>
<td align="center">0.7951 &#xb1; 0.0317</td>
<td align="center">
<bold>0.8953 &#xb1; 0.0284</bold>
</td>
</tr>
<tr>
<td align="left">Dataset 2</td>
<td align="center">
<bold>0.9559 &#xb1; 0.0160</bold>
</td>
<td align="center">0.8603 &#xb1; 0.0363</td>
<td align="center">0.5992 &#xb1; 0.1601</td>
<td align="center">0.8045 &#xb1; 0.0362</td>
<td align="center">0.9157 &#xb1; 0.0420</td>
</tr>
<tr>
<td rowspan="2" align="left">AUPR</td>
<td align="left">Dataset 1</td>
<td align="center">0.8934 &#xb1; 0.0387</td>
<td align="center">0.8163 &#xb1; 0.0537</td>
<td align="center">0.6355 &#xb1; 0.1217</td>
<td align="center">0.7914 &#xb1; 0.0542</td>
<td align="center">
<bold>0.9061 &#xb1; 0.0254</bold>
</td>
</tr>
<tr>
<td align="left">Dataset 2</td>
<td align="center">
<bold>0.9561 &#xb1; 0.0354</bold>
</td>
<td align="center">0.8292 &#xb1; 0.0680</td>
<td align="center">0.6040 &#xb1; 0.1476</td>
<td align="center">0.7630 &#xb1; 0.0717</td>
<td align="center">0.9122 &#xb1; 0.0436</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>The bold value denotes the best performance.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<table-wrap id="T3" position="float">
<label>TABLE 3</label>
<caption>
<p>Comparison of LDAenDL with the other four methods under CV3.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center"/>
<th align="left"/>
<th align="center">SDLDA</th>
<th align="center">LDNFSGB</th>
<th align="center">IPCARF</th>
<th align="center">LDASR</th>
<th align="center">LDAenDL</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td rowspan="2" align="left">Precision</td>
<td align="left">Dataset 1</td>
<td align="center">
<bold>0.8782 &#xb1; 0.0306</bold>
</td>
<td align="center">0.7782 &#xb1; 0.0270</td>
<td align="center">0.7069 &#xb1; 0.0478</td>
<td align="center">0.7695 &#xb1; 0.0393</td>
<td align="center">0.8637 &#xb1; 0.0312</td>
</tr>
<tr>
<td align="left">Dataset 2</td>
<td align="center">0.9178 &#xb1; 0.0154</td>
<td align="center">0.8548 &#xb1; 0.0156</td>
<td align="center">0.7693 &#xb1; 0.0850</td>
<td align="center">0.8553 &#xb1; 0.0189</td>
<td align="center">
<bold>0.9351 &#xb1; 0.0157</bold>
</td>
</tr>
<tr>
<td rowspan="2" align="left">Recall</td>
<td align="left">Dataset 1</td>
<td align="center">0.7256 &#xb1; 0.0376</td>
<td align="center">0.8169 &#xb1; 0.0408</td>
<td align="center">0.6155 &#xb1; 0.0652</td>
<td align="center">0.6836 &#xb1; 0.0342</td>
<td align="center">
<bold>0.8234 &#xb1; 0.0314</bold>
</td>
</tr>
<tr>
<td align="left">Dataset 2</td>
<td align="center">0.8824 &#xb1; 0.0198</td>
<td align="center">0.8818 &#xb1; 0.0204</td>
<td align="center">0.5034 &#xb1; 0.1469</td>
<td align="center">0.8204 &#xb1; 0.0238</td>
<td align="center">
<bold>0.8999 &#xb1; 0.0179</bold>
</td>
</tr>
<tr>
<td rowspan="2" align="left">Accuracy</td>
<td align="left">Dataset 1</td>
<td align="center">0.8120 &#xb1; 0.0216</td>
<td align="center">0.7916 &#xb1; 0.0256</td>
<td align="center">0.6793 &#xb1; 0.0403</td>
<td align="center">0.7385 &#xb1; 0.0283</td>
<td align="center">
<bold>0.8462 &#xb1; 0.0229</bold>
</td>
</tr>
<tr>
<td align="left">Dataset 2</td>
<td align="center">0.9015 &#xb1; 0.0114</td>
<td align="center">0.8658 &#xb1; 0.0127</td>
<td align="center">0.6793 &#xb1; 0.0753</td>
<td align="center">0.8405 &#xb1; 0.0129</td>
<td align="center">
<bold>0.9186 &#xb1; 0.0126</bold>
</td>
</tr>
<tr>
<td rowspan="2" align="left">F1-score</td>
<td align="left">Dataset 1</td>
<td align="center">0.7939 &#xb1; 0.0260</td>
<td align="center">0.7965 &#xb1; 0.0262</td>
<td align="center">0.6563 &#xb1; 0.0492</td>
<td align="center">0.7233 &#xb1; 0.0289</td>
<td align="center">
<bold>0.8426 &#xb1; 0.0232</bold>
</td>
</tr>
<tr>
<td align="left">Dataset 2</td>
<td align="center">0.8996 &#xb1; 0.0119</td>
<td align="center">0.8679 &#xb1; 0.0129</td>
<td align="center">0.5995 &#xb1; 0.1312</td>
<td align="center">0.8371 &#xb1; 0.0137</td>
<td align="center">
<bold>0.9171 &#xb1; 0.0130</bold>
</td>
</tr>
<tr>
<td rowspan="2" align="left">AUC</td>
<td align="left">Dataset 1</td>
<td align="center">0.8774 &#xb1; 0.0200</td>
<td align="center">0.8578 &#xb1; 0.0234</td>
<td align="center">0.7384 &#xb1; 0.0466</td>
<td align="center">0.8133 &#xb1; 0.0218</td>
<td align="center">
<bold>0.9110 &#xb1; 0.0197</bold>
</td>
</tr>
<tr>
<td align="left">Dataset 2</td>
<td align="center">0.9560 &#xb1; 0.0081</td>
<td align="center">0.9346 &#xb1; 0.0074</td>
<td align="center">0.7680 &#xb1; 0.0882</td>
<td align="center">0.9143 &#xb1; 0.0112</td>
<td align="center">
<bold>0.9708 &#xb1; 0.0062</bold>
</td>
</tr>
<tr>
<td rowspan="2" align="left">AUPR</td>
<td align="left">Dataset 1</td>
<td align="center">0.8952 &#xb1; 0.0177</td>
<td align="center">0.8489 &#xb1; 0.0289</td>
<td align="center">0.7409 &#xb1; 0.0515</td>
<td align="center">0.8131 &#xb1; 0.0277</td>
<td align="center">
<bold>0.9166 &#xb1; 0.0203</bold>
</td>
</tr>
<tr>
<td align="left">Dataset 2</td>
<td align="center">0.9639 &#xb1; 0.0063</td>
<td align="center">0.9273 &#xb1; 0.0098</td>
<td align="center">0.7689 &#xb1; 0.0924</td>
<td align="center">0.9100 &#xb1; 0.0136</td>
<td align="center">
<bold>0.9743 &#xb1; 0.0058</bold>
</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>The bold value denotes the best performance.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<table-wrap id="T4" position="float">
<label>TABLE 4</label>
<caption>
<p>Comparison of LDAenDL with individual models under CV1.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center"/>
<th align="left"/>
<th align="center">DNN</th>
<th align="center">LightGBM</th>
<th align="center">LDAenDL</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td rowspan="2" align="left">Precision</td>
<td align="left">Dataset 1</td>
<td align="center">
<bold>0.8772 &#xb1; 0.0461</bold>
</td>
<td align="center">0.8569 &#xb1; 0.0511</td>
<td align="center">0.8764 &#xb1; 0.0493</td>
</tr>
<tr>
<td align="left">Dataset 2</td>
<td align="center">0.9149 &#xb1; 0.0375</td>
<td align="center">0.9386 &#xb1; 0.0278</td>
<td align="center">
<bold>0.9391 &#xb1; 0.0290</bold>
</td>
</tr>
<tr>
<td rowspan="2" align="left">Recall</td>
<td align="left">Dataset 1</td>
<td align="center">0.6851 &#xb1; 0.0694</td>
<td align="center">0.7106 &#xb1; 0.0714</td>
<td align="center">
<bold>0.7019 &#xb1; 0.0639</bold>
</td>
</tr>
<tr>
<td align="left">Dataset 2</td>
<td align="center">
<bold>0.8337 &#xb1; 0.0510</bold>
</td>
<td align="center">0.8278 &#xb1; 0.0533</td>
<td align="center">0.8304 &#xb1; 0.0523</td>
</tr>
<tr>
<td rowspan="2" align="left">Accuracy</td>
<td align="left">Dataset 1</td>
<td align="center">0.7930 &#xb1; 0.0317</td>
<td align="center">0.7939 &#xb1; 0.0340</td>
<td align="center">
<bold>0.7996 &#xb1; 0.0312</bold>
</td>
</tr>
<tr>
<td align="left">Dataset 2</td>
<td align="center">0.8772 &#xb1; 0.0288</td>
<td align="center">0.8865 &#xb1; 0.0295</td>
<td align="center">
<bold>0.8879 &#xb1; 0.0289</bold>
</td>
</tr>
<tr>
<td rowspan="2" align="left">F1-score</td>
<td align="left">Dataset 1</td>
<td align="center">0.7664 &#xb1; 0.0429</td>
<td align="center">0.7737 &#xb1; 0.0446</td>
<td align="center">
<bold>0.7768 &#xb1; 0.0399</bold>
</td>
</tr>
<tr>
<td align="left">Dataset 2</td>
<td align="center">0.8711 &#xb1; 0.0321</td>
<td align="center">0.8786 &#xb1; 0.0344</td>
<td align="center">
<bold>0.8804 &#xb1; 0.0334</bold>
</td>
</tr>
<tr>
<td rowspan="2" align="left">AUC</td>
<td align="left">Dataset 1</td>
<td align="center">
<bold>0.8712 &#xb1; 0.0373</bold>
</td>
<td align="center">0.8622 &#xb1; 0.0340</td>
<td align="center">0.8701 &#xb1; 0.0339</td>
</tr>
<tr>
<td align="left">Dataset 2</td>
<td align="center">0.9308 &#xb1; 0.0209</td>
<td align="center">
<bold>0.9497 &#xb1; 0.0227</bold>
</td>
<td align="center">0.9490 &#xb1; 0.0220</td>
</tr>
<tr>
<td rowspan="2" align="left">AUPR</td>
<td align="left">Dataset 1</td>
<td align="center">0.8842 &#xb1; 0.0327</td>
<td align="center">0.8822 &#xb1; 0.0284</td>
<td align="center">
<bold>0.8903 &#xb1; 0.0273</bold>
</td>
</tr>
<tr>
<td align="left">Dataset 2</td>
<td align="center">0.9449 &#xb1; 0.0190</td>
<td align="center">
<bold>0.9586 &#xb1; 0.0171</bold>
</td>
<td align="center">0.9582 &#xb1; 0.0167</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>The bold value denotes the best performance.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<table-wrap id="T5" position="float">
<label>TABLE 5</label>
<caption>
<p>Comparison of LDAenDL with individual models under CV2.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center"/>
<th align="left"/>
<th align="center">DNN</th>
<th align="center">LightGBM</th>
<th align="center">LDAenDL</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td rowspan="2" align="left">Precision</td>
<td align="left">Dataset 1</td>
<td align="center">0.9049 &#xb1; 0.0383</td>
<td align="center">0.8927 &#xb1; 0.0309</td>
<td align="center">
<bold>0.9135 &#xb1; 0.0317</bold>
</td>
</tr>
<tr>
<td align="left">Dataset 2</td>
<td align="center">0.9274 &#xb1; 0.0412</td>
<td align="center">0.9439 &#xb1; 0.0283</td>
<td align="center">
<bold>0.9528 &#xb1; 0.0225</bold>
</td>
</tr>
<tr>
<td rowspan="2" align="left">Recall</td>
<td align="left">Dataset 1</td>
<td align="center">0.6182 &#xb1; 0.1006</td>
<td align="center">
<bold>0.6873 &#xb1; 0.0734</bold>
</td>
<td align="center">0.6649 &#xb1; 0.0814</td>
</tr>
<tr>
<td align="left">Dataset 2</td>
<td align="center">0.3426 &#xb1; 0.1457</td>
<td align="center">
<bold>0.5370 &#xb1; 0.1739</bold>
</td>
<td align="center">0.4616 &#xb1; 0.1702</td>
</tr>
<tr>
<td rowspan="2" align="left">Accuracy</td>
<td align="left">Dataset 1</td>
<td align="center">0.7759 &#xb1; 0.0453</td>
<td align="center">
<bold>0.8017 &#xb1; 0.0336</bold>
</td>
<td align="center">0.8005 &#xb1; 0.0381</td>
</tr>
<tr>
<td align="left">Dataset 2</td>
<td align="center">0.6580 &#xb1; 0.0689</td>
<td align="center">
<bold>0.7533 &#xb1; 0.0842</bold>
</td>
<td align="center">0.7196 &#xb1; 0.0821</td>
</tr>
<tr>
<td rowspan="2" align="left">F1-score</td>
<td align="left">Dataset 1</td>
<td align="center">0.7289 &#xb1; 0.0794</td>
<td align="center">
<bold>0.7740 &#xb1; 0.0493</bold>
</td>
<td align="center">0.7664 &#xb1; 0.0593</td>
</tr>
<tr>
<td align="left">Dataset 2</td>
<td align="center">0.4835 &#xb1; 0.1531</td>
<td align="center">
<bold>0.6678 &#xb1; 0.1537</bold>
</td>
<td align="center">0.6032 &#xb1; 0.1612</td>
</tr>
<tr>
<td rowspan="2" align="left">AUC</td>
<td align="left">Dataset 1</td>
<td align="center">0.8853 &#xb1; 0.0374</td>
<td align="center">0.8869 &#xb1; 0.0281</td>
<td align="center">
<bold>0.8953 &#xb1; 0.0284</bold>
</td>
</tr>
<tr>
<td align="left">Dataset 2</td>
<td align="center">0.8412 &#xb1; 0.0512</td>
<td align="center">
<bold>0.9164 &#xb1; 0.0441</bold>
</td>
<td align="center">0.9157 &#xb1; 0.0420</td>
</tr>
<tr>
<td rowspan="2" align="left">AUPR</td>
<td align="left">Dataset 1</td>
<td align="center">0.8882 &#xb1; 0.0368</td>
<td align="center">0.8981 &#xb1; 0.0257</td>
<td align="center">
<bold>0.9061 &#xb1; 0.0254</bold>
</td>
</tr>
<tr>
<td align="left">Dataset 2</td>
<td align="center">0.8416 &#xb1; 0.0530</td>
<td align="center">
<bold>0.9150 &#xb1; 0.0466</bold>
</td>
<td align="center">0.9122 &#xb1; 0.0436</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>The bold value denotes the best performance.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<table-wrap id="T6" position="float">
<label>TABLE 6</label>
<caption>
<p>Comparison of LDAenDL with individual models under CV3.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center"/>
<th align="left"/>
<th align="center">DNN</th>
<th align="center">LightGBM</th>
<th align="center">LDAenDL</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td rowspan="2" align="left">Precision</td>
<td align="left">Dataset 1</td>
<td align="center">0.8561 &#xb1; 0.0357</td>
<td align="center">0.8477 &#xb1; 0.0320</td>
<td align="center">
<bold>0.8637 &#xb1; 0.0312</bold>
</td>
</tr>
<tr>
<td align="left">Dataset 2</td>
<td align="center">0.9214 &#xb1; 0.0171</td>
<td align="center">0.9322 &#xb1; 0.0157</td>
<td align="center">
<bold>0.9351 &#xb1; 0.0157</bold>
</td>
</tr>
<tr>
<td rowspan="2" align="left">Recall</td>
<td align="left">Dataset 1</td>
<td align="center">
<bold>0.8241 &#xb1; 0.0373</bold>
</td>
<td align="center">0.8110 &#xb1; 0.0381</td>
<td align="center">0.8234 &#xb1; 0.0314</td>
</tr>
<tr>
<td align="left">Dataset 2</td>
<td align="center">0.8983 &#xb1; 0.0204</td>
<td align="center">0.8936 &#xb1; 0.0176</td>
<td align="center">
<bold>0.8999 &#xb1; 0.0179</bold>
</td>
</tr>
<tr>
<td rowspan="2" align="left">Accuracy</td>
<td align="left">Dataset 1</td>
<td align="center">0.8419 &#xb1; 0.0244</td>
<td align="center">0.8322 &#xb1; 0.0265</td>
<td align="center">
<bold>0.8462 &#xb1; 0.0229</bold>
</td>
</tr>
<tr>
<td align="left">Dataset 2</td>
<td align="center">0.9106 &#xb1; 0.0130</td>
<td align="center">0.9142 &#xb1; 0.0122</td>
<td align="center">
<bold>0.9186 &#xb1; 0.0126</bold>
</td>
</tr>
<tr>
<td rowspan="2" align="left">F1-score</td>
<td align="left">Dataset 1</td>
<td align="center">0.8389 &#xb1; 0.0247</td>
<td align="center">0.8284 &#xb1; 0.0277</td>
<td align="center">
<bold>0.8426 &#xb1; 0.0232</bold>
</td>
</tr>
<tr>
<td align="left">Dataset 2</td>
<td align="center">0.9095 &#xb1; 0.0134</td>
<td align="center">0.9124 &#xb1; 0.0126</td>
<td align="center">
<bold>0.9171 &#xb1; 0.0130</bold>
</td>
</tr>
<tr>
<td rowspan="2" align="left">AUC</td>
<td align="left">Dataset 1</td>
<td align="center">0.9076 &#xb1; 0.0225</td>
<td align="center">0.9015 &#xb1; 0.0204</td>
<td align="center">
<bold>0.9110 &#xb1; 0.0197</bold>
</td>
</tr>
<tr>
<td align="left">Dataset 2</td>
<td align="center">0.9562 &#xb1; 0.0107</td>
<td align="center">0.9692 &#xb1; 0.0064</td>
<td align="center">
<bold>0.9708 &#xb1; 0.0062</bold>
</td>
</tr>
<tr>
<td rowspan="2" align="left">AUPR</td>
<td align="left">Dataset 1</td>
<td align="center">0.9067 &#xb1; 0.0244</td>
<td align="center">0.9082 &#xb1; 0.0215</td>
<td align="center">
<bold>0.9166 &#xb1; 0.0203</bold>
</td>
</tr>
<tr>
<td align="left">Dataset 2</td>
<td align="center">0.9611 &#xb1; 0.0102</td>
<td align="center">0.9728 &#xb1; 0.0061</td>
<td align="center">
<bold>0.9743 &#xb1; 0.0058</bold>
</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>The bold value denotes the best performance.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<p>Under CV1, LDAenDL randomly took 80% of lncRNAs as training samples, and the rest were taken as test samples to investigate the LDA prediction ability for new lncRNAs. The results from <xref ref-type="table" rid="T1">Table 1</xref> show that our proposed LDAenDL approach obtained the best precision, recall, accuracy, F1-score, AUC, and AUPR on two datasets under CV1 except that it computed slightly lower precision on Dataset 2 (0.9391 vs. 0.9399). It computed the highest AUPRs of 0.8903 and 0.9582, and far exceeded the AUPR values computed by SDLDA (i.e., 0.8461 and 0.9533).</p>
<p>
<xref ref-type="fig" rid="F2">Figure 2</xref> shows the AUC and AUPR values computed by LDAenDL and the other four methods on two datasets under CV1. The results demonstrated that LDAenDL can discover possible diseases associated with a new lncRNA.</p>
<fig id="F2" position="float">
<label>FIGURE 2</label>
<caption>
<p>The AUC and AUPR values of five LDA prediction methods under CV1.</p>
</caption>
<graphic xlink:href="fgene-14-1238095-g002.tif"/>
</fig>
<p>Under CV2, LDAenDL randomly took 80% of diseases as training samples, and the rest were taken as test samples to investigate the LDA prediction ability for new diseases. The results from <xref ref-type="table" rid="T2">Table 2</xref> show that our proposed LDAenDL approach obtained better precision, AUC, and AUPR on two datasets under CV2. However, SDLDA computed higher recall, accuracy, and F1-score than LDAenDL, which may be caused by smaller disease samples.</p>
<p>
<xref ref-type="fig" rid="F3">Figure 3</xref> shows the AUC and AUPR values computed by LDAenDL and the other four methods on two datasets under CV2. The results show that LDAenDL can be applied to screen possible lncRNAs associated with a new disease.</p>
<fig id="F3" position="float">
<label>FIGURE 3</label>
<caption>
<p>The AUC and AUPR values of five LDA prediction methods under CV2.</p>
</caption>
<graphic xlink:href="fgene-14-1238095-g003.tif"/>
</fig>
<p>Under CV3, LDAenDL randomly took 80% of lncRNA-disease pairs as training samples, and the rest were taken as test samples to investigate the LDA prediction ability. The results from <xref ref-type="table" rid="T3">Table 3</xref> show that our proposed LDAenDL approach obtained the best precision, recall, accuracy, F1-score, AUC, and AUPR on two datasets under CV3. It computed the highest AUCs of 0.9110 and 0.9708 and far exceeded those computed by SDLDA (i.e., 0.8774 and 0.9560). Furthermore, our LDAenDL approach computed the highest AUPRs of 0.9166 and 0.9743 and far exceeded those computed by SDLDA (i.e., 0.8952, and 0.9639).</p>
<p>
<xref ref-type="fig" rid="F4">Figure 4</xref> shows the AUC and AUPR values computed by LDAenDL and the other four methods on two datasets under CV3. The results demonstrated that LDAenDL could find potential LDAs based on known LDAs.</p>
<fig id="F4" position="float">
<label>FIGURE 4</label>
<caption>
<p>The AUC and AUPR values of five LDA prediction methods under CV3.</p>
</caption>
<graphic xlink:href="fgene-14-1238095-g004.tif"/>
</fig>
</sec>
<sec id="s3-3">
<title>3.3 Comparison of LDAenDL with individual models</title>
<p>To measure the effect of the ensemble algorithm on LDA prediction performance, we compared LDAenDL with two individual models, DNN, and LightGBM. <xref ref-type="table" rid="T4">Tables 4</xref>&#x2013;<xref ref-type="table" rid="T6">6</xref> show the precision, recall, accuracy, F1-score, AUC, and AUPR of the DNN, LightGBM, and LDAenDL under CV1, CV2, and CV3, respectively.</p>
<p>Under CV1, as shown in <xref ref-type="table" rid="T4">Table 4</xref>, LDAenDL outperformed the DNN and LightGBM on two LDA datasets for the majority of conditions. LDAenDL computed the best accuracy and F1-score on the two datasets. Although LDAenDL computed slightly lower AUC value than the DNN on dataset 1, and still slightly lower AUC than LightGBM on dataset 2, their differences were very small. For example, the DNN computed an AUC of 0.8712 while LDAenDL computed 0.8701 on dataset 1, and the DNN calculated an AUC of 0.9497 while LDAenDL calculated 0.9490 on dataset 2. LDAenDL obtained the best AUPR on dataset 1, and LightGBM obtained an AUPR of 0.9586 while LDAenDL obtained an AUPR of 0.9582.</p>
<p>Under CV2, as shown in <xref ref-type="table" rid="T5">Table 5</xref>, LDAenDL outperformed the DNN under all conditions on two LDA datasets. Recall, accuracy, and F1-score computed by LightGBM were slightly better than LDAenDL on the two datasets. But it calculated the best AUC and AUPR on dataset 1.</p>
<p>Under CV3, as shown in <xref ref-type="table" rid="T6">Table 6</xref>, LDAenDL computed the highest precision, recall, accuracy, F1-score, AUC, and AUPR on the two LDA datasets except that it computed a slightly lower recall on dataset 1. The results demonstrate that LDAenDL is appropriate to predict possible LDAs from unknown lncRNA-disease pairs.</p>
</sec>
<sec id="s3-4">
<title>3.4 Case study</title>
<sec id="s3-4-1">
<title>3.4.1 Identifying possible lncRNA biomarkers for lung cancer</title>
<p>Lung cancer is one of the most prevalent causes of mortality globally. It mainly contains small cell lung cancer and non-small cell lung cancer. Targeted drug therapy is its one therapeutic option (<xref ref-type="bibr" rid="B13">Lahiri et al., 2023</xref>). We used the proposed LDAenDL method to predict possible lncRNA biomarkers for lung cancer. <xref ref-type="table" rid="T7">Table 7</xref> shows the predicted top 20 lncRNA biomarkers for lung cancer. The 20 lncRNA biomarkers associated with lung cancer have no known association information with lung cancer in the two datasets.</p>
<table-wrap id="T7" position="float">
<label>TABLE 7</label>
<caption>
<p>The predicted top 20 lncRNA biomarkers for lung cancer in each of the two datasets.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th colspan="3" align="center">Dataset 1</th>
<th colspan="3" align="center">Dataset 2</th>
</tr>
<tr>
<th align="center">Rank</th>
<th align="center">lncRNA</th>
<th align="center">Evidence</th>
<th align="center">Rank</th>
<th align="center">lncRNA</th>
<th align="center">Evidence</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">1</td>
<td align="center">TUG1</td>
<td align="center">27485439, 31532756</td>
<td align="center">1</td>
<td align="center">TUG1</td>
<td align="center">27485439, 31532756</td>
</tr>
<tr>
<td align="center">2</td>
<td align="center">CRNDE</td>
<td align="center">28550688, 30982057</td>
<td align="center">2</td>
<td align="center">DLEU2</td>
<td align="center">31721438</td>
</tr>
<tr>
<td align="center">3</td>
<td align="center">DANCR</td>
<td align="center">30535487, 32196604</td>
<td align="center">3</td>
<td align="center">WT1-AS</td>
<td align="center">32349718</td>
</tr>
<tr>
<td align="center">4</td>
<td align="center">MIAT</td>
<td align="center">29795987</td>
<td align="center">4</td>
<td align="center">CRNDE</td>
<td align="center">28550688, 30982057</td>
</tr>
<tr>
<td align="center">5</td>
<td align="center">NPTN-IT1</td>
<td align="center">27896272, 29416684</td>
<td align="center">5</td>
<td align="center">DANCR</td>
<td align="center">30535487, 32196604</td>
</tr>
<tr>
<td align="center">6</td>
<td align="center">HNF1A-AS1</td>
<td align="center">25863539</td>
<td align="center">6</td>
<td align="center">SNHG11</td>
<td align="center">32239719</td>
</tr>
<tr>
<td align="center">7</td>
<td align="center">LINC00032</td>
<td align="center">Unconfirmed</td>
<td align="center">7</td>
<td align="center">IFNG-AS1</td>
<td align="center">Unconfirmed</td>
</tr>
<tr>
<td align="center">8</td>
<td align="center">WT1-AS</td>
<td align="center">32349718</td>
<td align="center">8</td>
<td align="center">HULC</td>
<td align="center">30575912</td>
</tr>
<tr>
<td align="center">9</td>
<td align="center">CBR3-AS1</td>
<td align="center">32945466</td>
<td align="center">9</td>
<td align="center">XIST</td>
<td align="center">29812958</td>
</tr>
<tr>
<td align="center">10</td>
<td align="center">HULC</td>
<td align="center">30575912</td>
<td align="center">10</td>
<td align="center">PCA3</td>
<td align="center">Unconfirmed</td>
</tr>
<tr>
<td align="center">11</td>
<td align="center">CCDC26</td>
<td align="center">Unconfirmed</td>
<td align="center">11</td>
<td align="center">SRA1</td>
<td align="center">Unconfirmed</td>
</tr>
<tr>
<td align="center">12</td>
<td align="center">SNHG3</td>
<td align="center">31602642</td>
<td align="center">12</td>
<td align="center">HAR1A</td>
<td align="center">Unconfirmed</td>
</tr>
<tr>
<td align="center">13</td>
<td align="center">PVT1</td>
<td align="center">27904703</td>
<td align="center">13</td>
<td align="center">DSCAM-AS1</td>
<td align="center">32280246</td>
</tr>
<tr>
<td align="center">14</td>
<td align="center">BCAR4</td>
<td align="center">28537678</td>
<td align="center">14</td>
<td align="center">NPTN-IT1</td>
<td align="center">27896272, 29416684</td>
</tr>
<tr>
<td align="center">15</td>
<td align="center">PTENP1</td>
<td align="center">32698750</td>
<td align="center">15</td>
<td align="center">TCL6</td>
<td align="center">Unconfirmed</td>
</tr>
<tr>
<td align="center">16</td>
<td align="center">RMST</td>
<td align="center">Unconfirmed</td>
<td align="center">16</td>
<td align="center">PTENP1</td>
<td align="center">32698750</td>
</tr>
<tr>
<td align="center">17</td>
<td align="center">LSINCT5</td>
<td align="center">20214974</td>
<td align="center">17</td>
<td align="center">PANDAR</td>
<td align="center">28121347</td>
</tr>
<tr>
<td align="center">18</td>
<td align="center">MIR155HG</td>
<td align="center">32432745</td>
<td align="center">18</td>
<td align="center">TDRG1</td>
<td align="center">31742752</td>
</tr>
<tr>
<td align="center">19</td>
<td align="center">BOK-AS1</td>
<td align="center">Unconfirmed</td>
<td align="center">19</td>
<td align="center">KCNQ1OT1</td>
<td align="center">31486494</td>
</tr>
<tr>
<td align="center">20</td>
<td align="center">KCNQ1OT1</td>
<td align="center">31486494</td>
<td align="center">20</td>
<td align="center">IGF2-AS</td>
<td align="center">28471495</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>In dataset 1, LDAenDL predicted that CCDC26 could be associated with lung cancer. CCDC26 can enhance thyroid cancer malignant progression (<xref ref-type="bibr" rid="B24">Ma et al., 2021</xref>). It promotes imatinib resistance in human gastrointestinal stromal tumors (<xref ref-type="bibr" rid="B50">Yan et al., 2019</xref>). Its inhibition could increase the sensitivity of doxorubicin in MDR-CML cells (<xref ref-type="bibr" rid="B20">Liu et al., 2021b</xref>). In this study, we predicted that CCDC26 could be associated with lung cancer in dataset 1.</p>
<p>In dataset 2, LDAenDL predicted that IFNG-AS1 could be associated with lung cancer. IFNG-AS1 has been reported in long-lasting memory T cells (<xref ref-type="bibr" rid="B3">Castellucci et al., 2021</xref>). It can boost interferon gamma generation in human natural killer cells (<xref ref-type="bibr" rid="B37">Stein et al., 2019</xref>). We identified that IFNG-AS1 could be associated with lung cancer in Dataset 2.</p>
<p>
<xref ref-type="fig" rid="F5">Figure 5</xref> shows the top 20 predicted lncRNAs associated with lung cancer in each of the two datasets. Yellow solid lines and blue solid lines denote lncRNA-lung cancer associations confirmed by the literatures among the predicted top 20 associations on datasets 1 and 2, respectively. Grey solid lines denote the predicted and co-occurring lncRNA-lung cancer associations that can be confirmed by the literatures in the two datasets, and grey dashed lines denote the predicted and unconfirmed lncRNA-lung cancer associations in the two datasets. The repeated lncRNAs in the two datasets have been removed.</p>
<fig id="F5" position="float">
<label>FIGURE 5</label>
<caption>
<p>The top 20 predicted lncRNA biomarkers for lung cancer in each of the two datasets (The repeated lncRNAs in the two datasets have been removed). This figure was drawn using Cytoscape (<xref ref-type="bibr" rid="B35">Shannon et al., 2003</xref>).</p>
</caption>
<graphic xlink:href="fgene-14-1238095-g005.tif"/>
</fig>
</sec>
<sec id="s3-4-2">
<title>3.4.2 Identifying possible lncRNAs associated with PDL1 for lung cancer</title>
<p>Recent advances in lung cancer treatment have demonstrated significant responses in patients when they were treated with programmed death-1/programmed death-ligand 1 (PD-1/PD-L1) checkpoint blockade immunotherapies (<xref ref-type="bibr" rid="B13">Lahiri et al., 2023</xref>). To find possible lncRNAs associated with PDL1 for lung cancer, inspired by LPI-DLDN proposed by <xref ref-type="bibr" rid="B28">Peng et al. (2022a)</xref>, we first downloaded the sequence of PDL1 from the UniProt database. Next, we extracted the biological features of PDL1 and depicted PDL1 as a 10,029-dimensional vector using BioTriangle. Finally, we used cosine similarity to compute the similarities between PDL1 and the other proteins in a lncRNA-protein interaction dataset (<xref ref-type="bibr" rid="B15">Li et al., 2015</xref>) and found the top 3 proteins with the highest interaction probabilities with PDL1. The results show that SNHG3 has a higher interaction probability with PDL1 and has been reported to be associated with lung cancer.</p>
</sec>
<sec id="s3-4-3">
<title>3.4.3 Identifying possible lncRNA biomarkers for neuroblastoma</title>
<p>Neuroblastoma is the most frequent pediatric solid tumor and accounts for approximately 15% of childhood cancer-related mortality (<xref ref-type="bibr" rid="B54">Zafar et al., 2021</xref>). We used the proposed LDAenDL method to identify possible lncRNA biomarkers for neuroblastoma. <xref ref-type="table" rid="T8">Table 8</xref> shows the top 20 predicted lncRNA biomarkers for neuroblastoma in each of the two datasets. The repeated lncRNAs in the two datasets have been removed.</p>
<table-wrap id="T8" position="float">
<label>TABLE 8</label>
<caption>
<p>The top 20 predicted lncRNA biomarkers for neuroblastoma in each of the two datasets.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th colspan="3" align="center">Dataset 1</th>
<th colspan="3" align="center">Dataset 2</th>
</tr>
<tr>
<th align="center">Rank</th>
<th align="center">lncRNA</th>
<th align="center">Evidence</th>
<th align="center">Rank</th>
<th align="center">lncRNA</th>
<th align="center">Evidence</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">1</td>
<td align="center">HOTAIR</td>
<td align="center">Unconfirmed</td>
<td align="center">1</td>
<td align="center">BDNF-AS</td>
<td align="center">Unconfirmed</td>
</tr>
<tr>
<td align="center">2</td>
<td align="center">HNF1A-AS1</td>
<td align="center">Unconfirmed</td>
<td align="center">2</td>
<td align="center">SNHG4</td>
<td align="center">32614236</td>
</tr>
<tr>
<td align="center">3</td>
<td align="center">CDKN2B-AS1</td>
<td align="center">Unconfirmed</td>
<td align="center">3</td>
<td align="center">BANCR</td>
<td align="center">Unconfirmed</td>
</tr>
<tr>
<td align="center">4</td>
<td align="center">GAS5</td>
<td align="center">28035057</td>
<td align="center">4</td>
<td align="center">HAR1A</td>
<td align="center">Unconfirmed</td>
</tr>
<tr>
<td align="center">5</td>
<td align="center">CCAT1</td>
<td align="center">Unconfirmed</td>
<td align="center">5</td>
<td align="center">HCP5</td>
<td align="center">33189302</td>
</tr>
<tr>
<td align="center">6</td>
<td align="center">TUG1</td>
<td align="center">Unconfirmed</td>
<td align="center">6</td>
<td align="center">TUG1</td>
<td align="center">Unconfirmed</td>
</tr>
<tr>
<td align="center">7</td>
<td align="center">UCA1</td>
<td align="center">Unconfirmed</td>
<td align="center">7</td>
<td align="center">HOTAIR</td>
<td align="center">Unconfirmed</td>
</tr>
<tr>
<td align="center">8</td>
<td align="center">CRNDE</td>
<td align="center">Unconfirmed</td>
<td align="center">8</td>
<td align="center">SRA1</td>
<td align="center">Unconfirmed</td>
</tr>
<tr>
<td align="center">9</td>
<td align="center">WT1-AS</td>
<td align="center">Unconfirmed</td>
<td align="center">9</td>
<td align="center">TERC</td>
<td align="center">Unconfirmed</td>
</tr>
<tr>
<td align="center">10</td>
<td align="center">BANCR</td>
<td align="center">Unconfirmed</td>
<td align="center">10</td>
<td align="center">SPRY4-IT1</td>
<td align="center">Unconfirmed</td>
</tr>
<tr>
<td align="center">11</td>
<td align="center">WRAP53</td>
<td align="center">Unconfirmed</td>
<td align="center">11</td>
<td align="center">KCNQ1OT1</td>
<td align="center">31433907</td>
</tr>
<tr>
<td align="center">12</td>
<td align="center">SPRY4-IT1</td>
<td align="center">Unconfirmed</td>
<td align="center">12</td>
<td align="center">IGF2-AS</td>
<td align="center">30914706</td>
</tr>
<tr>
<td align="center">13</td>
<td align="center">CCAT2</td>
<td align="center">33475889</td>
<td align="center">13</td>
<td align="center">PTENP1</td>
<td align="center">Unconfirmed</td>
</tr>
<tr>
<td align="center">14</td>
<td align="center">CCDC26</td>
<td align="center">Unconfirmed</td>
<td align="center">14</td>
<td align="center">CCAT1</td>
<td align="center">Unconfirmed</td>
</tr>
<tr>
<td align="center">15</td>
<td align="center">PVT1</td>
<td align="center">Unconfirmed</td>
<td align="center">15</td>
<td align="center">PCAT1</td>
<td align="center">Unconfirmed</td>
</tr>
<tr>
<td align="center">16</td>
<td align="center">HULC</td>
<td align="center">Unconfirmed</td>
<td align="center">16</td>
<td align="center">NPTN-IT1</td>
<td align="center">Unconfirmed</td>
</tr>
<tr>
<td align="center">17</td>
<td align="center">CASC2</td>
<td align="center">Unconfirmed</td>
<td align="center">17</td>
<td align="center">DGCR5</td>
<td align="center">Unconfirmed</td>
</tr>
<tr>
<td align="center">18</td>
<td align="center">DANCR</td>
<td align="center">34050113</td>
<td align="center">18</td>
<td align="center">HULC</td>
<td align="center">Unconfirmed</td>
</tr>
<tr>
<td align="center">19</td>
<td align="center">KCNQ1OT1</td>
<td align="center">31433907</td>
<td align="center">19</td>
<td align="center">BOK-AS1</td>
<td align="center">Unconfirmed</td>
</tr>
<tr>
<td align="center">20</td>
<td align="center">7SK</td>
<td align="center">Unconfirmed</td>
<td align="center">20</td>
<td align="center">BCYRN1</td>
<td align="center">Unconfirmed</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>In dataset 1, we predicted that HOTAIR could be associated with neuroblastoma with the highest probability. HOTAIR is a novel oncogenic biomarker in human cancer (<xref ref-type="bibr" rid="B34">Rajagopal et al., 2020</xref>). Its knockdown can promote radiosensitivity in colorectal cancer (<xref ref-type="bibr" rid="B18">Liu et al., 2020</xref>). It also can enhance the carcinogenesis of gastric (<xref ref-type="bibr" rid="B56">Zhang et al., 2020</xref>). We identified that HOTAIR may be one biomarker of neuroblastoma in dataset 1.</p>
<p>In dataset 2, we predicted that BDNF-AS could be associated with neuroblastoma with the highest probability. PABPC1-induced stabilization of BDNF-AS helps the inhibition of malignant progression in glioblastoma cells (<xref ref-type="bibr" rid="B38">Su et al., 2020</xref>). It can regulate the miR-9-5p/BACE1 pathway that affects neurotoxicity in Alzheimer&#x2019;s disease (<xref ref-type="bibr" rid="B7">Ding et al., 2022</xref>). We identified that BDNF-AS is a possible biomarker of neuroblastoma in dataset 2.</p>
<p>
<xref ref-type="fig" rid="F6">Figure 6</xref> shows the top 20 predicted lncRNAs associated with neuroblastoma in each of the two datasets. Yellow solid lines and blue solid lines denote lncRNA-neuroblastoma associations confirmed by the literatures among the predicted top 20 associations on datasets 1 and 2, respectively. Grey solid lines denote the predicted and co-occurring lncRNA-neuroblastoma associations that can be confirmed by the literatures in the two datasets, and grey dashed lines denote the predicted and unconfirmed lncRNA-neuroblastoma associations in the two datasets. The repeated lncRNAs in the two datasets have been removed.</p>
<fig id="F6" position="float">
<label>FIGURE 6</label>
<caption>
<p>The top 20 predicted lncRNA biomarkers for neuroblastoma in each of the two datasets. (The repeated lncRNAs in the two datasets have been removed). This figure was drawn using Cytoscape (<xref ref-type="bibr" rid="B35">Shannon et al., 2003</xref>).</p>
</caption>
<graphic xlink:href="fgene-14-1238095-g006.tif"/>
</fig>
</sec>
</sec>
</sec>
<sec sec-type="conclusion" id="s4">
<title>4 Conclusion</title>
<p>Lung cancer and neuroblastoma are two human diseases that severely affect the human body. Detecting new biomarkers for them contributes to their diagnosis and therapy. Experimental biomarker identification methods are costly and laborious. Thus, we developed a machine learning-based method named LDAenDL to predict possible lncRNA biomarkers for the two diseases based on an ensemble of a deep neural network and LightGBM. LDAenDL first computed lncRNA similarity and disease similarity and then combined a GCN, GAT, and CNN to learn the biological features of lncRNAs and diseases. Finally, these features were fed to a DNN and LightGBM to find new LDAs.</p>
<p>LDAenDL was compared with the other four classical LDA prediction methods (i.e., SDLDA, LDNFSGB, IPCAF, and LDASR). The results showed that LDAenDL computed the best AUCs and AUPRs under three cross-validations on two LDA datasets, demonstrating the optimal LDA prediction performance of LDAenDL. We further identified possible lncRNA biomarkers for lung cancer and neuroblastoma. The results demonstrated that CCDC26 and IFNG-AS1 may be new biomarkers for lung cancer, SNHG3 may be associated with PDL1 for lung cancer, and HOTAIR and BDNF-AS may be potential biomarkers for neuroblastoma.</p>
<p>In the future, we will combine data from multiple sources, for example, miRNA, circRNA, and drugs, to improve LDA identification performance. We will also design a new deep-learning model to efficiently extract the biological features of lncRNAs and diseases for LDA prediction. We hope that the proposed LDAenDL can help the development of targeted therapies for these two diseases.</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 authors.</p>
</sec>
<sec id="s6">
<title>Author contributions</title>
<p>Conceptualization: ZS, HL, ZL, and LD; Investigation: ZS and HL; Methodology: ZS, HL, ZL, and LD; Project administration: YW and LD; Software: ZS and ZL; Writing-original draft: ZS and HL; Writing-review and editing: ZS, HL, ZL, and LD. All authors contributed to the article and approved the submitted version.</p>
</sec>
<sec sec-type="COI-statement" id="s7">
<title>Conflict of interest</title>
<p>Author YW was employed by Geneis (Beijing) Co., Ltd.</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="s8">
<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>
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