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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Microbiol.</journal-id>
<journal-title>Frontiers in Microbiology</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Microbiol.</abbrev-journal-title>
<issn pub-type="epub">1664-302X</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="doi">10.3389/fmicb.2023.1244527</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Microbiology</subject>
<subj-group>
<subject>Original Research</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>Predicting potential microbe-disease associations with graph attention autoencoder, positive-unlabeled learning, and deep neural network</article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author" equal-contrib="yes">
<name><surname>Peng</surname> <given-names>Lihong</given-names></name>
<xref ref-type="aff" rid="aff1"><sup>1</sup></xref>
<xref ref-type="aff" rid="aff2"><sup>2</sup></xref>
<xref ref-type="author-notes" rid="fn002"><sup>&#x02020;</sup></xref>
<uri xlink:href="http://loop.frontiersin.org/people/601035/overview"/>
</contrib>
<contrib contrib-type="author" equal-contrib="yes">
<name><surname>Huang</surname> <given-names>Liangliang</given-names></name>
<xref ref-type="aff" rid="aff1"><sup>1</sup></xref>
<xref ref-type="author-notes" rid="fn002"><sup>&#x02020;</sup></xref>
<uri xlink:href="http://loop.frontiersin.org/people/2390508/overview"/>
</contrib>
<contrib contrib-type="author">
<name><surname>Tian</surname> <given-names>Geng</given-names></name>
<xref ref-type="aff" rid="aff3"><sup>3</sup></xref>
<uri xlink:href="http://loop.frontiersin.org/people/875841/overview"/>
</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="http://loop.frontiersin.org/people/1541475/overview"/>
</contrib>
<contrib contrib-type="author">
<name><surname>Li</surname> <given-names>Guang</given-names></name>
<xref ref-type="aff" rid="aff4"><sup>4</sup></xref>
<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>
</contrib>
<contrib contrib-type="author">
<name><surname>Cao</surname> <given-names>Jianying</given-names></name>
<xref ref-type="aff" rid="aff4"><sup>4</sup></xref>
<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>
</contrib>
<contrib contrib-type="author">
<name><surname>Wang</surname> <given-names>Peng</given-names></name>
<xref ref-type="aff" rid="aff8"><sup>8</sup></xref>
</contrib>
<contrib contrib-type="author" corresp="yes">
<name><surname>Li</surname> <given-names>Zejun</given-names></name>
<xref ref-type="aff" rid="aff8"><sup>8</sup></xref>
<xref ref-type="corresp" rid="c001"><sup>&#x0002A;</sup></xref>
<uri xlink:href="http://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="aff4"><sup>4</sup></xref>
<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="corresp" rid="c002"><sup>&#x0002A;</sup></xref>
<uri xlink:href="http://loop.frontiersin.org/people/2343727/overview"/>
</contrib>
</contrib-group>
<aff id="aff1"><sup>1</sup><institution>School of Computer Science, Hunan University of Technology</institution>, <addr-line>Zhuzhou</addr-line>, <country>China</country></aff>
<aff id="aff2"><sup>2</sup><institution>College of Life Sciences and Chemistry, Hunan University of Technology</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>Faculty of Pediatrics, The Chinese PLA General Hospital</institution>, <addr-line>Beijing</addr-line>, <country>China</country></aff>
<aff id="aff5"><sup>5</sup><institution>Department of Pediatric Surgery, The Seventh Medical Center of PLA General Hospital</institution>, <addr-line>Beijing</addr-line>, <country>China</country></aff>
<aff id="aff6"><sup>6</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="aff7"><sup>7</sup><institution>Beijing Key Laboratory of Pediatric Organ Failure</institution>, <addr-line>Beijing</addr-line>, <country>China</country></aff>
<aff id="aff8"><sup>8</sup><institution>School of Computer Science, Hunan Institute of Technology</institution>, <addr-line>Hengyang</addr-line>, <country>China</country></aff>
<author-notes>
<fn fn-type="edited-by"><p>Edited by: Qi Zhao, University of Science and Technology Liaoning, China</p></fn>
<fn fn-type="edited-by"><p>Reviewed by: XianFang Tang, Wuhan Textile University, China; Chunchun Wang, Jiangnan University, China</p></fn>
<corresp id="c001">&#x0002A;Correspondence: Zejun Li <email>lzjfox&#x00040;hnit.edu.cn</email></corresp>
<corresp id="c002">Lian Duan <email>duanlian301&#x00040;163.com</email></corresp>
<fn fn-type="equal" id="fn002"><p>&#x02020;These authors have contributed equally to this work and share first authorship</p></fn></author-notes>
<pub-date pub-type="epub">
<day>18</day>
<month>09</month>
<year>2023</year>
</pub-date>
<pub-date pub-type="collection">
<year>2023</year>
</pub-date>
<volume>14</volume>
<elocation-id>1244527</elocation-id>
<history>
<date date-type="received">
<day>22</day>
<month>06</month>
<year>2023</year>
</date>
<date date-type="accepted">
<day>16</day>
<month>08</month>
<year>2023</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#x000A9; 2023 Peng, Huang, Tian, Wu, Li, Cao, Wang, Li and Duan.</copyright-statement>
<copyright-year>2023</copyright-year>
<copyright-holder>Peng, Huang, Tian, Wu, Li, Cao, Wang, 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>
<sec>
<title>Background</title>
<p>Microbes have dense linkages with human diseases. Balanced microorganisms protect human body against physiological disorders while unbalanced ones may cause diseases. Thus, identification of potential associations between microbes and diseases can contribute to the diagnosis and therapy of various complex diseases. Biological experiments for microbe&#x02013;disease association (MDA) prediction are expensive, time-consuming, and labor-intensive.</p></sec>
<sec>
<title>Methods</title>
<p>We developed a computational MDA prediction method called GPUDMDA by combining graph attention autoencoder, positive-unlabeled learning, and deep neural network. First, GPUDMDA computes disease similarity and microbe similarity matrices by integrating their functional similarity and Gaussian association profile kernel similarity, respectively. Next, it learns the feature representation of each microbe&#x02013;disease pair using graph attention autoencoder based on the obtained disease similarity and microbe similarity matrices. Third, it selects a few reliable negative MDAs based on positive-unlabeled learning. Finally, it takes the learned MDA features and the selected negative MDAs as inputs and designed a deep neural network to predict potential MDAs.</p></sec>
<sec>
<title>Results</title>
<p>GPUDMDA was compared with four state-of-the-art MDA identification models (i.e., MNNMDA, GATMDA, LRLSHMDA, and NTSHMDA) on the HMDAD and Disbiome databases under five-fold cross validations on microbes, diseases, and microbe-disease pairs. Under the three five-fold cross validations, GPUDMDA computed the best AUCs of 0.7121, 0.9454, and 0.9501 on the HMDAD database and 0.8372, 0.8908, and 0.8948 on the Disbiome database, respectively, outperforming the other four MDA prediction methods. Asthma is the most common chronic respiratory condition and affects &#x0007E;339 million people worldwide. Inflammatory bowel disease is a class of globally chronic intestinal disease widely existed in the gut and gastrointestinal tract and extraintestinal organs of patients. Particularly, inflammatory bowel disease severely affects the growth and development of children. We used the proposed GPUDMDA method and found that <italic>Enterobacter hormaechei</italic> had potential associations with both asthma and inflammatory bowel disease and need further biological experimental validation.</p></sec>
<sec>
<title>Conclusion</title>
<p>The proposed GPUDMDA demonstrated the powerful MDA prediction ability. We anticipate that GPUDMDA helps screen the therapeutic clues for microbe-related diseases.</p></sec></abstract>
<kwd-group>
<kwd>microbe-disease associations</kwd>
<kwd>graph attention autoencoder</kwd>
<kwd>positive-unlabeled learning</kwd>
<kwd><italic>K</italic>-means</kwd>
<kwd>XGBoost</kwd>
<kwd>deep neural network</kwd>
</kwd-group>
<contract-num rid="cn001">61803151</contract-num>
<contract-num rid="cn001">62172158</contract-num>
<contract-num rid="cn001">81500391</contract-num>
<contract-num rid="cn002">2023JJ50201</contract-num>
<contract-sponsor id="cn001">National Natural Science Foundation of China<named-content content-type="fundref-id">10.13039/501100001809</named-content></contract-sponsor>
<contract-sponsor id="cn002">Natural Science Foundation of Hunan Province<named-content content-type="fundref-id">10.13039/501100004735</named-content></contract-sponsor>
<counts>
<fig-count count="7"/>
<table-count count="4"/>
<equation-count count="15"/>
<ref-count count="66"/>
<page-count count="15"/>
<word-count count="7651"/>
</counts>
<custom-meta-wrap>
<custom-meta>
<meta-name>section-at-acceptance</meta-name>
<meta-value>Systems Microbiology</meta-value>
</custom-meta>
</custom-meta-wrap>
</article-meta>
</front>
<body>
<sec sec-type="intro" id="s1">
<title>1. Introduction</title>
<p>Microorganisms or microbes exist in the form of single cell or a group of cells. Microbes mainly contain bacteria, archaea, fungi, viruses, and protozoa (Wen et al., <xref ref-type="bibr" rid="B59">2021</xref>). They widely distribute on the human skin, oral cavity, respiratory tract, and gastrointestinal tract (Holmes et al., <xref ref-type="bibr" rid="B16">2015</xref>). Most of human microbes are beneficial to human health. They can promote nutrient absorption, protect human body against pathogens, and strengthen metabolic capability. In addition, they have the similar metabolic ability to the liver and are even taken as &#x0201C;forgotten organ&#x0201D; of human body (Gill et al., <xref ref-type="bibr" rid="B12">2006</xref>). However, their imbalance or dysbiosis could cause human diseases (Peng et al., <xref ref-type="bibr" rid="B41">2022c</xref>; Tian et al., <xref ref-type="bibr" rid="B51">2022</xref>), such as inflammatory bowel disease (IBD) (El Mouzan et al., <xref ref-type="bibr" rid="B10">2018</xref>), diabetes (Wen et al., <xref ref-type="bibr" rid="B58">2008</xref>), asthma (Demirci et al., <xref ref-type="bibr" rid="B8">2019</xref>), liver diseases (Henao-Mejia et al., <xref ref-type="bibr" rid="B15">2013</xref>), and cancer (Schwabe and Jobin, <xref ref-type="bibr" rid="B49">2013</xref>). Although many evidence demonstrated that microbes have close relationships with human diseases, a comprehensive understanding about how microbes influence human healths and produce diseases remains unknown.</p>
<p>Microbe&#x02013;disease association (MDA) identification not only help us to capture the mechanisms of complex diseases but also provide multiple possible biomarkers for their diagnosis and therapy. However, traditional wet lab remains costly, laborious, and time-consuming (Chen et al., <xref ref-type="bibr" rid="B7">2019</xref>, <xref ref-type="bibr" rid="B6">2020</xref>; Shen et al., <xref ref-type="bibr" rid="B50">2022</xref>; Chen and Huang, <xref ref-type="bibr" rid="B4">2023</xref>). With the advance of single cell sequencing (Peng et al., <xref ref-type="bibr" rid="B42">2022d</xref>, <xref ref-type="bibr" rid="B40">2023a</xref>,<xref ref-type="bibr" rid="B43">b</xref>; Wu et al., <xref ref-type="bibr" rid="B60">2022</xref>; Hu et al., <xref ref-type="bibr" rid="B17">2023a</xref>,<xref ref-type="bibr" rid="B18">b</xref>; Xu et al., <xref ref-type="bibr" rid="B61">2023</xref>) and wide application of artificial intelligence (Chen et al., <xref ref-type="bibr" rid="B5">2021</xref>; Lihong et al., <xref ref-type="bibr" rid="B27">2022</xref>; Peng et al., <xref ref-type="bibr" rid="B38">2022a</xref>; Wang et al., <xref ref-type="bibr" rid="B57">2022</xref>, <xref ref-type="bibr" rid="B56">2023</xref>; Zhang et al., <xref ref-type="bibr" rid="B64">2022a</xref>,<xref ref-type="bibr" rid="B65">b</xref>; Zhang and Wu, <xref ref-type="bibr" rid="B66">2023</xref>), many computational methods have been developed to discover potential MDAs. These methods mainly contain network-based algorithms and machine learning-based algorithms.</p>
<p>Network-based algorithms take MDA prediction as a random walk or label propagation problem. For example, to decode underlying MDAs, BRWMDA fused similarity networks and bi-random walk (Yan et al., <xref ref-type="bibr" rid="B62">2019</xref>), NBLPIHMDA developed a bidirectional label propagation algorithm (Wang et al., <xref ref-type="bibr" rid="B54">2019</xref>), MHEN constructed a multiplex heterogeneous network (Ma and Jiang, <xref ref-type="bibr" rid="B35">2020</xref>), WMGHMDA implemented iteratively weighted meta-graph search model (Long and Luo, <xref ref-type="bibr" rid="B31">2019</xref>), RWHMDA was a hypergraph-based random walk method (Niu et al., <xref ref-type="bibr" rid="B36">2019</xref>), BDHNS formulated a bi-directional heterogeneous MDA network (Guan et al., <xref ref-type="bibr" rid="B14">2022</xref>), and MNNMDA used low-rank matrix completion (Liu et al., <xref ref-type="bibr" rid="B29">2023</xref>).</p>
<p>Machine learning-based algorithms take MDA prediction as a classification problem. For example, to discover potential MDAs, BPNNHMDA (Li et al., <xref ref-type="bibr" rid="B26">2020</xref>) adopted a neural network structure, GATMDA (Long et al., <xref ref-type="bibr" rid="B32">2021</xref>) exploited a graph attention network with inductive matrix completion, DMFMDA (Liu et al., <xref ref-type="bibr" rid="B30">2020</xref>) utilized a deep neural network-based deep matrix factorization model, NinimHMDA (Ma and Jiang, <xref ref-type="bibr" rid="B35">2020</xref>) explored an end-to-end graph convolutional neural network structure, KGNMDA (Jiang et al., <xref ref-type="bibr" rid="B21">2022</xref>) used a graph neural network model, MGATMDA (Liu et al., <xref ref-type="bibr" rid="B28">2021</xref>) comprised decomposer, combiner, and predictor where the decomposer captured the latent components using node-level attention mechanism, the combiner obtained unified embedding using component-level attention mechanism, and unknown microbe&#x02013;disease pairs were classified by a fully connected network. HNGFL (Wang et al., <xref ref-type="bibr" rid="B57">2022</xref>) designed an embedding algorithm for feature learning and used support vector machine for MDA classification.</p>
<p>Although computational methods significantly improved MDA prediction and uncovered many potential MDAs, there are some limitations presented in this study. For example, network-based MDA inference methods cannot find associated entities for a new microbe or disease. Machine learning-based inference methods need reliable negative MDAs for implementing the MDA classification task. Here, we developed an MDA prediction method called GPUDMDA by combining feature extraction based on graph attention autoencoder (GATE), reliable negative MDA selection based on positive-unlabeled (PU) learning, and MDA classification based on deep neural network (DNN).</p></sec>
<sec sec-type="materials and methods" id="s2">
<title>2. Materials and methods</title>
<sec>
<title>2.1. Data preparation</title>
<p>We used two MDA databases to implement MDA prediction. One database is from the Human microbe&#x02013;disease Association Database (HMDAD; <ext-link ext-link-type="uri" xlink:href="http://www.cuilab.cn/hmdad">http://www.cuilab.cn/hmdad</ext-link>) and contain 450 MDAs between 292 microbes and 39 diseases (Ma et al., <xref ref-type="bibr" rid="B34">2017</xref>). The other comes from Disbiome (<ext-link ext-link-type="uri" xlink:href="https://disbiome.ugent.be/home">https://disbiome.ugent.be/home</ext-link>) (Janssens et al., <xref ref-type="bibr" rid="B20">2018</xref>) and contains 4,351 MDAs between 218 diseases and 1,052 microbes. Moreover, an MDA network <italic>Y</italic>&#x02208;&#x0211C;<sup><italic>n</italic>&#x000D7;<italic>m</italic></sup> is constructed by Eq. (1) as follows:</p>
<disp-formula id="E1"><label>(1)</label><mml:math id="M1"><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mtable><mml:mtr><mml:mtd><mml:mrow><mml:mn>1</mml:mn><mml:mo>,</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mtext>&#x000A0;if&#x000A0;&#x000A0;microbe&#x000A0;</mml:mtext><mml:msub><mml:mi>m</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mtext>&#x000A0;associates&#x000A0;with&#x000A0;disease&#x000A0;</mml:mtext><mml:msub><mml:mi>d</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mtext>&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;otherwise&#x000A0;</mml:mtext></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:mrow></mml:mrow></mml:math></disp-formula>
</sec>
<sec>
<title>2.2. Pipeline for MDA prediction</title>
<p>In this manuscript, we developed an MDA prediction method called GPUDMDA by combining graph attention autoencoder, positive-unlabeled learning, and deep neural network. First, GPUDMDA computes disease similarity and microbe similarity matrices by integrating their functional similarity and Gaussian association profile kernel (GAPK) similarity, respectively. Next, it learns features of each microbe&#x02013;disease pair using GATE. Third, it selects several reliable negative MDAs based on PU learning. Finally, it takes the extracted MDA features and the selected negative MDAs as inputs and proposes a DNN for discovering potential MDAs. <xref ref-type="fig" rid="F1">Figure 1</xref> shows the pipeline of GPUDMDA.</p>
<fig id="F1" position="float">
<label>Figure 1</label>
<caption><p>The pipeline of the MDA framework GPUDMDA.</p></caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmicb-14-1244527-g0001.tif"/>
</fig></sec>
<sec>
<title>2.3. Similarity computation</title>
<sec>
<title>2.3.1. Functional similarity of microbes</title>
<p>In the GATMDA, Long et al. (<xref ref-type="bibr" rid="B32">2021</xref>) computed microbe functional similarity according to their co-occurrences (Kamneva, <xref ref-type="bibr" rid="B22">2017</xref>). Similarly, we use the microbe function similarity method in GATMDA and then compute a functional similarity matrix <inline-formula><mml:math id="M2"><mml:msubsup><mml:mrow><mml:mi>S</mml:mi></mml:mrow><mml:mrow><mml:mi>m</mml:mi></mml:mrow><mml:mrow><mml:mi>f</mml:mi><mml:mi>u</mml:mi><mml:mi>n</mml:mi></mml:mrow></mml:msubsup></mml:math></inline-formula> between <italic>m</italic> microbes, where <inline-formula><mml:math id="M3"><mml:msubsup><mml:mrow><mml:mi>S</mml:mi></mml:mrow><mml:mrow><mml:mi>m</mml:mi></mml:mrow><mml:mrow><mml:mi>f</mml:mi><mml:mi>u</mml:mi><mml:mi>n</mml:mi></mml:mrow></mml:msubsup><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>m</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>m</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math></inline-formula> denotes the similarity between two microbes <italic>m</italic><sub><italic>i</italic></sub> and <italic>m</italic><sub><italic>j</italic></sub>.</p></sec>
<sec>
<title>2.3.2. Functional similarity of diseases</title>
<p>We use the disease functional similarity assessment method proposed by Long et al. (<xref ref-type="bibr" rid="B32">2021</xref>) and compute functional similarity matrix <inline-formula><mml:math id="M4"><mml:msubsup><mml:mrow><mml:mi>S</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow><mml:mrow><mml:mi>f</mml:mi><mml:mi>u</mml:mi><mml:mi>n</mml:mi></mml:mrow></mml:msubsup></mml:math></inline-formula> between <italic>n</italic> diseases, where <inline-formula><mml:math id="M5"><mml:msubsup><mml:mrow><mml:mi>S</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow><mml:mrow><mml:mi>f</mml:mi><mml:mi>u</mml:mi><mml:mi>n</mml:mi></mml:mrow></mml:msubsup><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>d</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>d</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math></inline-formula> denotes the similarity between two diseases <italic>d</italic><sub><italic>i</italic></sub> and <italic>d</italic><sub><italic>j</italic></sub>.</p></sec>
<sec>
<title>2.3.3. Gaussian association profile kernel similarity</title>
<p>GAPK function is a symmetric function along the radial direction. It can better cluster similar examples with linearly separable form (Wang et al., <xref ref-type="bibr" rid="B55">2020</xref>). Let <italic>V</italic><sub><italic>d</italic><sub><italic>i</italic></sub></sub> (the <italic>i</italic>th row of <italic>Y</italic>) and <italic>V</italic><sub><italic>d</italic><sub><italic>j</italic></sub></sub> (the <italic>j</italic>th row of <italic>Y</italic>) denote two diseases <italic>d</italic><sub><italic>i</italic></sub> and <italic>d</italic><sub><italic>j</italic></sub>, respectively, their similarity can be computed by Eq. (2) as follows:</p>
<disp-formula id="E2"><label>(2)</label><mml:math id="M6"><mml:mrow><mml:msub><mml:mi>G</mml:mi><mml:mi>d</mml:mi></mml:msub><mml:mo stretchy='false'>(</mml:mo><mml:msub><mml:mi>d</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>d</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo stretchy='false'>)</mml:mo><mml:mo>=</mml:mo><mml:mi>exp</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mo>&#x02212;</mml:mo><mml:msub><mml:mi>&#x003B8;</mml:mi><mml:mi>d</mml:mi></mml:msub><mml:msup><mml:mrow><mml:mrow><mml:mo>&#x02016;</mml:mo><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:msub><mml:mi>d</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:msub><mml:mo>&#x02212;</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:msub><mml:mi>d</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow></mml:msub></mml:mrow><mml:mo>&#x02016;</mml:mo></mml:mrow></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math></disp-formula>
<p>where</p>
<disp-formula id="E3"><label>(3)</label><mml:math id="M7"><mml:mrow><mml:msub><mml:mi>&#x003B8;</mml:mi><mml:mi>d</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mi>n</mml:mi></mml:mfrac><mml:mstyle displaystyle='true'><mml:munderover><mml:mo>&#x02211;</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>n</mml:mi></mml:munderover><mml:mrow><mml:mo stretchy='false'>&#x02016;</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:msub><mml:mi>d</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:msub><mml:msup><mml:mo stretchy='false'>&#x02016;</mml:mo><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:mstyle></mml:mrow></mml:math></disp-formula>
<p>Similarly, microbe GAPK similarity <italic>G</italic><sub><italic>m</italic></sub> is computed.</p></sec>
<sec>
<title>2.3.4. Similarity integration</title>
<p>Functional similarity is used to measure microbe/disease similarity from the aspect of biological properties. GAPK similarity is used to evaluate microbe/disease similarity from the topological structure of MDA network. As compared with two individual similarity measurements, the combination of functional similarity and GAPK similarity can more accurately assess microbe/disease similarity and further improve MDA identification performance. Thus, we use the two types of information for microbe/disease similarity evaluation. Moreover, the final disease similarity matrix <italic>S</italic><sub><italic>d</italic></sub> is computed by integrating their functional similarity and GAPK similarity by Eq. (4) as follows:</p>
<disp-formula id="E4"><label>(4)</label><mml:math id="M8"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi>d</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>d</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>d</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mtable columnalign='left'><mml:mtr><mml:mtd><mml:mfrac><mml:mrow><mml:msubsup><mml:mi>S</mml:mi><mml:mi>d</mml:mi><mml:mrow><mml:mi>f</mml:mi><mml:mi>u</mml:mi><mml:mi>n</mml:mi></mml:mrow></mml:msubsup><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>d</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>d</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:msub><mml:mi>G</mml:mi><mml:mi>d</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>d</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>d</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mn>2</mml:mn></mml:mfrac><mml:mtext>&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;if&#x000A0;</mml:mtext><mml:msubsup><mml:mi>S</mml:mi><mml:mi>d</mml:mi><mml:mrow><mml:mi>f</mml:mi><mml:mi>u</mml:mi><mml:mi>n</mml:mi></mml:mrow></mml:msubsup><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>d</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>d</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x02260;</mml:mo><mml:mn>0</mml:mn></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mtext>&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;</mml:mtext><mml:msub><mml:mi>G</mml:mi><mml:mi>d</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>d</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>d</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mtext>&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;otherwise.&#x000A0;</mml:mtext></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:mrow></mml:math></disp-formula>
<p>Similarly, microbe similarity matrix <italic>S</italic><sub><italic>m</italic></sub> is computed by Eq. (5) as follows:</p>
<disp-formula id="E5"><label>(5)</label><mml:math id="M9"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi>m</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>m</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>m</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mtable columnalign='left'><mml:mtr><mml:mtd><mml:mfrac><mml:mrow><mml:msubsup><mml:mi>S</mml:mi><mml:mi>m</mml:mi><mml:mrow><mml:mi>f</mml:mi><mml:mi>u</mml:mi><mml:mi>n</mml:mi></mml:mrow></mml:msubsup><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>m</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>m</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:msub><mml:mi>G</mml:mi><mml:mi>m</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>m</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>m</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mn>2</mml:mn></mml:mfrac><mml:mtext>&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;if&#x000A0;</mml:mtext><mml:msubsup><mml:mi>S</mml:mi><mml:mi>m</mml:mi><mml:mrow><mml:mi>f</mml:mi><mml:mi>u</mml:mi><mml:mi>n</mml:mi></mml:mrow></mml:msubsup><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>m</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>m</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x02260;</mml:mo><mml:mn>0</mml:mn></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mtext>&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;</mml:mtext><mml:msub><mml:mi>G</mml:mi><mml:mi>m</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>m</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>m</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mtext>&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;otherwise.&#x000A0;</mml:mtext></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:mrow></mml:math></disp-formula>
</sec></sec>
<sec>
<title>2.4. Feature extraction</title>
<p>GATE can efficiently learn features from structured graph data by stacking encoders and decoders (Deng et al., <xref ref-type="bibr" rid="B9">2022</xref>). In this study, we use GATE to extract features for each microbe&#x02013;disease pair. The GATE structure contain multiple encoders and decoders. In the encoders, each encoder uses a self-attention mechanism to generate new representations for nodes based on their neighborhood information (Veli&#x0010D;kovi&#x00107; et al., <xref ref-type="bibr" rid="B52">2017</xref>). In the <italic>k</italic>th layer of encoder, relationship between node <italic>i</italic> and its neighbor node <italic>j</italic> is computed by Eq. (6) as follows:</p>
<disp-formula id="E6"><label>(6)</label><mml:math id="M10"><mml:mtable class="eqnarray" columnalign="left"><mml:mtr><mml:mtd><mml:msubsup><mml:mrow><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>k</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:mo class="qopname">Sigmoid</mml:mo><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:msubsup><mml:mrow><mml:mi>V</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>k</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:msubsup><mml:mi>&#x003C3;</mml:mi><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:msup><mml:mrow><mml:mi>W</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>k</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:msup><mml:msubsup><mml:mrow><mml:mi>h</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>k</mml:mi><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:msubsup></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow><mml:mo>&#x0002B;</mml:mo><mml:msubsup><mml:mrow><mml:mi>V</mml:mi></mml:mrow><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>k</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:msubsup><mml:mi>&#x003C3;</mml:mi><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:msup><mml:mrow><mml:mi>W</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>k</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:msup><mml:msubsup><mml:mrow><mml:mi>h</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>k</mml:mi><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:msubsup></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
<p>where <italic>W</italic><sup>(<italic>k</italic>)</sup>, <inline-formula><mml:math id="M11"><mml:msubsup><mml:mrow><mml:mi>V</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>k</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:msubsup></mml:math></inline-formula>, and <inline-formula><mml:math id="M12"><mml:msubsup><mml:mrow><mml:mi>V</mml:mi></mml:mrow><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>k</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:msubsup></mml:math></inline-formula> denote the trainable parameters in the <italic>k</italic>th layer of encoder with the sigmoid activation function. <inline-formula><mml:math id="M13"><mml:msubsup><mml:mrow><mml:mi>h</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>k</mml:mi><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:msubsup></mml:math></inline-formula> and <inline-formula><mml:math id="M14"><mml:msubsup><mml:mrow><mml:mi>h</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>k</mml:mi><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:msubsup></mml:math></inline-formula> denote the feature representations of nodes <italic>i</italic> and <italic>j</italic> in the (<italic>k</italic>&#x02212;1)th layer, respectively. For the <italic>i</italic>th node, its associations with the other nodes are taken as its initial representation, that is, <inline-formula><mml:math id="M15"><mml:msubsup><mml:mrow><mml:mi>h</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mn>0</mml:mn></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>, and its representation in the <italic>k</italic>th layer is generated by Eq. (7) as follows:</p>
<disp-formula id="E7"><label>(7)</label><mml:math id="M16"><mml:mtable class="eqnarray" columnalign="left"><mml:mtr><mml:mtd><mml:msubsup><mml:mrow><mml:mi>h</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mn>0</mml:mn></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:msubsup><mml:mrow><mml:mi>h</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:munder class="msub"><mml:mrow><mml:mo>&#x02211;</mml:mo></mml:mrow><mml:mrow><mml:mi>j</mml:mi><mml:mo>&#x02208;</mml:mo><mml:msub><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:munder></mml:mstyle><mml:msubsup><mml:mrow><mml:mi>&#x003B1;</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>k</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:msubsup><mml:mi>&#x003C3;</mml:mi><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mrow><mml:msup><mml:mrow><mml:mi>W</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>k</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:msup><mml:msubsup><mml:mrow><mml:mi>h</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>k</mml:mi><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:msubsup></mml:mrow><mml:mo stretchy="true">)</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
<p>We use the softmax function to normalize coefficients of node <italic>i</italic>&#x00027;s neighbors and solve the comparability problem by Eq. (8) as follows:</p>
<disp-formula id="E8"><label>(8)</label><mml:math id="M17"><mml:mrow><mml:msubsup><mml:mi>&#x003B1;</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy='false'>(</mml:mo><mml:mi>k</mml:mi><mml:mo stretchy='false'>)</mml:mo></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mi>exp</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msubsup><mml:mi>c</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy='false'>(</mml:mo><mml:mi>k</mml:mi><mml:mo stretchy='false'>)</mml:mo></mml:mrow></mml:msubsup></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mstyle displaystyle='true'><mml:msub><mml:mo>&#x02211;</mml:mo><mml:mrow><mml:mi>l</mml:mi><mml:mo>&#x02208;</mml:mo><mml:msub><mml:mi>N</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:msub><mml:mrow><mml:mi>exp</mml:mi></mml:mrow></mml:mstyle><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msubsup><mml:mi>c</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>l</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy='false'>(</mml:mo><mml:mi>k</mml:mi><mml:mo stretchy='false'>)</mml:mo></mml:mrow></mml:msubsup></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mfrac></mml:mrow></mml:math></disp-formula>
<p>where <italic>N</italic><sub><italic>i</italic></sub> represents node <italic>i</italic> and its all neighbors. Moreover, the output in the final layer of encoder is considered the node representations.</p>
<p>In the decoder, the initial attributes of each node are reconstructed. Its input comes from the output in the final layer of encoder. Each neighbor of the current node is assigned to different weights by the attention mechanism. The normalized relevance between node <italic>i</italic> and its neighbor <italic>j</italic> in the <italic>k</italic>th layer of decoder is computed by Eqs (9) and (10) as follows:</p>
<disp-formula id="E9"><label>(9)</label><mml:math id="M18"><mml:mrow><mml:msubsup><mml:mover accent='true'><mml:mi>&#x003B1;</mml:mi><mml:mo>&#x0005E;</mml:mo></mml:mover><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy='false'>(</mml:mo><mml:mi>k</mml:mi><mml:mo stretchy='false'>)</mml:mo></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mi>exp</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msubsup><mml:mover accent='true'><mml:mi>c</mml:mi><mml:mo>&#x0005E;</mml:mo></mml:mover><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy='false'>(</mml:mo><mml:mi>k</mml:mi><mml:mo stretchy='false'>)</mml:mo></mml:mrow></mml:msubsup></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mstyle displaystyle='true'><mml:msub><mml:mo>&#x02211;</mml:mo><mml:mrow><mml:mi>l</mml:mi><mml:mo>&#x02208;</mml:mo><mml:msub><mml:mi>N</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:msub><mml:mrow><mml:mi>exp</mml:mi></mml:mrow></mml:mstyle><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msubsup><mml:mover accent='true'><mml:mi>c</mml:mi><mml:mo>&#x0005E;</mml:mo></mml:mover><mml:mrow><mml:mi>i</mml:mi><mml:mi>l</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy='false'>(</mml:mo><mml:mi>k</mml:mi><mml:mo stretchy='false'>)</mml:mo></mml:mrow></mml:msubsup></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mfrac></mml:mrow></mml:math></disp-formula>
<disp-formula id="E10"><label>(10)</label><mml:math id="M19"><mml:mrow><mml:msubsup><mml:mover accent='true'><mml:mi>c</mml:mi><mml:mo>&#x0005E;</mml:mo></mml:mover><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow><mml:mi>k</mml:mi></mml:msubsup><mml:mo>=</mml:mo><mml:mi>Sigmoid</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msubsup><mml:mover accent='true'><mml:mi>V</mml:mi><mml:mo>&#x0005E;</mml:mo></mml:mover><mml:mi>s</mml:mi><mml:mrow><mml:msup><mml:mrow><mml:mo stretchy='false'>(</mml:mo><mml:mi>k</mml:mi><mml:mo stretchy='false'>)</mml:mo></mml:mrow><mml:mi>T</mml:mi></mml:msup></mml:mrow></mml:msubsup><mml:mi>&#x003C3;</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msup><mml:mover accent='true'><mml:mi>W</mml:mi><mml:mo>&#x0005E;</mml:mo></mml:mover><mml:mrow><mml:mo stretchy='false'>(</mml:mo><mml:mi>k</mml:mi><mml:mo stretchy='false'>)</mml:mo></mml:mrow></mml:msup><mml:msubsup><mml:mover accent='true'><mml:mi>h</mml:mi><mml:mo>&#x0005E;</mml:mo></mml:mover><mml:mi>i</mml:mi><mml:mrow><mml:mo stretchy='false'>(</mml:mo><mml:mi>k</mml:mi><mml:mo stretchy='false'>)</mml:mo></mml:mrow></mml:msubsup></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:msubsup><mml:mover accent='true'><mml:mi>V</mml:mi><mml:mo>&#x0005E;</mml:mo></mml:mover><mml:mi>r</mml:mi><mml:mrow><mml:msup><mml:mrow><mml:mo stretchy='false'>(</mml:mo><mml:mi>k</mml:mi><mml:mo stretchy='false'>)</mml:mo></mml:mrow><mml:mi>T</mml:mi></mml:msup></mml:mrow></mml:msubsup><mml:mi>&#x003C3;</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msup><mml:mover accent='true'><mml:mi>W</mml:mi><mml:mo>&#x0005E;</mml:mo></mml:mover><mml:mrow><mml:mo stretchy='false'>(</mml:mo><mml:mi>k</mml:mi><mml:mo stretchy='false'>)</mml:mo></mml:mrow></mml:msup><mml:msubsup><mml:mover accent='true'><mml:mi>h</mml:mi><mml:mo>&#x0005E;</mml:mo></mml:mover><mml:mi>j</mml:mi><mml:mrow><mml:mo stretchy='false'>(</mml:mo><mml:mi>k</mml:mi><mml:mo stretchy='false'>)</mml:mo></mml:mrow></mml:msubsup></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math></disp-formula>
<p>where &#x00174;<sup>(<italic>k</italic>)</sup>, <inline-formula><mml:math id="M20"><mml:msubsup><mml:mrow><mml:mover accent="true"><mml:mrow><mml:mi>V</mml:mi></mml:mrow><mml:mo>^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>k</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:msubsup></mml:math></inline-formula>, and <inline-formula><mml:math id="M21"><mml:msubsup><mml:mrow><mml:mover accent="true"><mml:mrow><mml:mi>V</mml:mi></mml:mrow><mml:mo>^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>k</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:msubsup></mml:math></inline-formula> denote the trainable parameters in the <italic>k</italic>th layer of decoder. The <italic>k</italic>th layer in decoder reconstructs the node representations in the (<italic>k</italic>&#x02212;1)th layer by Eq. (11) as follows:</p>
<disp-formula id="E11"><label>(11)</label><mml:math id="M22"><mml:mrow><mml:msubsup><mml:mover accent='true'><mml:mi>h</mml:mi><mml:mo>&#x0005E;</mml:mo></mml:mover><mml:mi>i</mml:mi><mml:mrow><mml:mi>k</mml:mi><mml:mo>&#x02212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:mstyle displaystyle='true'><mml:munder><mml:mo>&#x02211;</mml:mo><mml:mrow><mml:mi>j</mml:mi><mml:mo>&#x02208;</mml:mo><mml:msub><mml:mi>N</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:munder><mml:mrow><mml:msubsup><mml:mover accent='true'><mml:mi>&#x003B1;</mml:mi><mml:mo>&#x0005E;</mml:mo></mml:mover><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy='false'>(</mml:mo><mml:mi>k</mml:mi><mml:mo stretchy='false'>)</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:mstyle><mml:mi>&#x003C3;</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msup><mml:mover accent='true'><mml:mi>W</mml:mi><mml:mo>&#x0005E;</mml:mo></mml:mover><mml:mrow><mml:mo stretchy='false'>(</mml:mo><mml:mi>k</mml:mi><mml:mo stretchy='false'>)</mml:mo></mml:mrow></mml:msup><mml:msubsup><mml:mover accent='true'><mml:mi>h</mml:mi><mml:mo>&#x0005E;</mml:mo></mml:mover><mml:mi>j</mml:mi><mml:mrow><mml:mo stretchy='false'>(</mml:mo><mml:mi>k</mml:mi><mml:mo stretchy='false'>)</mml:mo></mml:mrow></mml:msubsup></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math></disp-formula>
<p>The loss function is defined by Eq. (12) as follows:</p>
<disp-formula id="E12"><label>(12)</label><mml:math id="M23"><mml:mrow><mml:mi>L</mml:mi><mml:mi>o</mml:mi><mml:mi>s</mml:mi><mml:mi>s</mml:mi><mml:mo>=</mml:mo><mml:mstyle displaystyle='true'><mml:munderover><mml:mo>&#x02211;</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>N</mml:mi></mml:munderover><mml:mrow><mml:msub><mml:mrow><mml:mrow><mml:mo>&#x02016;</mml:mo><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>&#x02212;</mml:mo><mml:msub><mml:mover accent='true'><mml:mi>x</mml:mi><mml:mo>&#x0005E;</mml:mo></mml:mover><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo>&#x02016;</mml:mo></mml:mrow></mml:mrow><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:mstyle><mml:mo>&#x02212;</mml:mo><mml:mi>&#x003BB;</mml:mi><mml:mstyle displaystyle='true'><mml:munder><mml:mo>&#x02211;</mml:mo><mml:mrow><mml:mi>j</mml:mi><mml:mo>&#x02208;</mml:mo><mml:msub><mml:mi>N</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:munder><mml:mrow><mml:mi>log</mml:mi></mml:mrow></mml:mstyle><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mi>exp</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mo>&#x02212;</mml:mo><mml:msubsup><mml:mi>h</mml:mi><mml:mi>i</mml:mi><mml:mi>T</mml:mi></mml:msubsup><mml:msub><mml:mi>h</mml:mi><mml:mi>j</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mfrac></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math></disp-formula>
<p>where the first and second terms denote the reconstruction loss of node features and one of graph structure, respectively. &#x003BB; is a hyperparameter used to balance the contribution of two reconstruction loss terms. <italic>x</italic><sub><italic>i</italic></sub> and <inline-formula><mml:math id="M24"><mml:msub><mml:mrow><mml:mover accent="true"><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mo>^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> represent the initial features and the reconstructed features of node <italic>i</italic>, respectively. <italic>h</italic><sub><italic>j</italic></sub> is the representation of a neighboring node <italic>j</italic> of node <italic>i</italic>.</p>
<p>Finally, we compute microbe feature vectors and disease feature vectors using GATE, and then, a microbe-disease pair is characterized as a <italic>a</italic>-dimensional vector by concatenating features of both the microbe and the disease.</p></sec>
<sec>
<title>2.5. Reliable negative MDA selection</title>
<p>In the area of machine learning, negative samples are equally important to final classification performance. However, there are lack of reliable negative MDAs on existing MDA databases due to the limitations of biological experiments. Thus, we design a reliable negative MDA selection method based on PU learning.</p>
<p>PU learning can efficiently identify high-quality negative samples from unlabeled samples and has been widely used in various practical situations (Li et al., <xref ref-type="bibr" rid="B25">2022</xref>). The <italic>K</italic>-means clustering approach is one of the most popular unsupervised learning algorithms (Peng et al., <xref ref-type="bibr" rid="B44">2022b</xref>). In the HMDAD and Disbiome databases, there are a few positive MDAs and multiple unknown microbe&#x02013;disease pairs; that is, the two MDA databases are imbalanced. XGBoost has extremely fast parallel computation speed and demonstrates better performance in both balanced and imbalanced databases (Abdu-Aljabar and Awad, <xref ref-type="bibr" rid="B1">2021</xref>).</p>
<p>In this manuscript, we propose a PU learning algorithm to select reliable negative MDAs by combining <italic>K</italic>-means clustering and XGBoost. Let that positive sample set <italic>P</italic> and unlabeled example set <italic>U</italic> denote known MDAs and unknown microbe&#x02013;disease pairs, respectively. To select reliable negative MDAs from <italic>U</italic>, as shown in <xref ref-type="table" rid="T5">Algorithm 1</xref>, we design a PU learning algorithm.</p>
<table-wrap position="float" id="T5">
<label>Algorithm 1</label>
<caption><p>A PU learning algorithm for selecting reliable negative MDAs.</p></caption>
<table frame="hsides" rules="groups">
<tbody>
<tr><td align="left" valign="top"></td></tr>
<tr><td align="left" valign="top">1: Clustering each MDA sample with the <italic>K</italic>-means clustering algorithm based on the extracted MDA features using GATE.</td></tr>
<tr><td align="left" valign="top">2: Selecting the first <italic>t</italic> samples in <italic>P</italic> which have the smallest distance with cluster centroid as <italic>S</italic> and adding <italic>S</italic> into <italic>U</italic>.</td></tr>
<tr><td align="left" valign="top">2: Taking <italic>P</italic>&#x02212;<italic>S</italic> as positive samples, and <italic>U</italic>&#x0002B;<italic>S</italic> as negative samples.</td></tr>
<tr><td align="left" valign="top">3: Calculating association score matrix <italic>A</italic> for all microbe&#x02013;disease pairs based on XGBoost.</td></tr>
<tr><td align="left" valign="top">4: Ranking microbe&#x02013;disease pairs in <italic>S</italic> based on association scores in <italic>A</italic> and obtaining the minimum score <italic>A</italic><sub><italic>min</italic></sub> in <italic>S</italic>.</td></tr>
<tr><td align="left" valign="top">5: For every sample <italic>x</italic> in <italic>U</italic></td></tr>
<tr><td align="left" valign="top">6: If <italic>A</italic><sub><italic>x</italic></sub> satisfies <italic>A</italic><sub><italic>x</italic></sub>&#x0003C;<italic>A</italic><sub>min</sub></td></tr>
<tr><td align="left" valign="top">7: then <italic>RN</italic> &#x0003D; <italic>RN</italic>&#x0222A;<italic>x</italic></td></tr>
<tr><td align="left" valign="top">8: Endfor</td></tr>
<tr><td align="left" valign="top">9: Obtaining reliable negative MDA samples <italic>RN</italic>.</td></tr>  
</tbody>
</table>
</table-wrap>   
<p>Particularly, during PU learning, if spy samples are randomly selected from positive sample set <italic>P</italic> and placed into <italic>U</italic>, the obtained spy samples could be located at the boundary of the class cluster composed of samples in the entire <italic>P</italic> and belong to outliers. These spy samples have low spatial similarity with unknown positive examples in <italic>U</italic>. If a large number of noise or outliers are selected as spy samples, it will greatly affect the evaluation of the classifier on unlabeled samples, which could directly cause decreasing classification performance. Thus, we use <italic>K</italic>-means clustering algorithm for spy sample selection.</p></sec>
<sec>
<title>2.6. MDA prediction</title>
<p>We build a DNN to classify unknown microbe&#x02013;disease pairs based on the extracted MDA features, the selected reliable negative MDAs, and known MDAs. The DNN contains an input layer, multiple hidden layers, and an output layer. In the input layer with <italic>a</italic> neurons, each MDA sample <bold><italic>x</italic></bold> with <italic>a</italic>-dimensional features is fed into the model by Eq. (13) as follows:</p>
<disp-formula id="E13"><label>(13)</label><mml:math id="M25"><mml:mtable class="eqnarray" columnalign="left"><mml:mtr><mml:mtd><mml:mi>x</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo>&#x02026;</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>a</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
<p>where <italic>x</italic><sub><italic>i</italic></sub> denotes the <italic>i</italic>th feature in <bold><italic>x</italic></bold>.</p>
<p>The <italic>j</italic>th hidden layer outputs the results by Eq. (14) as follows:</p>
<disp-formula id="E14"><label>(14)</label><mml:math id="M26"><mml:mtable class="eqnarray" columnalign="left"><mml:mtr><mml:mtd><mml:mtable style="text-align:axis;" equalrows="false" columnlines="none" equalcolumns="false" class="array"><mml:mtr><mml:mtd><mml:mtable style="text-align:axis;" equalrows="false" columnlines="none" equalcolumns="false" class="array"><mml:mtr><mml:mtd><mml:msub><mml:mrow><mml:mi>h</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:munderover accentunder="false" accent="false"><mml:mrow><mml:mo>&#x02211;</mml:mo></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>a</mml:mi></mml:mrow></mml:munderover></mml:mstyle><mml:msub><mml:mrow><mml:mi>w</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>&#x0002B;</mml:mo><mml:msub><mml:mrow><mml:mi>b</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mi>f</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>h</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mi>R</mml:mi><mml:mi>e</mml:mi><mml:mi>L</mml:mi><mml:mi>U</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>h</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mtd></mml:mtr></mml:mtable></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
<p>where <italic>f</italic> denotes the ReLU activation function. Finally, the output layer with the sigmoid activation function outputs MDA classification results by Eq. (15) as follows:</p>
<disp-formula id="E15"><label>(15)</label><mml:math id="M27"><mml:mtable class="eqnarray" columnalign="left"><mml:mtr><mml:mtd><mml:mi>&#x003C3;</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>h</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>&#x0002B;</mml:mo><mml:msup><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mo>-</mml:mo><mml:msup><mml:mrow><mml:mi>h</mml:mi></mml:mrow><mml:mrow><mml:msup><mml:mrow></mml:mrow><mml:mrow><mml:mi>&#x02032;</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:msup></mml:mrow></mml:msup></mml:mrow></mml:mfrac></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
<p>where <italic>h</italic>&#x02032; denotes the output in the final hidden layer.</p></sec></sec>
<sec id="s3">
<title>3. Result</title>
<sec>
<title>3.1. Experimental settings</title>
<p>To evaluate the MDA prediction performance of our proposed GPUDMDA method, we compared it with other MDA identification methods (LRLSHMDA, NTSHMDA, GATMDA, and MNMDA) under five-fold cross validation (CV) on diseases, microbes, and microbe&#x02013;disease pairs for 20 times. LRLSHMDA (Wang et al., <xref ref-type="bibr" rid="B53">2017</xref>) is Laplacian regularized least square-based MDA identification algorithm, NTSHMDA (Luo and Long, <xref ref-type="bibr" rid="B33">2018</xref>) is integrated random walk and network topology similarity, GATMDA (Long et al., <xref ref-type="bibr" rid="B32">2021</xref>) combined inductive matrix completion and graph attention networks to complete missing MDAs, and MNNMDA (Liu et al., <xref ref-type="bibr" rid="B29">2023</xref>) used a low-rank matrix completion model for identifying possible MDAs. During MDA prediction, it is not enough to reflect the MDA identification performance of a computational model only through cross-validation on microbe&#x02013;disease pairs. Thus, in the study, we implemented cross-validations on microbes, diseases, and microbe&#x02013;disease pairs to comprehensively assess the model&#x00027;s performance. The detailed definitions about the above three cross-validations have been proposed by Peng et al. (<xref ref-type="bibr" rid="B39">2020</xref>). AUC and AUPR were applied to measure the performance of MDA prediction methods.</p>
<p>In this study, we used GATE to extract features of microbes and diseases from their similarity networks, both of which are 64 dimensional vectors. We selected <italic>t</italic> samples from positive sample set <italic>P</italic> to place unlabeled example set <italic>U</italic>. When <italic>t</italic> was set to 15% of <italic>P</italic> on the HMDAD database and 20% of <italic>P</italic> on the Disbiome database, GPUDMDA obtained the best performance. Thus, we set <italic>t</italic> to 15 and 20% of <italic>P</italic> on the two databases, respectively. For DNN with four layers, the input layer, the following three hidden layer, and the output layer have 128, 100, 100, 50, and one nodes, respectively. Learning rate and &#x0201C;dropout&#x0201D; were set to 0.001 and 0.2. The parameter &#x0201C;epoch_num,&#x0201D; denoting the number of training, was set to 300 and 1,500 on the two databases, respectively. Disbiome is a larger dataset, and the proposed computational model needs to be trained for enough times to obtain better classification performance; thus, the &#x0201C;epoch_num&#x0201D; value was much larger on the Disbiome database.</p>
<p>Additionally, the number of positive samples is the same as one of the known MDAs.The number of selected credible negative MDAs is related to the computed smallest association probability score <italic>A</italic><sub><italic>min</italic></sub>. Since the credible negative MDAs were selected from unknown microbe&#x02013;disease pairs, unknown microbe&#x02013;disease pairs were decreased but accounted for most of all microbe&#x02013;disease pairs.</p></sec>
<sec>
<title>3.2. Performance comparison under CV on diseases</title>
<p>Under CV on diseases, 80% diseases were taken as the training set and the remaining was test set. <xref ref-type="fig" rid="F2">Figure 2</xref> elucidates the receiver operating characteristic (ROC) and precision-recall (PR) curves of the five MDA prediction methods on the HMDAD and Disbiome databases under CV on diseases. Under CV on diseases, GPUDMDA obtained the best AUCs of 0.7121 and 0.8372, and the best AUPRs of 0.2022 and better AUPR of 0.2030 on the HMDAD and Disbiome databases, respectively, significantly outperforming LRLSHMDA, NTSHMDA, GATMDA, and MNMDA.</p>
<fig id="F2" position="float">
<label>Figure 2</label>
<caption><p>Performance comparison of five MDA prediction methods under five-fold CV on diseases. <bold>(A, B)</bold> The ROC and PR curves of the five methods on HMDAD. <bold>(C, D)</bold> The ROC and PR curves of the five methods on Disbiome.</p></caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmicb-14-1244527-g0002.tif"/>
</fig></sec>
<sec>
<title>3.3. Performance comparison under CV on microbes</title>
<p>Under CV on microbes, 80% microbes were taken as the training set and the remaining was test set. <xref ref-type="fig" rid="F3">Figure 3</xref> shows the ROC and PR curves of the five methods under CV on microbes. Under CV on microbes, GPUDMDA obtained better AUCs of 0.9454 and 0.8908 and AUPRs of 0.8529 and 0.4367 than LRLSHMDA, NTSHMDA, GATMDA, and MNMDA.</p>
<fig id="F3" position="float">
<label>Figure 3</label>
<caption><p>Performance comparison of five MDA prediction methods under five-fold CV on microbes. <bold>(A, B)</bold> The ROC and PR curves of the five methods on HMDAD. <bold>(C, D)</bold> The ROC and PR curves of the five methods on Disbiome.</p></caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmicb-14-1244527-g0003.tif"/>
</fig></sec>
<sec>
<title>3.4. Performance comparison under CV on microbe&#x02013;disease pairs</title>
<p>Under CV on microbe&#x02013;disease pairs, 80% microbe&#x02013;disease pairs were taken as the training set and the remaining was test set. <xref ref-type="fig" rid="F4">Figure 4</xref> illustrates the ROC and PR curves of the five MDA prediction methods under CV on microbe&#x02013;disease pairs. Under the CV, GPUDMDA computed better AUCs of 0.9501 and 0.8948, and the best AUPRs of 0.8545 and 0.4464 among the five methods.</p>
<fig id="F4" position="float">
<label>Figure 4</label>
<caption><p>Performance comparison of the five MDA prediction methods under five-fold CV on microbe&#x02013;disease pairs. <bold>(A, B)</bold> The ROC and PR curves of the five methods on HMDAD. <bold>(C, D)</bold> The ROC and PR curves of the five methods on Disbiome.</p></caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmicb-14-1244527-g0004.tif"/>
</fig></sec>
<sec>
<title>3.5. The affect of PU learning on performance</title>
<p>Reliable negative samples can improve the classification performance of a model. To evaluate the reliability of the identified negative MDAs by GPUDMDA, we compared its performance under negative sample selection. <xref ref-type="fig" rid="F5">Figure 5</xref> demonstrates the affect of negative samples selected by PU learning on performance. The results elucidated that GPUDMDA with PU learning outperformed one without PU learning. Particularly, the performance of GPUDMDA with PU learning obtained significant improvement on Disbiome. The results suggested that reliable negative MDAs selected by PU learning can boost the MDA prediction ability.</p>
<fig id="F5" position="float">
<label>Figure 5</label>
<caption><p>The impact of PU learning on performance in two databases.</p></caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmicb-14-1244527-g0005.tif"/>
</fig></sec>
<sec>
<title>3.6. Case study</title>
<p>In the above sections, we have confirmed the MDA identification accuracy of GPUDMDA. Next, we intend to find new microbes for asthma and IBD.</p>
<sec>
<title>3.6.1. Identifying new microbes for asthma</title>
<p>Asthma is a heterogeneous disease with respect to respiratory symptoms including chest tightness, shortness of breath, wheeze, and cough. It is the most common chronic respiratory condition and affects &#x0007E;339 million people worldwide. Approximately 5%&#x02013;10% of these patients have severe asthma. More than 10% of adults and 2.5% of children suffered from asthma have severe asthma (Brusselle and Koppelman, <xref ref-type="bibr" rid="B2">2022</xref>; Reddel et al., <xref ref-type="bibr" rid="B46">2022</xref>; Rattu et al., <xref ref-type="bibr" rid="B45">2023</xref>).</p>
<p>We used the proposed GPUDMDA method to find new microbes associated with asthma. <xref ref-type="table" rid="T1">Tables 1</xref>, <xref ref-type="table" rid="T2">2</xref> show the predicted top 30 microbes that may associate with asthma on the HMDAD and Disbiome databases. The predicted 30 asthma-associated microbes included microbes with known association information with asthma and microbes without association information with asthma on the two databases. As shown in <xref ref-type="table" rid="T1">Table 1</xref>, 23 and 29 microbes can be validated by each or both of two databases or existing literatures among the identified top 30 potential asthma-associated microbes on the two databases, respectively. Furthermore, we found that <italic>Enterobacter hormaechei</italic> could associate with asthma with the ranking of 15 on the HMDAD database. On the Disbiome database, GPUDMDA predicted that <italic>Enterobacter</italic> may be a sole and unknown asthma-associated microbe among the predicted top 30 microbes associated with asthma.</p>
<table-wrap position="float" id="T1">
<label>Table 1</label>
<caption><p>The predicted top 30 microbes associated with Asthma on HMDAD.</p></caption> 
<table frame="box" rules="all">
<thead>
<tr style="background-color:&#x00023;919498;color:&#x00023;ffffff">
<th valign="top" align="left"><bold>Rank</bold></th>
<th valign="top" align="left"><bold>Microbe</bold></th>
<th valign="top" align="left"><bold>Evidence</bold></th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left">1</td>
<td valign="top" align="left"><italic>Proteobacteria</italic></td>
<td valign="top" align="left">Confirmed by HMDAD and Disbiome</td>
</tr> <tr>
<td valign="top" align="left">2</td>
<td valign="top" align="left"><italic>Prevotella</italic></td>
<td valign="top" align="left">Confirmed by HMDAD and Disbiome</td>
</tr> <tr>
<td valign="top" align="left">3</td>
<td valign="top" align="left"><italic>Staphylococcus</italic></td>
<td valign="top" align="left">Confirmed by HMDAD and Disbiome</td>
</tr> <tr>
<td valign="top" align="left">4</td>
<td valign="top" align="left"><italic>Bacteroidetes</italic></td>
<td valign="top" align="left">Confirmed by HMDAD and Disbiome</td>
</tr> <tr>
<td valign="top" align="left">5</td>
<td valign="top" align="left"><italic>Enterobacteriaceae</italic></td>
<td valign="top" align="left">Confirmed by Disbiome</td>
</tr> <tr>
<td valign="top" align="left">6</td>
<td valign="top" align="left"><italic>Clostridium coccoides</italic></td>
<td valign="top" align="left">PMID: 1477358</td>
</tr> <tr>
<td valign="top" align="left">7</td>
<td valign="top" align="left"><italic>Firmicutes</italic></td>
<td valign="top" align="left">PMID: 23265859</td>
</tr> <tr>
<td valign="top" align="left">8</td>
<td valign="top" align="left"><italic>Comamonadaceae</italic></td>
<td valign="top" align="left">Confirmed by HMDAD and Disbiome</td>
</tr> <tr>
<td valign="top" align="left">9</td>
<td valign="top" align="left"><italic>Oxalobacteraceae</italic></td>
<td valign="top" align="left">Confirmed by HMDAD and Disbiome</td>
</tr> <tr>
<td valign="top" align="left">10</td>
<td valign="top" align="left"><italic>Sphingomonadaceae</italic></td>
<td valign="top" align="left">Confirmed by HMDAD and Disbiome</td>
</tr> <tr>
<td valign="top" align="left">11</td>
<td valign="top" align="left"><italic>Haemophilus</italic></td>
<td valign="top" align="left">Confirmed by HMDAD and Disbiome</td>
</tr> <tr>
<td valign="top" align="left">12</td>
<td valign="top" align="left"><italic>Helicobacter pylori</italic></td>
<td valign="top" align="left">Confirmed by HMDAD</td>
</tr> <tr>
<td valign="top" align="left">13</td>
<td valign="top" align="left"><italic>Enterococcus</italic></td>
<td valign="top" align="left">PMID: 29788027</td>
</tr> <tr>
<td valign="top" align="left">14</td>
<td valign="top" align="left"><italic>Enterobacter aerogenes</italic></td>
<td valign="top" align="left">PMID: 23842440</td>
</tr> <tr>
<td valign="top" align="left">15</td>
<td valign="top" align="left"><italic>Enterobacter hormaechei</italic></td>
<td valign="top" align="left">Unconfirmed</td>
</tr> <tr>
<td valign="top" align="left">16</td>
<td valign="top" align="left"><italic>Klebsiella pneumoniae</italic></td>
<td valign="top" align="left">PMID: 26953325</td>
</tr> <tr>
<td valign="top" align="left">17</td>
<td valign="top" align="left"><italic>Shigella dysenteriae</italic></td>
<td valign="top" align="left">Unconfirmed</td>
</tr> <tr>
<td valign="top" align="left">18</td>
<td valign="top" align="left"><italic>Lactobacillus</italic></td>
<td valign="top" align="left">Confirmed by Disbiome</td>
</tr> <tr>
<td valign="top" align="left">19</td>
<td valign="top" align="left"><italic>Clostridia</italic></td>
<td valign="top" align="left">PMID: 21477358</td>
</tr> <tr>
<td valign="top" align="left">20</td>
<td valign="top" align="left"><italic>Veillonella</italic></td>
<td valign="top" align="left">Confirmed by Disbiome</td>
</tr> <tr>
<td valign="top" align="left">21</td>
<td valign="top" align="left"><italic>Klebsiella</italic></td>
<td valign="top" align="left">Confirmed by Disbiome</td>
</tr> <tr>
<td valign="top" align="left">22</td>
<td valign="top" align="left"><italic>Prevotella copri</italic></td>
<td valign="top" align="left">Unconfirmed</td>
</tr> <tr>
<td valign="top" align="left">23</td>
<td valign="top" align="left"><italic>Actinobacteria</italic></td>
<td valign="top" align="left">PMID: 28947029</td>
</tr> <tr>
<td valign="top" align="left">24</td>
<td valign="top" align="left"><italic>Shuttleworthia</italic></td>
<td valign="top" align="left">Unconfirmed</td>
</tr> <tr>
<td valign="top" align="left">25</td>
<td valign="top" align="left"><italic>Desulfovibrio</italic></td>
<td valign="top" align="left">PMID: 29198875</td>
</tr> <tr>
<td valign="top" align="left">26</td>
<td valign="top" align="left"><italic>Clostridium difficile</italic></td>
<td valign="top" align="left">PMID: 21872915</td>
</tr> <tr>
<td valign="top" align="left">27</td>
<td valign="top" align="left"><italic>Oxalobacter formigenes</italic></td>
<td valign="top" align="left">Unconfirmed</td>
</tr> <tr>
<td valign="top" align="left">28</td>
<td valign="top" align="left"><italic>Fusobacteria</italic></td>
<td valign="top" align="left">Unconfirmed</td>
</tr> <tr>
<td valign="top" align="left">29</td>
<td valign="top" align="left"><italic>Porphyromonadaceae</italic></td>
<td valign="top" align="left">Confirmed by Disbiome</td>
</tr>
<tr>
<td valign="top" align="left">30</td>
<td valign="top" align="left"><italic>Verrucomicrobiaceae</italic></td>
<td valign="top" align="left">Unconfirmed</td>
</tr>
</tbody>
</table>
</table-wrap>
<table-wrap position="float" id="T2">
<label>Table 2</label>
<caption><p>The predicted top 30 microbes associated with Asthma on Disbiome.</p></caption> 
<table frame="box" rules="all">
<thead>
<tr style="background-color:&#x00023;919498;color:&#x00023;ffffff">
<th valign="top" align="left"><bold>Rank</bold></th>
<th valign="top" align="left"><bold>Microbe</bold></th>
<th valign="top" align="left"><bold>Evidence</bold></th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left">1</td>
<td valign="top" align="left"><italic>Actinomyces</italic></td>
<td valign="top" align="left">Confirmed by Disbiome</td>
</tr> <tr>
<td valign="top" align="left">2</td>
<td valign="top" align="left"><italic>Bacteroides stercoris</italic></td>
<td valign="top" align="left">Confirmed by Disbiome</td>
</tr> <tr>
<td valign="top" align="left">3</td>
<td valign="top" align="left"><italic>Bifidobacterium</italic></td>
<td valign="top" align="left">Confirmed by Disbiome</td>
</tr> <tr>
<td valign="top" align="left">4</td>
<td valign="top" align="left"><italic>Blautia</italic></td>
<td valign="top" align="left">Confirmed by Disbiome</td>
</tr> <tr>
<td valign="top" align="left">5</td>
<td valign="top" align="left"><italic>Clostridiaceae</italic></td>
<td valign="top" align="left">Confirmed by Disbiome</td>
</tr> <tr>
<td valign="top" align="left">6</td>
<td valign="top" align="left"><italic>Clostridium neonatale</italic></td>
<td valign="top" align="left">Confirmed by Disbiome</td>
</tr> <tr>
<td valign="top" align="left">7</td>
<td valign="top" align="left"><italic>Comamonadaceae</italic></td>
<td valign="top" align="left">Confirmed by HMDAD and Disbiome</td>
</tr> <tr>
<td valign="top" align="left">8</td>
<td valign="top" align="left"><italic>Corynebacterium</italic></td>
<td valign="top" align="left">Confirmed by Disbiome</td>
</tr> <tr>
<td valign="top" align="left">9</td>
<td valign="top" align="left"><italic>Faecalibacterium</italic></td>
<td valign="top" align="left">Confirmed by Disbiome</td>
</tr> <tr>
<td valign="top" align="left">10</td>
<td valign="top" align="left"><italic>Gallibacterium</italic></td>
<td valign="top" align="left">Confirmed by Disbiome</td>
</tr> <tr>
<td valign="top" align="left">11</td>
<td valign="top" align="left"><italic>Gammaproteobacteria</italic></td>
<td valign="top" align="left">Confirmed by Disbiome</td>
</tr> <tr>
<td valign="top" align="left">12</td>
<td valign="top" align="left"><italic>Gemella</italic></td>
<td valign="top" align="left">Confirmed by Disbiome</td>
</tr> <tr>
<td valign="top" align="left">13</td>
<td valign="top" align="left"><italic>Klebsiella</italic></td>
<td valign="top" align="left">Confirmed by Disbiome</td>
</tr> <tr>
<td valign="top" align="left">14</td>
<td valign="top" align="left"><italic>Leclercia</italic></td>
<td valign="top" align="left">Confirmed by Disbiome</td>
</tr> <tr>
<td valign="top" align="left">15</td>
<td valign="top" align="left"><italic>Moraxella</italic></td>
<td valign="top" align="left">Confirmed by Disbiome</td>
</tr> <tr>
<td valign="top" align="left">16</td>
<td valign="top" align="left"><italic>Neisseria</italic></td>
<td valign="top" align="left">Confirmed by Disbiome</td>
</tr> <tr>
<td valign="top" align="left">17</td>
<td valign="top" align="left"><italic>Nitrosomonadaceae</italic></td>
<td valign="top" align="left">Confirmed by Disbiome</td>
</tr> <tr>
<td valign="top" align="left">18</td>
<td valign="top" align="left"><italic>Oxalobacteraceae</italic></td>
<td valign="top" align="left">Confirmed by HMDAD and Disbiome</td>
</tr> <tr>
<td valign="top" align="left">19</td>
<td valign="top" align="left"><italic>Planococcaceae</italic></td>
<td valign="top" align="left">Confirmed by Disbiome</td>
</tr> <tr>
<td valign="top" align="left">20</td>
<td valign="top" align="left"><italic>Prevotella</italic></td>
<td valign="top" align="left">Confirmed by HMDAD and Disbiome</td>
</tr> <tr>
<td valign="top" align="left">21</td>
<td valign="top" align="left"><italic>Pseudomonadaceae</italic></td>
<td valign="top" align="left">Confirmed by Disbiome</td>
</tr> <tr>
<td valign="top" align="left">22</td>
<td valign="top" align="left"><italic>Sphingomonadaceae</italic></td>
<td valign="top" align="left">Confirmed by HMDAD and Disbiome</td>
</tr> <tr>
<td valign="top" align="left">23</td>
<td valign="top" align="left"><italic>Staphylococcus</italic></td>
<td valign="top" align="left">Confirmed by HMDAD and Disbiome</td>
</tr> <tr>
<td valign="top" align="left">24</td>
<td valign="top" align="left"><italic>Stenotrophomonas</italic></td>
<td valign="top" align="left">Confirmed by Disbiome</td>
</tr> <tr>
<td valign="top" align="left">25</td>
<td valign="top" align="left"><italic>Streptococcus</italic></td>
<td valign="top" align="left">Confirmed by Disbiome</td>
</tr> <tr>
<td valign="top" align="left">26</td>
<td valign="top" align="left"><italic>Sutterella wadsworthensis</italic></td>
<td valign="top" align="left">Confirmed by Disbiome</td>
</tr> <tr>
<td valign="top" align="left">27</td>
<td valign="top" align="left"><italic>Veillonella</italic></td>
<td valign="top" align="left">Confirmed by Disbiome</td>
</tr> <tr>
<td valign="top" align="left">28</td>
<td valign="top" align="left"><italic>Weeksella</italic></td>
<td valign="top" align="left">Confirmed by Disbiome</td>
</tr> <tr>
<td valign="top" align="left">29</td>
<td valign="top" align="left"><italic>Propionibacterium</italic></td>
<td valign="top" align="left">PMID: 13268970</td>
</tr>
<tr>
<td valign="top" align="left">30</td>
<td valign="top" align="left"><italic>Enterobacter</italic></td>
<td valign="top" align="left">Unconfirmed</td>
</tr>
</tbody>
</table>
</table-wrap>
<p><italic>Enterobacter hormaechei</italic> (Yeh et al., <xref ref-type="bibr" rid="B63">2022</xref>) is a member and the most common nosocomial pathogen of the <italic>Enterobacter cloacae</italic> complex. It plays a key role in infectious diseases including, urinary tract infections, pneumonia, biliary tract infections, bacteremia, colitis and cellulitis. It is commonly found to be a high-pathogenicity island on its chromosome and is more virulent compared with other <italic>E. cloacae</italic> complex. In this study, GPUDMDA identified that <italic>E. hormaechei</italic> could associate with asthma.</p>
<p><xref ref-type="fig" rid="F6">Figure 6</xref> shows the association network between the predicted top 53 asthma-associated microbes and asthma, after removing the repeated associations on the two databases. In <xref ref-type="fig" rid="F6">Figure 6</xref>, the gray solid lines and blue dashed lines denote known associations between microbes and asthma and the predicted associations between microbes and asthma, respectively.</p>
<fig id="F6" position="float">
<label>Figure 6</label>
<caption><p>The predicted top 53 microbes associated with asthma on the two databases.</p></caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmicb-14-1244527-g0006.tif"/>
</fig></sec>
<sec>
<title>3.6.2. Identifying new microbes for inflammatory bowel disease</title>
<p>IBD is a class of globally chronic intestinal disease (Chang, <xref ref-type="bibr" rid="B3">2020</xref>; Kaplan and Windsor, <xref ref-type="bibr" rid="B23">2021</xref>). It widely exists in the gut and gastrointestinal tract and extraintestinal organs in many patients (Rogler et al., <xref ref-type="bibr" rid="B47">2021</xref>). Up to 2 million Europeans and 1.5 million North Americans suffer from this disease (Jairath and Feagan, <xref ref-type="bibr" rid="B19">2020</xref>). It mainly comprises Crohn&#x00027;s disease, ulcerative colitis, and indeterminate colitis (Flynn and Eisenstein, <xref ref-type="bibr" rid="B11">2019</xref>). Many studies thought that it is the result of interactions between microbial, environmental, and immune-mediated factors. In particular, microbiome has been reported to have potential roles in the development, progression, and treatment of IBD. The gut microbiome is different in the IBD patients from one in healthy bodies (Glassner et al., <xref ref-type="bibr" rid="B13">2020</xref>).</p>
<p>In particular, IBD is very common in children. Many pediatricians and the other pediatric clinicians meet children suffered from IBD. The IBD pediatric populations demonstrate the classic features of abdominal pain, bloody diarrhea, and weight loss as well as non-classic features of anemia, isolated poor growth, or the other extraintestinal symptoms. Recently, the IBD children patients show a rising incidence (Rosen et al., <xref ref-type="bibr" rid="B48">2015</xref>; Oliveira and Monteiro, <xref ref-type="bibr" rid="B37">2017</xref>). In total, 25%&#x02013;30% of patients with Crohn&#x00027;s disease and 20% of patients with ulcerative colitis have been diagnosed in &#x0003C; 20 years of age. Moreover, 4% of pediatric IBD patients have been detected before 5 years (Kelsen and Baldassano, <xref ref-type="bibr" rid="B24">2008</xref>). IBD severely affects normal growth and development of children. When treating children with newly diagnosed IBD, we need to consider their affects on growth and development and bone health (Rosen et al., <xref ref-type="bibr" rid="B48">2015</xref>).</p>
<p>In this manuscript, we used the proposed GPUDMDA method to find potential microbes associated with IBD. <xref ref-type="table" rid="T3">Tables 3</xref>, <xref ref-type="table" rid="T4">4</xref> show the predicted top 30 IBD-associated microbes on the two MDA databases. The predicted 30 IBD-associated microbes included microbes with known association information with IBD and microbes without association information with IBD. In total, 20 and 28 predicted IBD-associated microbes can be validated by databases or existing publications among all predicted top 30 microbes on the two databases, respectively. On HMDAD, GPUDMDA predicted that <italic>E. hormaechei</italic> could associate with IBD with the ranking of 7. On Disbiome, the former 28 microbes have been confirmed to associate with IBD, and GPUDMDA also identified that <italic>E. hormaechei</italic> could link with IBD with the ranking of 29.</p>
<table-wrap position="float" id="T3">
<label>Table 3</label>
<caption><p>The predicted top 30 microbes associated with IBD on HMDAD.</p></caption> 
<table frame="box" rules="all">
<thead>
<tr style="background-color:&#x00023;919498;color:&#x00023;ffffff">
<th valign="top" align="left"><bold>Rank</bold></th>
<th valign="top" align="left"><bold>Microbe</bold></th>
<th valign="top" align="left"><bold>Evidence</bold></th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left">1</td>
<td valign="top" align="left"><italic>Clostridium difficile</italic></td>
<td valign="top" align="left">PMID: 27499718</td>
</tr> <tr>
<td valign="top" align="left">2</td>
<td valign="top" align="left"><italic>Helicobacter pylori</italic></td>
<td valign="top" align="left">PMID: 22221289</td>
</tr> <tr>
<td valign="top" align="left">3</td>
<td valign="top" align="left"><italic>Staphylococcus</italic></td>
<td valign="top" align="left">PMID: 27239107</td>
</tr> <tr>
<td valign="top" align="left">4</td>
<td valign="top" align="left"><italic>Clostridia</italic></td>
<td valign="top" align="left">PMID: 31142855</td>
</tr> <tr>
<td valign="top" align="left">5</td>
<td valign="top" align="left"><italic>Clostridium coccoides</italic></td>
<td valign="top" align="left">PMID: 19235886</td>
</tr> <tr>
<td valign="top" align="left">6</td>
<td valign="top" align="left"><italic>Enterobacter aerogenes</italic></td>
<td valign="top" align="left">PMID: 4061480</td>
</tr> <tr>
<td valign="top" align="left">7</td>
<td valign="top" align="left"><italic>Enterobacter hormaechei</italic></td>
<td valign="top" align="left">Unconfirmed</td>
</tr> <tr>
<td valign="top" align="left">8</td>
<td valign="top" align="left"><italic>Klebsiella pneumoniae</italic></td>
<td valign="top" align="left">PMID: 9930068</td>
</tr> <tr>
<td valign="top" align="left">9</td>
<td valign="top" align="left"><italic>Shigella dysenteriae</italic></td>
<td valign="top" align="left">Unconfirmed</td>
</tr> <tr>
<td valign="top" align="left">10</td>
<td valign="top" align="left"><italic>Prevotella copri</italic></td>
<td valign="top" align="left">Unconfirmed</td>
</tr> <tr>
<td valign="top" align="left">11</td>
<td valign="top" align="left"><italic>Enterococcus</italic></td>
<td valign="top" align="left">PMID: 24629344</td>
</tr> <tr>
<td valign="top" align="left">12</td>
<td valign="top" align="left"><italic>Klebsiella</italic></td>
<td valign="top" align="left">PMID: 29573336</td>
</tr> <tr>
<td valign="top" align="left">13</td>
<td valign="top" align="left"><italic>Actinobacteria</italic></td>
<td valign="top" align="left">Confirmed by HMDAD</td>
</tr> <tr>
<td valign="top" align="left">14</td>
<td valign="top" align="left"><italic>Bifidobacterium</italic></td>
<td valign="top" align="left">PMID: 24478468</td>
</tr> <tr>
<td valign="top" align="left">15</td>
<td valign="top" align="left"><italic>Dietzia maris</italic></td>
<td valign="top" align="left">Unconfirmed</td>
</tr> <tr>
<td valign="top" align="left">16</td>
<td valign="top" align="left"><italic>Staphylococcus epidermidis</italic></td>
<td valign="top" align="left">Unconfirmed</td>
</tr> <tr>
<td valign="top" align="left">17</td>
<td valign="top" align="left"><italic>Oxalobacter formigenes</italic></td>
<td valign="top" align="left">Unconfirmed</td>
</tr> <tr>
<td valign="top" align="left">18</td>
<td valign="top" align="left"><italic>Tropheryma whipplei</italic></td>
<td valign="top" align="left">Unconfirmed</td>
</tr> <tr>
<td valign="top" align="left">19</td>
<td valign="top" align="left"><italic>Staphylococcus aureus</italic></td>
<td valign="top" align="left">PMID: 11424320</td>
</tr> <tr>
<td valign="top" align="left">20</td>
<td valign="top" align="left"><italic>Bacteroides vulgatus</italic></td>
<td valign="top" align="left">PMID: 29454108</td>
</tr> <tr>
<td valign="top" align="left">21</td>
<td valign="top" align="left"><italic>Actinomyces</italic></td>
<td valign="top" align="left">PMID: 30545401</td>
</tr> <tr>
<td valign="top" align="left">22</td>
<td valign="top" align="left"><italic>Porphyromonas gingivalis</italic></td>
<td valign="top" align="left">PMID: 31652577</td>
</tr> <tr>
<td valign="top" align="left">23</td>
<td valign="top" align="left"><italic>Selenomonas</italic></td>
<td valign="top" align="left">Unconfirmed</td>
</tr> <tr>
<td valign="top" align="left">24</td>
<td valign="top" align="left"><italic>Treponema</italic></td>
<td valign="top" align="left">PMID: 31851086</td>
</tr> <tr>
<td valign="top" align="left">25</td>
<td valign="top" align="left"><italic>Fusobacterium nucleatum</italic></td>
<td valign="top" align="left">PMID: 26718210</td>
</tr> <tr>
<td valign="top" align="left">26</td>
<td valign="top" align="left"><italic>Bacteroides ovatus</italic></td>
<td valign="top" align="left">PMID: 30666959</td>
</tr> <tr>
<td valign="top" align="left">27</td>
<td valign="top" align="left"><italic>Verrucomicrobiaceae</italic></td>
<td valign="top" align="left">PMID: 22572638</td>
</tr> <tr>
<td valign="top" align="left">28</td>
<td valign="top" align="left"><italic>Desulfovibrio</italic></td>
<td valign="top" align="left">Confirmed by Disbiome</td>
</tr> <tr>
<td valign="top" align="left">29</td>
<td valign="top" align="left"><italic>Clostridiales</italic></td>
<td valign="top" align="left">Unconfirmed</td>
</tr>
<tr>
<td valign="top" align="left">30</td>
<td valign="top" align="left"><italic>Escherichia coli</italic></td>
<td valign="top" align="left">PMID: 29573336</td>
</tr>
</tbody>
</table>
</table-wrap>
<table-wrap position="float" id="T4">
<label>Table 4</label>
<caption><p>The predicted top 30 microbes associated with IBD on Disbiome.</p></caption> 
<table frame="box" rules="all">
<thead>
<tr style="background-color:&#x00023;919498;color:&#x00023;ffffff">
<th valign="top" align="left"><bold>Rank</bold></th>
<th valign="top" align="left"><bold>Microbe</bold></th>
<th valign="top" align="left"><bold>Evidence</bold></th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left">1</td>
<td valign="top" align="left"><italic>Anaerostipes</italic></td>
<td valign="top" align="left">Confirmed by Disbiome</td>
</tr> <tr>
<td valign="top" align="left">2</td>
<td valign="top" align="left"><italic>Bacillus licheniformis</italic></td>
<td valign="top" align="left">Confirmed by Disbiome</td>
</tr> <tr>
<td valign="top" align="left">3</td>
<td valign="top" align="left"><italic>Blautia</italic></td>
<td valign="top" align="left">Confirmed by Disbiome</td>
</tr> <tr>
<td valign="top" align="left">4</td>
<td valign="top" align="left"><italic>Bradyrhizobiaceae</italic></td>
<td valign="top" align="left">Confirmed by Disbiome</td>
</tr> <tr>
<td valign="top" align="left">5</td>
<td valign="top" align="left"><italic>Butyricimonas</italic></td>
<td valign="top" align="left">Confirmed by Disbiome</td>
</tr> <tr>
<td valign="top" align="left">6</td>
<td valign="top" align="left"><italic>Comamonadaceae</italic></td>
<td valign="top" align="left">Confirmed by Disbiome</td>
</tr> <tr>
<td valign="top" align="left">7</td>
<td valign="top" align="left"><italic>Christensenellaceae</italic></td>
<td valign="top" align="left">Confirmed by Disbiome</td>
</tr> <tr>
<td valign="top" align="left">8</td>
<td valign="top" align="left"><italic>Dehalobacter</italic></td>
<td valign="top" align="left">Confirmed by Disbiome</td>
</tr> <tr>
<td valign="top" align="left">9</td>
<td valign="top" align="left"><italic>Desulfovibrio</italic></td>
<td valign="top" align="left">Confirmed by Disbiome</td>
</tr> <tr>
<td valign="top" align="left">10</td>
<td valign="top" align="left"><italic>Dorea formicigenerans</italic></td>
<td valign="top" align="left">Confirmed by Disbiome</td>
</tr> <tr>
<td valign="top" align="left">11</td>
<td valign="top" align="left"><italic>Eubacterium biforme</italic></td>
<td valign="top" align="left">Confirmed by Disbiome</td>
</tr> <tr>
<td valign="top" align="left">12</td>
<td valign="top" align="left"><italic>Gemella</italic></td>
<td valign="top" align="left">Confirmed by Disbiome</td>
</tr> <tr>
<td valign="top" align="left">13</td>
<td valign="top" align="left"><italic>Gluconobacter oxydan</italic>s</td>
<td valign="top" align="left">Confirmed by Disbiome</td>
</tr> <tr>
<td valign="top" align="left">14</td>
<td valign="top" align="left"><italic>Lachnobacterium</italic></td>
<td valign="top" align="left">Confirmed by Disbiome</td>
</tr> <tr>
<td valign="top" align="left">15</td>
<td valign="top" align="left"><italic>Methanobrevibacter smithii</italic></td>
<td valign="top" align="left">Confirmed by Disbiome</td>
</tr> <tr>
<td valign="top" align="left">16</td>
<td valign="top" align="left"><italic>Mogibacterium</italic></td>
<td valign="top" align="left">Confirmed by Disbiome</td>
</tr> <tr>
<td valign="top" align="left">17</td>
<td valign="top" align="left"><italic>Moraxellaceae</italic></td>
<td valign="top" align="left">Confirmed by Disbiome</td>
</tr> <tr>
<td valign="top" align="left">18</td>
<td valign="top" align="left"><italic>Pseudomonas straminea</italic></td>
<td valign="top" align="left">Confirmed by Disbiome</td>
</tr> <tr>
<td valign="top" align="left">19</td>
<td valign="top" align="left"><italic>Ruminococcus bromii</italic></td>
<td valign="top" align="left">Confirmed by Disbiome</td>
</tr> <tr>
<td valign="top" align="left">20</td>
<td valign="top" align="left"><italic>Saccharomyces cerevisiae</italic></td>
<td valign="top" align="left">Confirmed by Disbiome</td>
</tr> <tr>
<td valign="top" align="left">21</td>
<td valign="top" align="left"><italic>Streptococcus anginosus</italic></td>
<td valign="top" align="left">Confirmed by Disbiome</td>
</tr> <tr>
<td valign="top" align="left">22</td>
<td valign="top" align="left"><italic>Bacteroides ovatus</italic></td>
<td valign="top" align="left">PMID: 30666959</td>
</tr> <tr>
<td valign="top" align="left">23</td>
<td valign="top" align="left"><italic>Enterobacter aerogenes</italic></td>
<td valign="top" align="left">PMID: 4061480</td>
</tr> <tr>
<td valign="top" align="left">24</td>
<td valign="top" align="left"><italic>Fusobacterium</italic></td>
<td valign="top" align="left">PMID: 25307765</td>
</tr> <tr>
<td valign="top" align="left">25</td>
<td valign="top" align="left"><italic>Klebsiella pneumoniae</italic></td>
<td valign="top" align="left">PMID: 9930068</td>
</tr> <tr>
<td valign="top" align="left">26</td>
<td valign="top" align="left"><italic>Paraprevotella</italic></td>
<td valign="top" align="left">PMID: 25307765</td>
</tr> <tr>
<td valign="top" align="left">27</td>
<td valign="top" align="left"><italic>Propionibacterium acnes</italic></td>
<td valign="top" align="left">PMID: 28630242</td>
</tr> <tr>
<td valign="top" align="left">28</td>
<td valign="top" align="left"><italic>Staphylococcus</italic></td>
<td valign="top" align="left">PMID: 27239107</td>
</tr> <tr>
<td valign="top" align="left">29</td>
<td valign="top" align="left"><italic>Oxalobacteraceae</italic></td>
<td valign="top" align="left">Unconfirmed</td>
</tr>
<tr>
<td valign="top" align="left">30</td>
<td valign="top" align="left"><italic>Enterobacter hormaechei</italic></td>
<td valign="top" align="left">Unconfirmed</td>
</tr>
</tbody>
</table>
</table-wrap>
<p><xref ref-type="fig" rid="F7">Figure 7</xref> shows the association network between the predicted top 54 IBD-associated microbes and IBD, after removing the repeated associations on the two databases. In <xref ref-type="fig" rid="F7">Figure 7</xref>, the gray solid lines and blue dashed lines denote known associations between microbes and IBD and the predicted associations between microbes and IBD, respectively.</p>
<fig id="F7" position="float">
<label>Figure 7</label>
<caption><p>The predicted top 54 microbes associated with IBD on the two databases.</p></caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmicb-14-1244527-g0007.tif"/>
</fig></sec></sec></sec>
<sec id="s4">
<title>4. Discussion and conclusion</title>
<p>Microbes manifest dense relationships with various human complex diseases. Predicting underlying MDAs can contribute to analyzing complex disease-causing mechanisms and screening potential biomarkers for the diagnosis and therapy of these diseases. Traditional wet lab methods are expensive, time-consuming, and laborious. Consequently, <italic>in silico</italic> methods have been increasingly developed as an efficient complementary to experimental methods.</p>
<p>In this study, we developed a deep learning model called GPUDMDA to capture new linkages between microbes and various human complex diseases. GPUDMDA first computed disease similarity and microbe similarity matrices based on their functional similarity and GIPK similarity, respectively. Next, it extracted features for each microbe&#x02013;disease pair with GATE. Third, it selected a few reliable negative MDAs based on PU learning with <italic>K</italic>-means clustering and XGBoost. Finally, it took the extracted MDA features and the selected negative MDAs as inputs and designed a DNN to predict potential MDAs.</p>
<p>GPUDMDA was compared with four state-of-the-art MDA identification models (i.e., MNNMDA, GATMDA, LRLSHMDA, and NTSHMDA) on the HMDAD and Disbiome databases under five-fold CVs on microbes, diseases, and microbe&#x02013;disease pairs. Under the three CVs, GPUDMDA computed the best AUCs and AUPRs on the two databases, suggesting that GPUDMDA could improve MDA prediction performance. Finally, we implemented case studies for asthma and IBD. The results showed that <italic>E. hormaechei</italic> could densely associate with asthma and IBD and need further biological experimental validation.</p>
<p>In future, we will combine biological features of microbe, diseases, and MDA network to design more accurate negative MDA selection method. In addition, we will also develop novel deep learning model to improve MDA classification performance based on the selected reliable negative MDA samples. Interestingly, we have conducted several computational models including existing classical MDA prediction methods. But the results elucidated that many models failed to compute better AUPR on the Disbiome database. It may be caused by different data structures of Disbiome. In future, we will further design a better robust computational method to improve MDA prediction on the Disbiome database. We hope that the proposed GPUDMDA method helps to identify microbes associated with related diseases and further contributes to mining the clues of treatment.</p></sec>
<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. The HMDAD and Disbiome databases are available at: <ext-link ext-link-type="uri" xlink:href="http://www.cuilab.cn/hmdad">http://www.cuilab.cn/hmdad</ext-link> and <ext-link ext-link-type="uri" xlink:href="https://disbiome.ugent.be/">https://disbiome.ugent.be/</ext-link>, respectively. Accession numbers can be downloaded at <ext-link ext-link-type="uri" xlink:href="https://github.com/plhhnu/GPUDMDA">https://github.com/plhhnu/GPUDMDA</ext-link>.</p></sec>
<sec sec-type="author-contributions" id="s6">
<title>Author contributions</title>
<p>LP and LH: conceptualization and methodology. LP, ZL, and LD: funding acquisition. LP, GT, YW, ZL, and LD: project administration. LH: writing&#x02014;original draft and software. LP, LH, PW, and ZL: writing&#x02014;reviewing and editing. LP, LH, GT, GL, JC, and LD: investigation. LH, GL, JC, and LD: validation. All authors contributed to the article and approved the submitted version.</p></sec>
</body>
<back>
<sec sec-type="funding-information" id="s7">
<title>Funding</title>
<p>LD was supported by the National Natural Science Foundation of China under Grant No. 81500391. LP was supported by the National Natural Science Foundation of China under Grant No. 61803151 and the Natural Science Foundation of Hunan province Grant No. 2023JJ50201. ZL was supported by the National Natural Science Foundation of China under Grant No. 62172158. PW was supported by the Excellent Youth Project of Hunan Provincial Education Department Grant No. 21B0802.</p>
</sec>
<ack><p>The authors would like to thank all the authors of the cited references.</p>
</ack>
<sec sec-type="COI-statement" id="conf1">
<title>Conflict of interest</title>
<p>GT and YW were employed by Geneis (Beijing) Co. Ltd. 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&#x00027;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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