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<title>Classification double</title>

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<h1 id="firstHeading" class="firstHeading mw-first-heading">Classification double</h1>

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<div id="mw-content-text" class="mw-body-content mw-content-ltr" lang="fr" dir="ltr"><div class="mw-content-ltr mw-parser-output" lang="fr" dir="ltr">La Classification double ou « Biclustering » est une technique d'<a href="Exploration_de_donn%C3%A9es" title="Exploration de données">exploration de données</a> non-supervisée permettant de segmenter simultanément les lignes et les colonnes d'une matrice. Plus formellement<a href="#cite_note-1">[1]</a>, la définition de la classification double peut s'exprimer de la manière suivante (pour le type de classification par colonne) :

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<annotation encoding="application/x-tex">{\displaystyle \mathrm {E} }</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/be1811407dea8b43727d28dbe8da7251985b03e8.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.583ex; height:2.176ex;" alt="{\displaystyle \mathrm {E} }" loading="lazy"> une matrice <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {M} \times \mathrm {N} }">

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<annotation encoding="application/x-tex">{\displaystyle \mathrm {M} \times \mathrm {N} }</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/8e5805fb3c2e922fdc2e072f28cb92fe6c0d58fa.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.714ex; height:2.176ex;" alt="{\displaystyle \mathrm {M} \times \mathrm {N} }" loading="lazy">, soient <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {I} \subseteq \mathrm {M} {\text{ , }}J\subseteq \mathrm {N} }">

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<annotation encoding="application/x-tex">{\displaystyle \mathrm {I} \subseteq \mathrm {M} {\text{ , }}J\subseteq \mathrm {N} }</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/03e480a9c35e4659afba90d449cf5ea2a627409a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.19ex; height:2.509ex;" alt="{\displaystyle \mathrm {I} \subseteq \mathrm {M} {\text{ , }}J\subseteq \mathrm {N} }" loading="lazy">, alors <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {E} _{IJ}}">

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<annotation encoding="application/x-tex">{\displaystyle \mathrm {E} _{IJ}}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/251b444492e793f1f77fcd08433e5b3e60417692.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.684ex; height:2.509ex;" alt="{\displaystyle \mathrm {E} _{IJ}}" loading="lazy"> est appelé « bicluster » de <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {E} }">

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<annotation encoding="application/x-tex">{\displaystyle \mathrm {E} }</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/be1811407dea8b43727d28dbe8da7251985b03e8.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.583ex; height:2.176ex;" alt="{\displaystyle \mathrm {E} }" loading="lazy"> lorsque <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {E} _{i_{1},j}=\mathrm {E} _{i_{2},j}=..=\mathrm {E} _{i_{m},j}}">

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<annotation encoding="application/x-tex">{\displaystyle \mathrm {E} _{i_{1},j}=\mathrm {E} _{i_{2},j}=..=\mathrm {E} _{i_{m},j}}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/cf133230e5d8bdc58991f53bb6b5e78718eff099.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:23.624ex; height:2.843ex;" alt="{\displaystyle \mathrm {E} _{i_{1},j}=\mathrm {E} _{i_{2},j}=..=\mathrm {E} _{i_{m},j}}" loading="lazy"> pour tout <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle j\in J{\text{ et }}(i_{1},i_{2},...i_{m})\in \mathrm {M} }">

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<annotation encoding="application/x-tex">{\displaystyle j\in J{\text{ et }}(i_{1},i_{2},...i_{m})\in \mathrm {M} }</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/e1fab5248ebf18e22c13209b4cf92a2679dbf074.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.027ex; width:26.537ex; height:2.843ex;" alt="{\displaystyle j\in J{\text{ et }}(i_{1},i_{2},...i_{m})\in \mathrm {M} }" loading="lazy"></div>

<div class="mw-heading mw-heading2"><h2 id="Application">Application</h2></div>

Le « biclustering » a été utilisé massivement en biologie<a href="#cite_note-2">[2]</a> - par exemple dans l'analyse de l'<a href="Expression_g%C3%A9n%C3%A9tique" class="mw-redirect" title="Expression génétique">expression génétique</a> par Yizong Cheng et George M. Church<a href="#cite_note-3">[3]</a> , <a href="#cite_note-4">[4]</a> -, mais aussi dans d'autres domaines tels que la compression d'image de synthèse<a href="#cite_note-5">[5]</a>, l'analyse médicale - par exemple pour l'étude des traitements de l'épilepsie<a href="#cite_note-6">[6]</a> par <a href="Stimulation_vagale" title="Stimulation vagale">stimulation vagale</a>, la caractérisation d'émetteurs de <a href="Spam" title="Spam">pourriels</a> (« spam »)<a href="#cite_note-7">[7]</a>, l'analyse du mouvement<a href="#cite_note-8">[8]</a>, l'analyse des termes publicitaires sur internet<a href="#cite_note-9">[9]</a>, ...

<div class="mw-heading mw-heading2"><h2 id="Types">Types</h2></div>

Dans les différents algorithmes qui utilisent la classification double, on trouve différents types de bicluster :

<ul><li>« Bi-cluster » à valeurs constantes (a),</li>

<li>« Bi-cluster » à valeurs constantes en lignes (b) ou en colonnes (c),</li>

<li>« Bi-cluster » à valeurs cohérentes (d, e).</li></ul>

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<caption>a) « Bi-cluster » à valeurs constantes

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<td>7,6

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<td>7,6

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<td>7,6

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<td>7,6

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<td>7,6

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<caption>b)« Bi-cluster » à valeurs constantes en lignes

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<td>1,2

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<td>2,1

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<td>3,2

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<td>4,1

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<td>4,2

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<caption>c)« Bi-cluster » à valeurs constantes en colonnes

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<td>5,0

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<td>5,0

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<td>5,0

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<td>5,0

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<td>5,0

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<caption>d) « Bi-cluster » à valeurs cohérentes (additives)

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<td>1.5

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<td>4.5

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<td>3.5

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<td>5.5

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<td>2.5

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<caption>e)« Bi-cluster » à valeurs cohérentes (multiplicative)

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<td>0.8

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<td>1.6

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<td>2.4

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<td>3.2

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<td>4.0

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En d) la notion d'additivité se comprend comme ceci : <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle +3,-1,+2,-3}">

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<annotation encoding="application/x-tex">{\displaystyle +3,-1,+2,-3}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/9fa13df7ac89536c20a5cb059a6eda5b8f69e0ce.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.984ex; height:2.509ex;" alt="{\displaystyle +3,-1,+2,-3}" loading="lazy"> en colonnes, <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle +3,+1,-5,+1,5}">

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<annotation encoding="application/x-tex">{\displaystyle +3,+1,-5,+1,5}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/ab54ede491b66348b93086cdd77d09020e72057d.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:17.181ex; height:2.509ex;" alt="{\displaystyle +3,+1,-5,+1,5}" loading="lazy"> en lignes; en e) le motif est <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {1}{2}},*4,{\frac {1}{10}},*4}">

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<annotation encoding="application/x-tex">{\displaystyle {\frac {1}{2}},*4,{\frac {1}{10}},*4}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/fd62ec8ba49f45f99dd2ef169880d08984f8c0f7.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:12.911ex; height:5.176ex;" alt="{\displaystyle {\frac {1}{2}},*4,{\frac {1}{10}},*4}" loading="lazy"> en colonnes et <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle *2,*1.5,{\frac {4}{3}},{\frac {5}{4}}}">

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<annotation encoding="application/x-tex">{\displaystyle *2,*1.5,{\frac {4}{3}},{\frac {5}{4}}}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/33884fffd8b17ec14e192772d57390dbf4de31de.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:13.558ex; height:5.176ex;" alt="{\displaystyle *2,*1.5,{\frac {4}{3}},{\frac {5}{4}}}" loading="lazy">.

<div class="mw-heading mw-heading2"><h2 id="Algorithmes">Algorithmes</h2></div>

Le but des algorithmes de classification double est de trouver, s'il existe, le plus grand « bi-cluster » contenu dans une matrice, en maximisant une <a href="Fonction_objectif" title="Fonction objectif">fonction objectif</a>. On peut prendre comme fonction, avec les notations adoptées ci-dessus : <div class="center"> <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f_{1}=\left|\mathrm {I} \right|+\left|J\right|}">

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<annotation encoding="application/x-tex">{\displaystyle f_{1}=\left|\mathrm {I} \right|+\left|J\right|}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/b6f307c33f328e372d0eee7087d3bba95ccfc154.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.031ex; height:2.843ex;" alt="{\displaystyle f_{1}=\left|\mathrm {I} \right|+\left|J\right|}" loading="lazy"> ou <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f_{2}=\left|\mathrm {I} \right|*\left|J\right|}">

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<annotation encoding="application/x-tex">{\displaystyle f_{2}=\left|\mathrm {I} \right|*\left|J\right|}</annotation>

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</math><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/da319df8b09f5aebb80ad9ca47401722fedbad1a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.385ex; height:2.843ex;" alt="{\displaystyle f_{2}=\left|\mathrm {I} \right|*\left|J\right|}" loading="lazy"><a href="#cite_note-10">[10]</a></div>

De nombreux algorithmes ont été développés notamment par la <a href="Bio-informatique" title="Bio-informatique">bio-informatique</a>, dont :

« Block clustering », CTWC (« Coupled Two-Way Clustering ») , ITWC (« Interrelated Two-Way Clustering »), δ-bicluster, δ-pCluster, δ-pattern, FLOC, OPC, « Plaid Model », OPSMs (« Order-preserving submatrixes »), Gibbs, SAMBA (« Statistical-Algorithmic Method for Bicluster Analysis »)<a href="#cite_note-11">[11]</a>, RoBA (« Robust Biclustering Algorithm »), « Crossing Minimization »<a href="#cite_note-ahsan-12">[12]</a>

, cMonkey<a href="#cite_note-13">[13]</a>, PRMs, DCC, LEB (« Localize and Extract Biclusters »), QUBIC (« QUalitative BIClustering »), BCCA (« Bi-Correlation Clustering Algorithm »), FABIA (« Factor Analysis for Bicluster Acquisition »)<a href="#cite_note-14">[14]</a>. Certains de ces algorithmes ont été comparés par Doruk Bozda, Ashwin S. Kumar et Umit V. Catalyurek<a href="#cite_note-15">[15]</a> en termes de type de motifs recherchés.

Le package « biclust »<a href="#cite_note-16">[16]</a> propose un ensemble d'outils pour la classification double dans le <a href="R_(logiciel)" class="mw-redirect" title="R (logiciel)">logiciel R</a>.

<div class="mw-heading mw-heading2"><h2 id="Articles_connexes">Articles connexes</h2></div>

<ul><li><a href="Classification" title="Classification">Classification</a></li>

<li><a href="Classification_automatique" class="mw-redirect" title="Classification automatique">Classification automatique</a></li>

<li><a href="Segmentation_(sciences_humaines)" title="Segmentation (sciences humaines)">Segmentation (sciences humaines)</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="Notes_et_références">Notes et références</h2></div>

<div style="font-size:85%; padding-left:1.6em; margin:0.3em 0;"><abbr class="abbr indicateur-langue" title="Langue : anglais">(en)</abbr> Cet article est partiellement ou en totalité issu de l’article de Wikipédia en anglais intitulé « <a class="external text" href="https://en.wikipedia.org/wiki/Biclustering?oldid=412909627">Biclustering</a> » (<a class="external text" href="https://en.wikipedia.org/wiki/Biclustering?action=history">voir la liste des auteurs</a>).</div>

<li id="cite_note-1"><a href="#cite_ref-1">↑</a> Tran Trang, Nguyen Cam Chi, Hoang Ngoc Minh,<a rel="nofollow" class="external text" href="http://www.genopole-lille.fr/spip/IMG/pdf/TSI_Post_Genomique.pdf">Bi-clustering des données de biopuces par les arbres pondérés de plus long préﬁxe - Chapitre 1 Introduction</a>

</li>

<li id="cite_note-2"><a href="#cite_ref-2">↑</a> Sara C. Madeira, Arlindo L. Oliveira,<a rel="nofollow" class="external text" href="http://www.cs.princeton.edu/courses/archive/spr05/cos598E/Biclustering.pdf">Biclustering Biological Data Analysis</a>

</li>

<li id="cite_note-3"><a href="#cite_ref-3">↑</a> <abbr class="abbr indicateur-langue" title="Langue : anglais">(en)</abbr> Cheng Y, Church GM, « <cite style="font-style:normal" lang="en">Biclustering of expression data</cite> », Proceedings of the 8th International Conference on Intelligent Systems for Molecular Biology,‎ <time>2000</time>, <abbr class="abbr" title="pages">p.</abbr> 93–103<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Biclustering+of+expression+data&rft.jtitle=Proceedings+of+the+8th+International+Conference+on+Intelligent+Systems+for+Molecular+Biology&rft.au=Cheng+Y%2C+Church+GM&rft.date=2000&rft.pages=93%E2%80%93103&rfr_id=info%3Asid%2Ffr.wikipedia.org%3AClassification+double">

</li>

<li id="cite_note-4"><a href="#cite_ref-4">↑</a> Yizong Cheng, George M. Church <a rel="nofollow" class="external text" href="ftp://ftp.npaci.edu/pub/sdsc/biology/ISMB00/157.pdf">Biclustering of Expression Data</a>

</li>

<li id="cite_note-5"><a href="#cite_ref-5">↑</a> Xin Sun, Qiming Hou,Zhong Ren, Kun Zhou, Baining Guo,<a rel="nofollow" class="external text" href="http://www.kunzhou.net/2010/biclustering-preprint.pdf">Radiance Transfer Biclustering for Real-time All-frequency Bi-scale Rendering</a>

</li>

<li id="cite_note-6"><a href="#cite_ref-6">↑</a> Stanislav Busygin,Nikita Boyko, Panos M. Pardalos,Michael Bewernitz, Georges Ghacibeh,<a rel="nofollow" class="external text" href="http://www.ise.ufl.edu/cao/Book_DMSAOB/014busygin.pdf">Biclustering EEG data from epileptic patients treated with vagus nerve stimulation</a>

</li>

<li id="cite_note-7"><a href="#cite_ref-7">↑</a> Kevin S. Xu, Mark Kliger, Alfred O. Hero III, <a rel="nofollow" class="external text" href="http://www.eecs.umich.edu/~xukevin/xu_spam_dm_2010_poster.pdf">Identifying Spammers by Their Resource Usage Patterns</a>

</li>

<li id="cite_note-8"><a href="#cite_ref-8">↑</a> Keren Erez, Jacob Goldberger, Ronen Sosnik, Moshe Shemesh, Susan Rothstein,Moshe Abeles, <a rel="nofollow" class="external text" href="http://www.eng.biu.ac.il/~goldbej/papers/JCNS_2009.pdf">Analyzing Movement Trajectories Using a Markov Bi-Clustering Method</a>

</li>

<li id="cite_note-9"><a href="#cite_ref-9">↑</a> Dmitry I. Ignatov, <a rel="nofollow" class="external text" href="http://reasoningweb.org/2010/participants-material/paper_ignatov.pdf">Concept-based Biclustering for Internet Advertisement </a>

</li>

<li id="cite_note-10"><a href="#cite_ref-10">↑</a> Stefano Lonardi, Qiaofeng Yang, Wojciech Szpankowski,<a rel="nofollow" class="external text" href="http://www.cs.ucr.edu/~stelo/cpm/cpm04/08_Lonardi.pdf">Finding biclusters by random projections</a>

</li>

<abbr class="abbr indicateur-langue" title="Langue : anglais">(en)</abbr> Tanay A, Sharan R, Kupiec M and Sahmir R, « <cite style="font-style:normal" lang="en">Revealing modularity and organization in the yeast molecular network by integrated analysis of highly heterogeneous genomewide data</cite> », Proc Natl Acad Sci USA, <abbr class="abbr" title="volume">vol.</abbr> 101, <abbr class="abbr" title="numéro">no</abbr> 9,‎ <time>2004</time>, <abbr class="abbr" title="pages">p.</abbr> 2981-2986 (<a href="PubMed" title="PubMed">PMID</a> <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pubmed/16749936">16749936</a>, <a href="PubMed_Central" title="PubMed Central">PMCID</a> <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/14973197">14973197</a>, <a href="Digital_Object_Identifier" title="Digital Object Identifier">DOI</a> <a rel="nofollow" class="external text" href="https://dx.doi.org/10.1073/pnas.0308661100">10.1073/pnas.0308661100</a>)<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Revealing+modularity+and+organization+in+the+yeast+molecular+network+by+integrated+analysis+of+highly+heterogeneous+genomewide+data&rft.jtitle=Proc+Natl+Acad+Sci+USA&rft.issue=9&rft.au=Tanay+A%2C+Sharan+R%2C+Kupiec+M+and+Sahmir+R&rft.date=2004&rft.volume=101&rft.pages=2981-2986&rft_id=info%3Adoi%2F10.1073%2Fpnas.0308661100&rft_id=info%3Apmid%2F16749936&rfr_id=info%3Asid%2Ffr.wikipedia.org%3AClassification+double">

</li>

<li id="cite_note-ahsan-12"><a href="#cite_ref-ahsan_12-0">↑</a> Ahsan Abdullah, <a rel="nofollow" class="external text" href="http://dspacedev.stir.ac.uk/bitstream/1893/252/3/Thesis-AhsanAbdullah-2007.pdf">Data Mining Using the Crossing Minimization Paradigm</a>

</li>

<abbr class="abbr indicateur-langue" title="Langue : anglais">(en)</abbr> Reiss DJ, Baliga NS, Bonneau R, « <cite style="font-style:normal" lang="en">Integrated biclustering of heterogeneous genome-wide datasets for the inference of global regulatory networks</cite> », BMC Bioinformatics, <abbr class="abbr" title="volume">vol.</abbr> 2, <abbr class="abbr" title="numéro">no</abbr> 7,‎ <time>2006</time>, <abbr class="abbr" title="pages">p.</abbr> 280–302 (<a href="PubMed" title="PubMed">PMID</a> <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pubmed/16749936">16749936</a>, <a href="PubMed_Central" title="PubMed Central">PMCID</a> <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/1502140">1502140</a>, <a href="Digital_Object_Identifier" title="Digital Object Identifier">DOI</a> <a rel="nofollow" class="external text" href="https://dx.doi.org/10.1186/1471-2105-7-280">10.1186/1471-2105-7-280</a>)<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Integrated+biclustering+of+heterogeneous+genome-wide+datasets+for+the+inference+of+global+regulatory+networks&rft.jtitle=BMC+Bioinformatics&rft.issue=7&rft.au=Reiss+DJ%2C+Baliga+NS%2C+Bonneau+R&rft.date=2006&rft.volume=2&rft.pages=280%E2%80%93302&rft_id=info%3Adoi%2F10.1186%2F1471-2105-7-280&rft_id=info%3Apmid%2F16749936&rfr_id=info%3Asid%2Ffr.wikipedia.org%3AClassification+double">

</li>

<abbr class="abbr indicateur-langue" title="Langue : anglais">(en)</abbr> Hochreiter S, Bodenhofer U, Heusel M, Mayr A, Mitterecker A, Kasim A, Khamiakova T, Van Sanden S, Lin D, Talloen W, Bijnens L, Gohlmann HWH, Shkedy Z, Clevert DA, « <cite style="font-style:normal" lang="en">FABIA: factor analysis for bicluster acquisition</cite> », Bioinformatics, <abbr class="abbr" title="volume">vol.</abbr> 26, <abbr class="abbr" title="numéro">no</abbr> 12,‎ <time>2010</time>, <abbr class="abbr" title="pages">p.</abbr> 1520–1527 (<a href="PubMed" title="PubMed">PMID</a> <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pubmed/20418340">20418340</a>, <a href="PubMed_Central" title="PubMed Central">PMCID</a> <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/2881408">2881408</a>, <a href="Digital_Object_Identifier" title="Digital Object Identifier">DOI</a> <a rel="nofollow" class="external text" href="https://dx.doi.org/10.1093/bioinformatics/btq227">10.1093/bioinformatics/btq227</a>)<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=FABIA%3A+factor+analysis+for+bicluster+acquisition&rft.jtitle=Bioinformatics&rft.issue=12&rft.au=Hochreiter+S%2C+Bodenhofer+U%2C+Heusel+M%2C++Mayr+A%2C+Mitterecker+A%2C+Kasim+A%2C+Khamiakova+T%2C+Van+Sanden+S%2C+Lin+D%2C+Talloen+W%2C++Bijnens+L%2C+Gohlmann+HWH%2C+Shkedy+Z%2C+Clevert+DA&rft.date=2010&rft.volume=26&rft.pages=1520%E2%80%931527&rft_id=info%3Adoi%2F10.1093%2Fbioinformatics%2Fbtq227&rft_id=info%3Apmid%2F20418340&rfr_id=info%3Asid%2Ffr.wikipedia.org%3AClassification+double">

</li>

<li id="cite_note-15"><a href="#cite_ref-15">↑</a> Doruk Bozda, Ashwin S. Kumar et Umit V. Catalyurek, <a rel="nofollow" class="external text" href="http://bmi.osu.edu/hpc/papers/Bozdag10-BCB.pdf">Comparative Analysis of Biclustering Algorithms</a>

</li>

<li id="cite_note-16"><a href="#cite_ref-16">↑</a> Sebastian Kaiser, Friedrich Leisch, <a rel="nofollow" class="external text" href="http://epub.ub.uni-muenchen.de/3293/1/S_Kaiser_biclust.pdf">A Toolbox for Bicluster Analysis in R</a>

</li>

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