{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,12]],"date-time":"2026-03-12T00:28:27Z","timestamp":1773275307921,"version":"3.50.1"},"reference-count":34,"publisher":"Springer Science and Business Media LLC","issue":"1","content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["BMC Bioinformatics"],"published-print":{"date-parts":[[2008,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:sec><jats:title>Background<\/jats:title><jats:p>In DNA microarray experiments, discovering groups of genes that share similar transcriptional characteristics is instrumental in functional annotation, tissue classification and motif identification. However, in many situations a subset of genes only exhibits consistent pattern over a subset of conditions. Conventional clustering algorithms that deal with the entire row or column in an expression matrix would therefore fail to detect these useful patterns in the data. Recently, biclustering has been proposed to detect a subset of genes exhibiting consistent pattern over a subset of conditions. However, most existing biclustering algorithms are based on searching for sub-matrices within a data matrix by optimizing certain heuristically defined merit functions. Moreover, most of these algorithms can only detect a restricted set of bicluster patterns.<\/jats:p><\/jats:sec><jats:sec><jats:title>Results<\/jats:title><jats:p>In this paper, we present a novel geometric perspective for the biclustering problem. The biclustering process is interpreted as the detection of linear geometries in a high dimensional data space. Such a new perspective views biclusters with different patterns as hyperplanes in a high dimensional space, and allows us to handle different types of linear patterns simultaneously by matching a specific set of linear geometries. This geometric viewpoint also inspires us to propose a generic bicluster pattern, i.e. the linear coherent model that unifies the seemingly incompatible additive and multiplicative bicluster models. As a particular realization of our framework, we have implemented a Hough transform-based hyperplane detection algorithm. The experimental results on human lymphoma gene expression dataset show that our algorithm can find biologically significant subsets of genes.<\/jats:p><\/jats:sec><jats:sec><jats:title>Conclusion<\/jats:title><jats:p>We have proposed a novel geometric interpretation of the biclustering problem. We have shown that many common types of bicluster are just different spatial arrangements of hyperplanes in a high dimensional data space. An implementation of the geometric framework using the Fast Hough transform for hyperplane detection can be used to discover biologically significant subsets of genes under subsets of conditions for microarray data analysis.<\/jats:p><\/jats:sec>","DOI":"10.1186\/1471-2105-9-209","type":"journal-article","created":{"date-parts":[[2008,4,24]],"date-time":"2008-04-24T06:13:55Z","timestamp":1209017635000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":69,"title":["Discovering biclusters in gene expression data based on high-dimensional linear geometries"],"prefix":"10.1186","volume":"9","author":[{"given":"Xiangchao","family":"Gan","sequence":"first","affiliation":[]},{"given":"Alan Wee-Chung","family":"Liew","sequence":"additional","affiliation":[]},{"given":"Hong","family":"Yan","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2008,4,23]]},"reference":[{"issue":"5","key":"2194_CR1","doi-asserted-by":"publisher","first-page":"504","DOI":"10.1053\/ejso.2001.1116","volume":"27","author":"DA Rew","year":"2001","unstructured":"Rew DA: DNA microarray technology in cancer research. European Journal of Surgical Oncology. 2001, 27 (5): 504-508.","journal-title":"European Journal of Surgical Oncology"},{"issue":"5439","key":"2194_CR2","doi-asserted-by":"publisher","first-page":"531","DOI":"10.1126\/science.286.5439.531","volume":"286","author":"TR Golub","year":"1999","unstructured":"Golub TR, Slonim DK, Tamayo P, Huard C, Gaasenbeek M, Mesirov JP, Coller H, Loh ML, Downing JR, Caligiuri MA: Molecular classification of cancer: class discovery and class prediction by gene expression monitoring. Science. 1999, 286 (5439): 531-537.","journal-title":"Science"},{"issue":"5499","key":"2194_CR3","doi-asserted-by":"publisher","first-page":"2144","DOI":"10.1126\/science.290.5499.2144","volume":"290","author":"MT Laub","year":"2000","unstructured":"Laub MT, McAdams HH, Feldblyum T, Fraser CM, Shapiro L: Global analysis of the genetic network controlling a bacterial cell cycle. Science. 2000, 290 (5499): 2144-2148.","journal-title":"Science"},{"issue":"5338","key":"2194_CR4","doi-asserted-by":"publisher","first-page":"680","DOI":"10.1126\/science.278.5338.680","volume":"278","author":"JL DeRisi","year":"1997","unstructured":"DeRisi JL, Iyer VR, Brown PO: Exploring the metabolic and genetic control of gene expression on a genomic scale. Science. 1997, 278 (5338): 680-686.","journal-title":"Science"},{"issue":"3","key":"2194_CR5","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1038\/10343","volume":"22","author":"S Tavazoie","year":"1999","unstructured":"Tavazoie S, Hughes JD, Campbell MJ, Cho RJ, Church GM: Systematic determination of genetic network architecture. Nature genetics. 1999, 22 (3): 281-285.","journal-title":"Nature genetics"},{"issue":"25","key":"2194_CR6","doi-asserted-by":"publisher","first-page":"14863","DOI":"10.1073\/pnas.95.25.14863","volume":"95","author":"MB Eisen","year":"1998","unstructured":"Eisen MB, Spellman PT, Brown PO, Botstein D: Cluster analysis and display of genome-wide expression patterns. Proceedings of the National Academy of Sciences of the United States of America. 1998, 95 (25): 14863-14868.","journal-title":"Proceedings of the National Academy of Sciences of the United States of America"},{"issue":"6","key":"2194_CR7","doi-asserted-by":"publisher","first-page":"2907","DOI":"10.1073\/pnas.96.6.2907","volume":"96","author":"P Tamayo","year":"1999","unstructured":"Tamayo P, Slonim D, Mesirov J, Zhu Q, Kitareewan S, Dmitrovsky E, Lander ES, Golub TR: Interpreting patterns of gene expression with self-organizing maps: methods and application to hematopoietic differentiation. Proceedings of the National Academy of Sciences of the United States of America. 1999, 96 (6): 2907-2912.","journal-title":"Proceedings of the National Academy of Sciences of the United States of America"},{"issue":"1","key":"2194_CR8","doi-asserted-by":"publisher","first-page":"24","DOI":"10.1109\/TCBB.2004.2","volume":"1","author":"SC Madeira","year":"2004","unstructured":"Madeira SC, Oliveira AL: Biclustering algorithms for biological data analysis: a survey. IEEE\/ACM Trans Comput Biol Bioinform. 2004, 1 (1): 24-45.","journal-title":"IEEE\/ACM Trans Comput Biol Bioinform"},{"key":"2194_CR9","doi-asserted-by":"publisher","first-page":"280","DOI":"10.1186\/1471-2105-7-280","volume":"7","author":"DJ Reiss","year":"2006","unstructured":"Reiss DJ, Baliga NS, Bonneau R: Integrated biclustering of heterogeneous genome-wide datasets for the inference of global regulatory networks. BMC bioinformatics. 2006, 7: 280-","journal-title":"BMC bioinformatics"},{"issue":"Suppl 1","key":"2194_CR10","doi-asserted-by":"publisher","first-page":"S136","DOI":"10.1093\/bioinformatics\/18.suppl_1.S136","volume":"18","author":"A Tanay","year":"2002","unstructured":"Tanay A, Sharan R, Shamir R: Discovering statistically significant biclusters in gene expression data. Bioinformatics. 2002, 18 (Suppl 1): S136-144.","journal-title":"Bioinformatics"},{"issue":"337","key":"2194_CR11","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1080\/01621459.1972.10481214","volume":"67","author":"JA Hartigan","year":"1972","unstructured":"Hartigan JA: Direct Clustering of a Data Matrix. Journal of the American Statistical Association. 1972, 67 (337): 123-129.","journal-title":"Journal of the American Statistical Association"},{"issue":"22","key":"2194_CR12","doi-asserted-by":"publisher","first-page":"12079","DOI":"10.1073\/pnas.210134797","volume":"97","author":"G Getz","year":"2000","unstructured":"Getz G, Levine E, Domany E: Coupled two-way clustering analysis of gene microarray data. Proceedings of the National Academy of Sciences of the United States of America. 2000, 97 (22): 12079-12084.","journal-title":"Proceedings of the National Academy of Sciences of the United States of America"},{"key":"2194_CR13","first-page":"75","volume-title":"Proceedings of the International Conference on Intelligent Systems for Molecular Biology","author":"A Califano","year":"2000","unstructured":"Califano A, Stolovitzky G, Tu Y: Analysis of gene expression microarrays for phenotype classification. Proceedings of the International Conference on Intelligent Systems for Molecular Biology. 2000, 75-85."},{"issue":"suppl_2","key":"2194_CR14","doi-asserted-by":"crossref","first-page":"ii196","DOI":"10.1093\/bioinformatics\/btg1078","volume":"19","author":"Q Sheng","year":"2003","unstructured":"Sheng Q, Moreau Y, De Moor B: Biclustering microarray data by Gibbs sampling. Bioinformatics. 2003, 19 (suppl_2): ii196-205.","journal-title":"Bioinformatics"},{"key":"2194_CR15","volume-title":"Proceedings of the Eighth International Conference on Intelligent Systems for Molecular Biology","author":"Y Cheng","year":"2000","unstructured":"Cheng Y, Church GM: Biclustering of Expression Data. Proceedings of the Eighth International Conference on Intelligent Systems for Molecular Biology. 2000, AAAI Press"},{"key":"2194_CR16","first-page":"114","volume-title":"Proceedings of the Fourth SIAM International Conference on Data Mining","author":"H Cho","year":"2004","unstructured":"Cho H, Dhillon I, Guan Y, Sra S: Minimum sum squared residue co-clustering of gene expression data. Proceedings of the Fourth SIAM International Conference on Data Mining. 2004, 114-125."},{"issue":"1","key":"2194_CR17","first-page":"61","volume":"12","author":"L Lazzeroni","year":"2002","unstructured":"Lazzeroni L, Owen AB: Plaid models for gene expression data. Statistica Sinica. 2002, 12 (1): 61-86.","journal-title":"Statistica Sinica"},{"issue":"9","key":"2194_CR18","doi-asserted-by":"publisher","first-page":"1122","DOI":"10.1093\/bioinformatics\/btl060","volume":"22","author":"A Prelic","year":"2006","unstructured":"Prelic A, Bleuler S, Zimmermann P, Wille A, Buhlmann P, Gruissem W, Hennig L, Thiele L, Zitzler E: A systematic comparison and evaluation of biclustering methods for gene expression data. Bioinformatics. 2006, 22 (9): 1122-1129.","journal-title":"Bioinformatics"},{"issue":"4","key":"2194_CR19","doi-asserted-by":"publisher","first-page":"703","DOI":"10.1101\/gr.648603","volume":"13","author":"Y Kluger","year":"2003","unstructured":"Kluger Y, Basri R, Chang JT, Gerstein M: Spectral biclustering of microarray data: coclustering genes and conditions. Genome Res. 2003, 13 (4): 703-716.","journal-title":"Genome Res"},{"key":"2194_CR20","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1109\/BIBE.2001.974410","volume-title":"Proceedings of the IEEE 2nd International Symposium on Bioinformatics and Bioengineering Conference","author":"C Tang","year":"2001","unstructured":"Tang C, Zhang L, Zhang A, Ramanathan M: Interrelated two-way clustering: an unsupervised approach for gene expression data analysis. Proceedings of the IEEE 2nd International Symposium on Bioinformatics and Bioengineering Conference. 2001, 41-48."},{"key":"2194_CR21","first-page":"3388","volume-title":"Proceedings of the International Conference on Machine Learning and Cybernetics","author":"X Gan","year":"2005","unstructured":"Gan X, Liew AWC, Yan H: Biclustering gene expression data based on a high dimensional geometric method. Proceedings of the International Conference on Machine Learning and Cybernetics. 2005, 3388-3393."},{"issue":"6769","key":"2194_CR22","doi-asserted-by":"publisher","first-page":"503","DOI":"10.1038\/35000501","volume":"403","author":"AA Alizadeh","year":"2000","unstructured":"Alizadeh AA, Eisen MB, Davis RE, Ma C, Lossos IS, Rosenwald A, Boldrick JC, Sabet H, Tran T, Yu X: Distinct types of diffuse large B-cell lymphoma identified by gene expression profiling. Nature. 2000, 403 (6769): 503-511.","journal-title":"Nature"},{"issue":"5","key":"2194_CR23","doi-asserted-by":"publisher","first-page":"1608","DOI":"10.1093\/nar\/gkl047","volume":"34","author":"X Gan","year":"2006","unstructured":"Gan X, Liew AWC, Yan H: Microarray missing data imputation based on a set theoretic framework and biological knowledge. Nucleic Acids Res. 2006, 34 (5): 1608-1619.","journal-title":"Nucleic Acids Res"},{"key":"2194_CR24","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1145\/565196.565203","volume-title":"Proceedings of the Sixth Annual International Conference on Computational Biology","author":"A Ben-Dor","year":"2002","unstructured":"Ben-Dor A, Chor B, Karp R, Yakhini Z: Discovering local structure in gene expression data: the order-preserving submatrix problem. Proceedings of the Sixth Annual International Conference on Computational Biology. 2002, 49-57."},{"issue":"4","key":"2194_CR25","doi-asserted-by":"crossref","first-page":"370","DOI":"10.1038\/ng941","volume":"31","author":"J Ihmels","year":"2002","unstructured":"Ihmels J, Friedlander G, Bergmann S, Sarig O, Ziv Y, Barkai N: Revealing modular organization in the yeast transcriptional network. Nature genetics. 2002, 31 (4): 370-377.","journal-title":"Nature genetics"},{"key":"2194_CR26","first-page":"77","volume-title":"Proceedings of the Pacific Symposium on Biocomputing","author":"TM Murali","year":"2003","unstructured":"Murali TM, Kasif S: Extracting conserved gene expression motifs from gene expression data. Proceedings of the Pacific Symposium on Biocomputing. 2003, 77-88."},{"issue":"18","key":"2194_CR27","doi-asserted-by":"publisher","first-page":"2502","DOI":"10.1093\/bioinformatics\/btg363","volume":"19","author":"GF Berriz","year":"2003","unstructured":"Berriz GF, King OD, Bryant B, Sander C, Roth FP: Characterizing gene sets with FuncAssociate. Bioinformatics. 2003, 19 (18): 2502-2504.","journal-title":"Bioinformatics"},{"key":"2194_CR28","volume-title":"Resampling-based multiple testing: examples and methods for P-value adjustment","author":"PH Westfall","year":"1993","unstructured":"Westfall PH, Young SS: Resampling-based multiple testing: examples and methods for P-value adjustment. 1993, New York, Chichester, Wiley"},{"issue":"1","key":"2194_CR29","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1111\/j.1541-0420.2007.00843.x","volume":"64","author":"HD Bondell","year":"2008","unstructured":"Bondell HD, Reich BJ: Simultaneous Regression Shrinkage, Variable Selection, and Supervised Clustering of Predictors with OSCAR. Biometrics. 2008, 64 (1): 115-123.","journal-title":"Biometrics"},{"key":"2194_CR30","volume-title":"Computer vision","author":"DH Ballard","year":"1982","unstructured":"Ballard DH, Brown CM: Computer vision. 1982, Englewood Cliffs, N.J., Prentice-Hall"},{"key":"2194_CR31","doi-asserted-by":"publisher","first-page":"256","DOI":"10.1186\/1471-2105-8-256","volume":"8","author":"H Zhao","year":"2007","unstructured":"Zhao H, Yan H: HoughFeature, a novel method for assessing drug effects in three-color cDNA microarray experiments. BMC Bioinformatics. 2007, 8: 256-","journal-title":"BMC Bioinformatics"},{"issue":"2","key":"2194_CR32","doi-asserted-by":"publisher","first-page":"264","DOI":"10.1016\/j.jtbi.2007.11.030","volume":"251","author":"H Zhao","year":"2008","unstructured":"Zhao H, Liew AW, Xie X, Yan H: A new geometric biclustering algorithm based on the Hough transform for analysis of large-scale microarray data. J Theor Biol. 2008, 251 (2): 264-274.","journal-title":"J Theor Biol"},{"issue":"1","key":"2194_CR33","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1016\/S0734-189X(88)80033-1","volume":"44","author":"J Illingworth","year":"1988","unstructured":"Illingworth J, Kittler J: A survey of the Hough transform. Comput Vision Graph Image Process. 1988, 44 (1): 87-116.","journal-title":"Comput Vision Graph Image Process"},{"issue":"2\u20133","key":"2194_CR34","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1016\/0734-189X(86)90073-3","volume":"36","author":"H Li","year":"1986","unstructured":"Li H, Lavin MA, Master RJL: Fast Hough transform: A hierarchical approach. Comput Vision Graph Image Process. 1986, 36 (2\u20133): 139-161.","journal-title":"Comput Vision Graph Image Process"}],"container-title":["BMC Bioinformatics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/1471-2105-9-209.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,17]],"date-time":"2023-05-17T22:39:36Z","timestamp":1684363176000},"score":1,"resource":{"primary":{"URL":"https:\/\/bmcbioinformatics.biomedcentral.com\/articles\/10.1186\/1471-2105-9-209"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,4,23]]},"references-count":34,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2008,12]]}},"alternative-id":["2194"],"URL":"https:\/\/doi.org\/10.1186\/1471-2105-9-209","relation":{},"ISSN":["1471-2105"],"issn-type":[{"value":"1471-2105","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,4,23]]},"assertion":[{"value":"27 July 2007","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 April 2008","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 April 2008","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"209"}}