Sparse Biclustering of Transposable Data

Kean Ming Tan, Daniela M. Witten

Research output: Contribution to journalArticlepeer-review

35 Scopus citations


We consider the task of simultaneously clustering the rows and columns of a large transposable data matrix. We assume that the matrix elements are normally distributed with a bicluster-specific mean term and a common variance, and perform biclustering by maximizing the corresponding log-likelihood. We apply an ℓ1 penalty to the means of the biclusters to obtain sparse and interpretable biclusters. Our proposal amounts to a sparse, symmetrized version of k-means clustering. We show that k-means clustering of the rows and of the columns of a data matrix can be seen as special cases of our proposal, and that a relaxation of our proposal yields the singular value decomposition. In addition, we propose a framework for biclustering based on the matrix-variate normal distribution. The performances of our proposals are demonstrated in a simulation study and on a gene expression dataset. This article has supplementary material online.

Original languageEnglish (US)
Pages (from-to)985-1008
Number of pages24
JournalJournal of Computational and Graphical Statistics
Issue number4
StatePublished - Oct 25 2014

Bibliographical note

Publisher Copyright:
© 2014, © 2014 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America.


  • Clustering
  • Gene expression
  • Matrix-variate normal distribution
  • Unsupervised learning
  • ℓ penalty


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