title: Sparse Biclustering of Transposable Data.
abstract: 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 ℓ1penalty to the means of the biclusters in order to obtain sparse and interpretable biclusters. Our proposal amounts to a sparse, symmetrized version ofk-means clustering. We show thatk-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 bi-clustering based on the matrix-variate normal distribution. The performances of our proposals are demonstrated in a simulation study and on a gene expression data set. This article has supplementary material online.
authors.affiliation: Department of Biostatistics, University of Washington, Seattle, WA 98115.
authors.forename: Kean Ming
authors.initials: KM
authors.lastname: Tan
authors.affiliation: Department of Biostatistics, University of Washington, 1705 NE Pacific Street, Box 357232, F-649 Health Sciences Building, Seattle, WA 98195-7232.
authors.forename: Daniela M
authors.initials: DM
authors.lastname: Witten
keywords: Clustering; Gene expression; Matrix-variate normal distribution; Unsupervised learning; ℓ1 penalty