Sparse Biclustering of Transposable Data

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 ℓ 1 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.