Sparse Biclustering of Transposable Data Using the Matrix Normal Distribution

• Activity Number: 356
• Type: Contributed
• Date/Time: Tuesday, July 31, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Kean Ming Tan*+ and Daniela Witten
• Companies: University of Washington and University of Washington
• Keywords: biclustering ; matrix-variate normal distribution ; sparsity ; clustering ; unsupervised learning ; gene expression

Abstract

We consider the problem of simultaneously clustering both the rows and the columns of a large transposable data matrix. A number of approaches for biclustering have been proposed in recent years, but these proposals have tended to be somewhat ad hoc. Here, we develop a rigorous statistical approach for biclustering that is motivated by the matrix-variate normal distribution. We perform biclustering by maximizing the log likelihood of the data under the assumption that it follows a matrix-variate normal distribution; we further assume that the overall mean structure of the data is sparse, in order to obtain sparse biclustering using a penalized log likelihood approach. Furthermore, we show that k-means clustering of the rows and of the columns of the data matrix can be seen as a special case of our proposal, and that a relaxation of our proposal yields the singular value decomposition. We demonstrate the performance of our sparse biclustering method relative to existing approaches in a simulation study and on two gene expression data sets.