Bi-clustering via MDL-based matrix factorization

Abstract

Bi-clustering, or co-clustering, refers to the task of finding sub-matrices (indexed by a group of columns and a group of rows) within a matrix such that the elements of each sub-matrix are related in some way, for example, that they are similar under some metric. As in traditional clustering, a crucial parameter in bi-clustering methods is the number of groups that one expects to find in the data, something which is not always available or easy to guess. The present paper proposes a novel method for performing bi-clustering based on the concept of low-rank sparse non-negative matrix factorization (S-NMF), with the additional benefit that the optimum rank k is chosen automatically using a minimum description length (MDL) selection procedure, which favors models which can represent the data with fewer bits. This MDL procedure is tested in combination with three different S-NMF algorithms, two of which are novel, on a simulated example in order to assess the validity of the procedure. © Springer-Verlag 2013.