Co-Clustering for Object by Variable Data Matrices

Abstract

Co-clustering means the simultaneous clustering of the rows and columns of a two-dimensional data table (biclustering, two-way clustering), in contrast to separately clustering the rows and the columns. Practical applications may be met, e.g., in economics, social sciences, bioinformatics, etc. Various co-clustering models, criteria, and algorithms have been proposed that differ with respect to the considered data types (real-valued, integers, binary data, contingency tables), and also the meaning of rows and columns (samples, variables, factors, time,...). This paper concentrates on the case where rows correspond to (independent) samples or objects, and columns to (typically dependent) variables. We emphasize that here, in general, different similarity or homogeneity concepts must be used for rows and columns. We propose two probabilistic co-clustering approaches: a situation where clusters of objects and of variables refer to two different distribution parameters, and a situation where clusters of ‘highly correlated’ variables (by regression to a latent class-specific factor) are crossed with object clusters that are distinguished by additive effects only. We emphasize here the classical ‘classification approach’, where maximum likelihood criteria are optimized by generalized alternating k-means type algorithms.