MMSE: A generalized coherence measure for identifying linear patterns

Biclustering is very useful in bioinformatics, information retrieval, electoral data analysis, dimension reduction, and so on. It is usually formulated as an optimization problem of searching maximal subsets of rows and columns satisfying some coherence criteria. The found submatrices are called as biclusters. There are several quantitative coherence measurements for linear patterns proposed. However, they are either lack the capability of properly evaluating all subtypes of linear patterns, or sensitive to the noise. In this paper, we propose a coherence measurement for the general linear patterns, the minimal mean squared error (MMSE). By using MMSE, the biclustering algorithms are expected to identify all types of linear patterns, including shifting (additive), scaling (multiplicative), and the general linear (the mixed form of shifting and scaling) ones, if they are presented in the data. Our comparative experimental results have highlighted that MMSE can actually help to identify significant general linear biclusters in artificial and real application data.