Biclustering gene-feature matrices for statistically significant dense patterns

Biclustering is an important problem that arises in diverse applications, including analysis of gene expression and drug interaction data. The problem can be formalized in various ways through different interpretation of data and associated optimization functions. We focus on the problem of finding unusually dense patterns in binary (0-1) matrices. This formulation is appropriate for analyzing experimental datasets that come from not only binary quantization of gene expression data, but also more comprehensive datasets such as gene-feature matrices that include functions of coded proteins and motifs in the coding sequence. We formalize the notion of an "unusually" dense submatrix to evaluate the interestingness of a pattern in terms of statistical significance based on the assumption of a uniform memoryless source. We then simplify it to assess statistical significance of discovered patterns. Using statistical significance as an objective function, we formulate the problem as one of finding significant dense submatrices of a large sparse matrix. Adopting a simple iterative heuristic along with randomized initialization techniques, we derive fast algorithms for discovering binary biclusters. We conduct experiments on a binary gene-feature matrix and a quantized breast tumor gene expression matrix. Our experimental results show that the proposed method quickly discovers all interesting patterns in these datasets.