Maximal-Sum submatrix search using a hybrid contraint programming/linear programming approach

A Maximal-Sum Submatrix (MSS) maximizes the sum of the entries corresponding to the Cartesian product of a subset of rows and columns from an original matrix (with positive and negative entries). Despite being NP-hard, this recently introduced problem was already proven to be useful for practical data-mining applications. It was used for identifying bi-clusters in gene expression data or to extract a submatrix that is then visualized in a circular plot. The state-of-the-art results for MSS are obtained using an advanced Constraint Programing approach that combines a custom filtering algorithm with a Large Neighborhood Search. We improve the state-of-the-art approach by introducing new upper bounds based on linear and mixed-integer programming formulations, along with dedicated pruning algorithms. We experiment on both synthetic and real-life data, and show that our approach outperforms the previous methods.