Finding checkerboard patterns via fractional 0-1 programming

Biclustering is a data mining technique used to simultaneously partition the set of samples and the set of their attributes (features) into subsets (clusters). Samples and features clustered together are supposed to have a high relevance to each other. In this paper we provide a new mathematical programming formulation for unsupervised biclustering. The proposed model involves the solution of a fractional 0-1 programming problem. A linear-mixed 0-1 reformulation as well as two heuristic-based approaches are developed. Encouraging computational results on clustering real DNA microarray data sets are presented. In addition, we also discuss theoretical computational complexity issues related to biclustering.