SPHier: Scalable Parallel Biclustering Using Weighted Bigraph Crossing Minimization

Biclustering is used for discovering correlations among subsets of attributes with subsets of transactions in a transaction database. It has an extensive set of applications ranging from Gene co-regulation analysis[4], documentkeyword clustering[12] and collaborative filtering for online recommendation systems[13]. In this paper, we propose optimal biclustering problem as maximal crossing number reduction in a weighted bipartite graph. Based on the problem formulation, we then present SPHier, a novel parallel biclustering algorithm based on weighted bigraph crossing minimization problem. Crossing minimization has been extensively used in Graph Drawing and VLSI Circuit Layouts for reducing wire congestion while its application to scalable parallel biclustering problem, to the best of our knowledge, is being investigated for the first time in this paper. We show that crossing minimization approach provides a simple and intuitive method to identify bi-clusters. Moreover, it is much easier to parallelize with excellent speedup characteristics. We have validated SPHier on synthetic and biological data sets. We show performance results on an AMD Athlon based 32-node Linux Cluster.