Computational Complexity Of Bi-clustering

Abstract

In this work we formalize a new natural objective (or cost) function for bi-clustering - Monochromatic bi-clustering. Our objective function is suitable for detecting meaningful homogenous clusters based on categorical valued input matrices. Such problems have arisen recently in systems biology where researchers have inferred functional classifications of biological agents based on their pairwise interactions. We analyze the computational complexity of the resulting optimization problems. We show that finding optimal solutions is NP-hard and complement this result by introducing a polynomial time approximation algorithm for this bi-clustering task. This is the first positive approximation guarantee for bi-clustering algorithms. We also show that bi-clustering with our objective function can be viewed as a generalization of correlation clustering.