Directly Solving the Original Ratiocut Problem for Effective Data Clustering

Jing Li, Feiping Nie, Xuelong Li

Abstract: This paper focuses on the original RatioCut problem, which is one of the most representative clustering paradigms. The RatioCut criterion looks for a partition of the graph to achieve the mincut cost while keeping each partition reasonably large. This well-known problem is NP hard and its relaxed form has been widely used in the past several decades. However, the relaxed RatioCut usually suffers two problems: not satisfactory stable clustering performance, and undesired two-stage optimization. In this work, we solve the original RatioCut problem by learning a new similarity matrix which has as many connected components as the cluster number, so that the original RatioCut constraint can be directly satisfied. An easily implemented algorithm is derived to iteratively optimize the proposed method. Experimental results on various real-world benchmark datasets exhibit the effectiveness of the proposed method to solve the RatioCut problem.