M3IC: Maximum Margin Multiple Instance Clustering

Clustering, classification, and regression, are three major research topics in machine learning. So far, much work has been conducted in solving multiple instance classification and multiple instance regression problems, where supervised training patterns are given as bags and each bag consists of some instances. But the research on unsupervised multiple instance clustering is still limited . This paper formulates a novel Maximum Margin Multiple Instance Clustering (MIC) problem for the multiple instance clustering task. To avoid solving a nonconvex optimization problem directly, MIC is further relaxed, which enables an efficient optimization solution with a combination of Constrained Concave-Convex Procedure (CCCP) and the Cutting Plane method. Furthermore, this paper analyzes some important properties of the proposed method and the relationship between the proposed method and some other related ones. An extensive set of empirical results demonstrate the advantages of the proposed method against existing research for both effectiveness and efficiency.