Cluster analysis via projection onto convex sets

Abstract

This paper proposes a data clustering algorithm that is inspired by the prominent convergence property of the Projection onto Convex Sets (POCS) method, termed the POCS-based clustering algorithm. For disjoint convex sets, the form of simultaneous projections of the POCS method can result in a minimum mean square error solution. Relying on this important property, the proposed POCS-based clustering algorithm treats each data point as a convex set and simultaneously projects the cluster prototypes onto respective member data points, the projections are convexly combined via adaptive weight values in order to minimize a predefined objective function for data clustering purposes. The performance of the proposed POCS-based clustering algorithm has been verified through a large scale of experiments and data sets. The experimental results have shown that the proposed POCS-based algorithm is competitive in terms of both effectiveness and efficiency against some of the prevailing clustering approaches such as the K-Means/K-Means+⁣+ and Fuzzy C-Means (FCM) algorithms. Based on extensive comparisons and analyses, we can confirm the validity of the proposed POCS-based clustering algorithm for practical purposes.