A Novel Piecewise Linear Clustering Technique Based on Hyper Plane Adjustment

Abstract

In this paper, a novel clustering method is proposed which is done by some hyper planes in the feature space. Training these hyper-planes is performed by adjusting suitable bias and finding a proper direction for their perpendicular vector so as to minimize Mean-Squared Error. For this purpose, combination of training a hyper plane and a fundamental search method named Mountain-Climbing is utilized to find a local optimum solution. The approach achieves a satisfactory result in comparison with the well known clustering methods such as k-means, RPCL, and also two hierarchical methods, namely, Single-Link and Complete-Link. Low number of parameters and linear boundaries are only some merits of the proposed approach. In addition, it finds the number of clusters dynamically. Some two dimensional artificial datasets are used to assess and compare these clustering methods visually.