Non-Euclidean c-means clustering algorithms

Abstract

This paper introduces non-Euclidean c-means clustering algorithms. These algorithms rely on weighted norms to measure the distance between the feature vectors and the prototypes that represent the clusters. The proposed algorithms are developed by solving a constrained minimization problem in an iterative fashion. The norm weights are determined from the data in an attempt to produce partitions of the feature vectors that are consistent with the structure of the feature space. A series of experiments on three different data sets reveal that the proposed non-Euclidean c-means algorithms provide an attractive alternative to Euclidean c-means clustering in applications that involve data sets containing clusters of different shapes and sizes.