Non-Euclidean c-means clustering algorithms

Article type: Research Article

Authors: Karayiannis, Nicolaos B.^a | Randolph-Gips, Mary M.^b

Affiliations: [a] Department of Electrical and Computer Engineering, N308 Engineering Building 1, University of Houston, Houston, TX 77204-4005, USA | [b] Department of Electrical and Computer Engineering, University of Houston-Clear Lake, 2700 Bay Area Boulevard, Houston, TX 77058, USA

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.

Keywords: c-means clustering, generalized mean, non-Euclidean norm, reformulation, weighted norm

DOI: 10.3233/IDA-2003-7503

Journal: Intelligent Data Analysis, vol. 7, no. 5, pp. 405-425, 2003