Pattern Recognition, 4th Edition

Chapter 14. Clustering Algorithms III: Schemes Based on Function Optimization

14.1. Introduction

One of the most commonly used families of clustering schemes relies on the optimization of a cost function J using differential calculus techniques (e.g., see [Duda 01, Bezd 80, Bobr 91, Kris 95a, Kris 95b]). The cost J is a function of the vectors of the data set X and it is parameterized in terms of an unknown parameter vector, θ. For most of the schemes of the family, the number of clusters, m, is assumed to be known.

Our goal is the estimation of θ that characterizes best the clusters underlying X. The parameter vector θ is strongly dependent on the shape of the clusters. For example, for compact clusters (see Figure 14.1a), it is reasonable ...