Objective Function Clustering

Abstract

S8 illustrates some of the difficulties inherent with cluster analysis; its aim is to alert investigators to the fact that various algorithms can suggest radically different substructures in the same data set. The balance of Chapter 3 concerns objective functional methods based on fuzzy c-partitions of finite data. The nucleus for all these methods is optimization of nonlinear objectives involving the weights u _ik ; functionals using these weights will be differentiable over M _fc —but not over M _c —a decided advantage for the fuzzy embedding of hard c-partition space. Classical first- and second-order conditions yield iterative algorithms for finding the optimal fuzzy c-partitions defined by various clustering criteria.