Detection and Characterization of Cluster Substructure II. Fuzzy <i>c</i>-Varieties and Convex Combinations Thereof

This work generalizes the straight line prototype of a cluster developed in Part I to any r-dimensional linear variety of $R^s ,( 0\leqq r < s)$ and considers a distance functional which utilizes convex combinations of the distance functionals developed here and in Part II.

Abstract

In Part I [SIAM J. Appl. Math., 40 (1981), pp. 339–357], Fuzzy c-Lines was introduced as an algorithm for detection and characterization of linearly clustered data. In Part II, we address two extensions of the theory in Part I. Specifically, we will first generalize the straight line prototype of a cluster developed in Part I to any r-dimensional linear variety of $R^s ,( 0\leqq r < s)$; secondly, we will consider a distance functional which utilizes convex combinations of the distance functionals developed here and in Part I. All of the notation and symbols used here are unchanged from Part I.