Stability analysis in K ‐means clustering

Abstract

This paper develops a new procedure, called stability analysis, for K ‐means clustering. Instead of ignoring local optima and only considering the best solution found, this procedure takes advantage of additional information from a K ‐means cluster analysis. The information from the locally optimal solutions is collected in an object by object co‐occurrence matrix. The co‐occurrence matrix is clustered and subsequently reordered by a steepest ascent quadratic assignment procedure to aid visual interpretation of the multidimensional cluster structure. Subsequently, measures are developed to determine the overall structure of a data set, the number of clusters and the multidimensional relationships between the clusters.