Validation indices for projective clustering

Cluster validation is a major issue in cluster analysis of data mining, which is the process of evaluating performance of clustering algorithms under varying input conditions. Many existing validity indices address clustering results of low-dimensional data. Within high-dimensional data, many of the dimensions are irrelevant, and the clusters usually only exist in some projected subspaces spanned by different combinations of dimensions. This paper presents a solution to the problem of cluster validation for projective clustering. We propose two new measurements for the intracluster compactness and intercluster separation of projected clusters. Based on these measurements and the conventional indices, three new cluster validity indices are presented. Combined with a fuzzy projective clustering algorithm, the new indices are used to determine the number of projected clusters in high-dimensional data. The suitability of our proposal has been demonstrated through an empirical study using synthetic and real-world datasets.