An Indicator for the Number of Clusters: Using a Linear Map to Simplex Structure

Abstract

The problem of clustering data can be formulated as a graph partitioning problem. In this setting, spectral methods for obtaining optimal solutions have received a lot of attention recently. We describe Perron Cluster Cluster Analysis (PCCA) and establish a connection to spectral graph partitioning. We show that in our approach a clustering can be efficiently computed by mapping the eigenvector data onto a simplex. To deal with the prevalent problem of noisy and possibly overlapping data we introduce the Min-chi indicator which helps in confirming the existence of a partition of the data and in selecting the number of clusters with quite favorable performance. Furthermore, if no hard partition exists in the data, the Min-chi can guide in selecting the number of modes in a mixture model. We close with showing results on simulated data generated by a mixture of Gaussians.