Noise, histogram and cluster validity for Gaussian-mixtured data

Abstract

In this study, a critique of the clustering methodology is carried out for the definition of a cluster, determination of the number of clusters and evaluation of heuristic partitional clustering algorithms, when the data is a noisy Gaussian Mixture. The effects of noise in determining the number of clusters and the clustering parameters are investigated. Two cluster validity criteria, namely, the likelihood information criterion and the sum of squared error are described. It is concluded that these criteria can be used as a guide in deciding on the number of valid clusters. By using the proposed sum of squared error criterion, an improvement algorithm which reduces the effect of noise on the results of heuristic clustering algorithms is described.