New concepts of principal component analysis based on maximum separation of clusters

It is common to apply dimension reduction techniques like principal component analysis before performing cluster analysis of multivariate data. However, it is not guaranteed that the most useful information for separating different groups is concentrated in the first few principal components. To improve the performance of clustering, a novel nonparametric method is constructed by redefining the principal component based on the linear combination of attributes that maximizes a newly proposed measure of separation of clusters. An efficient dynamic programing algorithm with complexity is described, where n is the number of observations and p is the number of attributes. The applications of the proposed methods are discussed with examples in credit card issuance and privacy protection under randomized multiple response techniques.