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

Abstract

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 $O(n^2\max \{n,p\})$ 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.

Keywords:

• Cluster analysis
• Data privacy
• Knapsack problem
• Principal component analysis
• Randomized multiple response

Additional information

Funding

Chi Tim, Ng’s work is supported by National Research Foundation of Korea (NRF) grant funded by the Korea government(MSIP) (No. NRF-2017R1C1B2011652) and 2018 Chonnam National University Research Program grant (No. 2018-3428). Myung Hwan, Na’s work is supported by the Research Program of Rural Development Administration (Project No. PJ0138672019).