Multi-population Principal Component Analysis Based on Spectral Graph Technique for Data Analysis

Abstract

Principal component analysis is a multivariate statistical method that makes the complex cross-correlation between the variables simpler. The basic idea of principal component analysis is to project the original observation data into a new low-dimensional space in the sense of information loss minimization and then to solve the problem with a significantly reduced size, but the classical principal component analysis does not take the category information into account in data analysis. In this paper, a multi-population principal component analysis approach based on spectral graph technique is proposed. The novel approach incorporates the category information from samples to construct an adjacency undirected graph to handle the case of many groups, which puts the problem into solving eigenvalue and eigenvector of a matrix. Experimental results on two data sets show that the ratio of cumulative variance contributions of new approach outperforms that of classical method. The proposed method is feasible and effective.