Sparse Principal Component Analysis Using Particle Swarm Optimization

Abstract

Principal component analysis (PCA) has been widely applied in chemometrics and process monitoring. Because the principal component (PC) is a combination of all original variables, its interpretation is often not straightforward. Recently, sparse PCA methods have been developed to generate sparse loading vectors. The obtained sparse principal component (SPC) is much easier to interpret. However, the sparser loading vectors and the lower variance are achieved by SPCs. The sparsity-variance trade-off is usually represented by the index of sparseness which is determined by the number of non-zero loadings on each SPC. In this paper, we propose a novel method for the selection of NNZL using particle swarm optimization (PSO) for sparse PCA. The proposed method is applied to process monitoring. Two case studies are used to verify the capability and efficiency of the proposed method.