Overview of principal component analysis algorithm

Abstract

Principal component analysis (PCA) algorithm has been extensively employed in face recognition. However, existing PCA algorithms have some limitations in face recognition. In order to overcome these limitations, researchers proposed some extended-PCA algorithms. In this paper, we present algorithm implementation of the original PCA algorithm and main extended-PCA algorithms including two-dimensional PCA (2DPCA), 2DPCA-based feature fusion approach, the kernel PCA (KPCA), the modular PCA, improved KPCA (IKPCA), efficient sparse KPCA (ESKPCA) and incremental PCA (IPCA). 2DPCA directly computes the projection of a matrix onto a transforming axis. 2DPCA-based feature fusion approach combines the features generated from the two schemes of 2DPCA. KPCA can perform well in extracting features from samples whose components have nonlinear relations. The modular PCA approach divides the original face image into sub-images and applies the original PCA approach to each of these sub-images. The IKPCA algorithm improves KPCA for more efficient feature extraction. The efficient sparse KPCA (ESKPCA) improves the computational efficiency of the previous sparse KPCA methods on large-scale training sample sets. Incremental PCA (IPCA) overcomes the limitation which is hard to scale up the developed systems. In order to compare the recognition rate of these algorithms in face recognition, a series of experiments are performed on three face image databases: ORL, Yale and NIR face databases.