Linear and nonlinear dimensionality reduction for face recognition

Principal component analysis (PCA) has long been a simple, efficient technique for dimensionality reduction. However, many nonlinear methods such as local linear embedding and curvilinear component analysis have been proposed for increasingly complex nonlinear data recently. In this paper, we investigate and compare linear PCA and various nonlinear methods for face recognition. Results drawn from experiments on real-world face databases show that both linear and nonlinear methods yield similar performance and differences in classification rate are insignificant to conclude which method is always superior. A nonlinearity measure is derived to quantify the degree of nonlinearity of a data set in the reduced subspace. It can be used to indicate the effectiveness of nonlinear or linear dimensionality reduction.