Nonlinear principal component analysis-based on principal curves and neural networks

Abstract

Many applications of principal component analysis (PCA) can be found in the literature. But principal component analysis is a linear method, and most engineering problems are nonlinear. Sometimes using the linear PCA method in nonlinear problems can bring distorted and misleading results. So there is a need for a nonlinear principal component analysis (NLPCA) method. The principal curve algorithm was a breakthrough of solving the NLPCA problem, but the algorithm does not yield an NLPCA model which can be used for predictions. In this paper the authors present an NLPCA method which integrates the principal curve algorithm and neural networks. The results on both simulated and real problems show that the method is excellent for solving nonlinear principal component problems. Potential applications of NLPCA are also discussed in this paper.