Simplified nonlinear principal component analysis

Principal component analysis (PCA) is widely used to extract the linear relations between variables in a dataset. To detect nonlinear relations, the nonlinear principal component analysis (NLPCA) by a 3-hidden-layer auto-associative neural network was proposed by Kramer (1991) [Kramer, MA, pp.233-243, 1991], which has been used to analyze datasets from many fields. However, the 3-hidden-layer NLPCA can be rather unstable, often resulting in the over fitting of data, especially for noisy datasets with rather few samples. This paper shows that the instability and tendency to overfit in the 3-hidden-layer NLPCA can be well alleviated in a simplified 2-hidden-layer NLPCA. The new method is tested with the tropical Pacific sea surface temperature fluctuations, the Lorenz chaotic system, and the stratospheric quasi-biennial wind oscillations.