A Simulation Study on Nonlinear Principal Component Analysis

Abstract

In statistical practice multicollinearity of predictor variables is rather the rule than the exception and appropriate models are needed to avoid instability of predictions. Feature extraction methods reflect the idea that latent variables not measurable directly are underlying the original data. They try to reduce the dimension of the data by constructing new independent variables which keep as much information as possible from the original measurements. A common feature extraction method is Principal Component Analysis (PCA), which in its classical form is restricted to linear relationships among predictor variables. This paper is concerned with nonlinear principal component analysis (NLPCA) as introduced by Kramer (1991), who modelled his approach with help of artificial neural networks. By means of first simulation studies data derived from semicircles and circles are investigated with respect to their ability to be described by nonlinear principal components among the predictors.