Quasi-objective nonlinear principal component analysis.

By means of mathematical analysis and numerical experimentation, this study shows that the problems of non-uniqueness of solutions and data over-fitting, that plague the multilayer feedforward neural network for NonLinear Principal Component Analysis (NLPCA), are caused by inappropriate architecture of the neural network. A simplified two-hidden-layer feedforward neural network, which has no encoding layer and no bias term in the mathematical definitions of bottleneck and output neurons, is proposed to conduct NLPCA. This new, compact NLPCA model alleviates the aforementioned problems encountered when using the more complex neural network architecture for NLPCA.