Nonlinear principal component analysis by neural networks

Nonlinear Principal Component Analysis by Neural Networks

Nonlinear principal component analysis (NLPCA) can be performed by a neural network model which nonlinearly generalizes the classical principal component analysis (PCA) method. The presence of local minima in the cost function renders the NLPCA somewhat unstable, as optimizations started from different initial parameters often converge to different minima. Regularization by adding weight penalt...

Complex-valued neural networks for nonlinear complex principal component analysis

Principal component analysis (PCA) has been generalized to complex principal component analysis (CPCA), which has been widely applied to complex-valued data, two-dimensional vector fields, and complexified real data through the Hilbert transform. Nonlinear PCA (NLPCA) can also be performed using auto-associative feed-forward neural network (NN) models, which allows the extraction of nonlinear f...

A Study of Nonlinear Principal Component Analysis Using Neural Networks

Nonlinear Principal Component Analysis Using Autoassociative Neural Networks

Nonlinear principal component analysis is a novel technique for multivariate data analysis, similar to the well-known method of principal component analysis. NLPCA, like PCA, is used to identify and remove correlations among problem variables as an aid to dimensionality reduction, visualization, and exploratory data analysis. While PCA identifies only linear correlations between variables, NLPC...

Nonlinear Principal Component Analysis

A. Two quite different forms of nonlinear principal component analysis have been proposed in the literature. The first one is associated with the names of Guttman, Burt, Hayashi, Benzécri, McDonald, De Leeuw, Hill, Nishisato. We call itmultiple correspondence analysis. The second form has been discussed by Kruskal, Shepard, Roskam, Takane, Young, De Leeuw, Winsberg, Ramsay. We call it no...