Nonlinear principal component analysis using autoassociative neural networks

TLDR

Nonlinear principal component analysis (NLPCA) extends traditional PCA by uncovering both linear and nonlinear correlations in multivariate data, enabling dimensionality reduction, visualization, and exploratory analysis. NLPCA trains a feedforward neural network with a bottleneck hidden layer to reconstruct its inputs, forcing a compact representation that captures underlying structure, as demonstrated on simulated batch reaction data. The method effectively reduces dimensionality and yields a feature space map that mirrors the true distribution of system parameters.

Abstract

Abstract 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, NLPCA uncovers both linear and nonlinear correlations, without restriction on the character of the nonlinearities present in the data. NLPCA operates by training a feedforward neural network to perform the identity mapping, where the network inputs are reproduced at the output layer. The network contains an internal “bottleneck” layer (containing fewer nodes than input or output layers), which forces the network to develop a compact representation of the input data, and two additional hidden layers. The NLPCA method is demonstrated using time‐dependent, simulated batch reaction data. Results show that NLPCA successfully reduces dimensionality and produces a feature space map resembling the actual distribution of the underlying system parameters.