Robust PCA based on neural networks

Abstract

One way to improve the robustness of principal component analysis (PCA) is studied. The typical two kinds of aspects to analyze the robustness of PCA algorithm are proposed and compared: one is based on the independent among the acquired principal components and the other is based on reducing the effects of the outliers in the training sample set. A new self-organizing algorithm of robust PCA is presented based on the structure of a single-layer neural network (NN) with the modification of the cost function which stands for the reconstruction error of the input signal. The new nonlinear robust PCA algorithm can recognize the outliers in the training sample set automatically and exterminate their effects to the accuracy and convergence of the PCA algorithm through proper processing to the recognized outliers. The comparison simulation experiments are designed to show that robust PCA algorithms developed in this paper are better than the statistical PCA algorithm based on eigenvalue decomposition and the linear self-organizing PCA algorithms based on single-layer NN.