A class of learning algorithms for principal component analysis and minor component analysis

摘要

In this paper, we first propose a differential equation for the generalized eigenvalue problem. We prove that the stable points of this differential equation are the eigenvectors corresponding to the largest eigenvalue. Based on this generalized differential equation, a class of principal component analysis (PCA) and minor component analysis (MCA) learning algorithms can be obtained. We demonstrate that many existing PCA and MCA learning algorithms are special cases of this class, and this class includes some new and simpler MCA learning algorithms. Our results show that all the learning algorithms of this class have the same order of convergence speed, and they are robust to implementation error.