Perturbation analysis on PCA plus graph embedding methods and PCA plus exponential graph embedding methods

Abstract

PCA plus graph embedding (PCA+GE) methods are popular techniques for dimensionality reduction and face recognition. In these methods, the principal component analysis (PCA) is used first, and then some graph embedding methods are applied. In practice, the data is often perturbed or contaminated, and it has been found that PCA is sensitive to noise, which may affect the accuracy of the subsequent classification. Moreover, the PCA+GE methods can be unstable after data perturbation. To the best of our knowledge, however, there are few results on perturbation analysis of this type of methods. In this work, we show the reason from a matrix perturbation analysis point of view. The main aim of this paper is to look for the reasons that cause the instability. To overcome the difficulty of instability, a framework of PCA plus exponential graph embedding methods is proposed to take the place of the conventional PCA plus graph embedding methods. The computational cost of the proposed methods is comparable to that of the original counterparts, and our methods are much more stable in terms of recognition accuracy. Numerical experiments show the effectiveness of our theoretical results, and demonstrate the efficiency of the new methods on some real-world data sets.