A Family of Fuzzy Learning Algorithms for Robust Principal Component Analysis Neural Networks

In this paper, we analyze Xu and Yuille´s robust principal component analysis (RPCA) learning algorithms by means of the distance measurement in space. Based on the analysis, a family of fuzzy RPCA learning algorithms is proposed, which is robust against outliers. These algorithms can explicitly be understood from the viewpoint of fuzzy set theory, though Xu and Yuille´s algorithms were proposed based on a statistical physics approach. In the proposed algorithms, an adaptive learning procedure overcomes the difficulty of selection of learning parameters in Xu and Yuille´s algorithms. Furthermore, the robustness of proposed algorithms is investigated by using the theory of influence functions. Simulations are carried out to illustrate the robustness of these algorithms.