Robust principal component analysis algorithm based on adversarial training
In current robust principal component analysis,when an attacker trains a given data matrix by adding an arbitrary matrix with a bounded norm,the robust principal component analysis has high computational cost and poor generalization ability.Inspired by adversarial training,an efficient algorithm combining adversarial training and robust principal component analysis is proposed.The algorithm assumes that the adversary adds an adversarial matrix R on a bounded set to the data matrix X,and the adversarial matrix R can maximize the Frobenius norm between the data matrix X and the decomposition.Then the Lagrange multiplier method and maximization and minimization method are combined to find the approximate solution of the anti-PCA,and the matrix and coefficient matrix of the PCA with enhanced generalization ability are obtained.The experimental results show that the adversarial training robust PCA algorithm is superior to the standard PCA algorithm on synthetic data sets and open standard test data sets CBCL,Moffet,Madonna.
robust principal component analysisconfrontation trainingdimensionality reduction
万方数据
维普
