A Robust Weighted Kernel Principal Component Analysis Algorithm

Kernel principal component analysis (KPCA) fails to detect the nonlinear structure of data well when outliers exist. To reduce this problem, this paper presents a novel algorithm, named robust weighted KPCA (RWKPCA). RWKPCA works well in dealing with outliers, and can be carried out in an iterative manner. This algorithm gives the weighted means vector and weighted covariance matrix based on M-estimator in robust statistics, then the weight on each datum can be got by an iterative computing and the outliers can be exterminated by the weights. The RWKPCA algorithm not only remains non-linearity property of KPCA but gets better robustness and improves the accuracy of KPCA. The simulation experiments show that the RWKPCA algorithm developed is better than the KPCA algorithm.