Robust kernel PCA using fuzzy membership

Abstract

Principal component analysis (PCA) is widely used for dimensionality reduction in pattern recognition. Although PCA has been applied in many areas successfully, it suffers from sensitivity to noise and is limited to linear principal components. The noise sensitivity problem comes from the least-squares measure used in PCA and the limitation to linear components originates from the fact that PCA uses an affine transform defined by eigenvectors of the covariance matrix and the mean of the data. In this paper, a robust kernel PCA method that extends Scholkopf et al.'s kernel PCA and uses fuzzy memberships is introduced to tackle the two problems simultaneously. We first propose an iterative method to find a robust covariance matrix called robust fuzzy PCA (RF-PCA). The RF-PCA is introduced to reduce the sensitivity to noise with the help of robust estimation technique. The RF-PCA method is then extended to a non-linear one, robust kernel fuzzy PCA (RKF-PCA), using kernels. Experimental results suggest that the proposed algorithm works well on artificial and real world data sets.