title: RKF-PCA: robust kernel fuzzy PCA.
abstract: Principal component analysis (PCA) is a mathematical method that reduces the dimensionality of the data while retaining most of the variation in the data. 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 the kernel PCA and uses fuzzy memberships is introduced to tackle the two problems simultaneously. We first introduce an iterative method to find robust principal components, called Robust Fuzzy PCA (RF-PCA), which has a connection with robust statistics and entropy regularization. The RF-PCA method is then extended to a non-linear one, Robust Kernel Fuzzy PCA (RKF-PCA), using kernels. The modified kernel used in the RKF-PCA satisfies the Mercer's condition, which means that the derivation of the K-PCA is also valid for the RKF-PCA. Formal analyses and experimental results suggest that the RKF-PCA is an efficient non-linear dimension reduction method and is more noise-robust than the original kernel PCA.
authors: Computer and Information Science and Engineering, University of Florida, United States. gheo@cise.ufl.edu
authors: Gyeongyong
authors: G
authors: Heo
authors: Paul
authors: P
authors: Gader
authors: Hichem
authors: H
authors: Frigui
mesh_terms: D000465:Algorithms; D016001:Confidence Intervals; D017143:Fuzzy Logic; D016014:Linear Models; D017711:Nonlinear Dynamics; D025341:Principal Component Analysis / Q000379:methods*; D012984:Software