Title: Exactly Robust Kernel Principal Component Analysis,
Abstract: We propose a novel method called robust kernel principal component analysis
(RKPCA) to decompose a partially corrupted matrix as a sparse matrix plus a
high or full-rank matrix whose columns are drawn from a nonlinear
low-dimensional latent variable model. RKPCA can be applied to many problems
such as noise removal and subspace clustering and is so far the only
unsupervised nonlinear method robust to sparse noises. We also provide
theoretical guarantees for RKPCA. The optimization of RKPCA is challenging
because it involves nonconvex and indifferentiable problems simultaneously. We
propose two nonconvex optimization algorithms for RKPCA: alternating direction
method of multipliers with backtracking line search and proximal linearized
minimization with adaptive step size. Comparative studies on synthetic data and
nature images corroborate the effectiveness and superiority of RKPCA in noise
removal and robust subspace clustering.