期刊
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
卷 31, 期 3, 页码 749-761出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TNNLS.2019.2909686
关键词
Sparse matrices; Principal component analysis; Minimization; Kernel; Matrix decomposition; Feature extraction; Optimization; High rank; kernel; low rank; noise removal; robust principal component analysis (RPCA); sparse; subspace clustering
类别
资金
- [9220083]
Robust principal component analysis (RPCA) can recover low-rank matrices when they are corrupted by sparse noises. In practice, many matrices are, however, of high rank and, hence, cannot be recovered by RPCA. 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 with low latent dimensionality. RKPCA can be applied to many problems such as noise removal and subspace clustering and is still the only unsupervised nonlinear method robust to sparse noises. Our theoretical analysis shows that, with high probability, RKPCA can provide high recovery accuracy. The optimization of RKPCA involves nonconvex and indifferentiable problems. We propose two nonconvex optimization algorithms for RKPCA. They are alternating direction method of multipliers with backtracking line search and proximal linearized minimization with adaptive step size (AdSS). Comparative studies in noise removal and robust subspace clustering corroborate the effectiveness and the superiority of RKPCA.
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