Exactly Robust Kernel Principal Component Analysis

@article{Fan2020ExactlyRK,
title={Exactly Robust Kernel Principal Component Analysis},
author={Jicong Fan and Tommy W. S. Chow},
journal={IEEE Transactions on Neural Networks and Learning Systems},
year={2020},
volume={31},
pages={749-761}
}
• Published 1 March 2018
• Computer Science
• IEEE Transactions on Neural Networks and Learning Systems
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…
23 Citations

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References

SHOWING 1-10 OF 57 REFERENCES
Reinforced Robust Principal Component Pursuit
• Computer Science
IEEE Transactions on Neural Networks and Learning Systems
• 2018
It is argued that it is necessary to study the presence of outliers not only in the observed data matrix but also in the orthogonal complement subspace of the authentic principal subspace, because the latter can seriously skew the estimation of the principal components.
Robust principal component analysis?
• Computer Science
JACM
• 2011
It is proved that under some suitable assumptions, it is possible to recover both the low-rank and the sparse components exactly by solving a very convenient convex program called Principal Component Pursuit; among all feasible decompositions, this suggests the possibility of a principled approach to robust principal component analysis.
R1-PCA: rotational invariant L1-norm principal component analysis for robust subspace factorization
• Computer Science
ICML
• 2006
Experiments on several real-life datasets show R1-PCA can effectively handle outliers and it is shown that L1-norm K-means leads to poor results while R2-K-MEans outperforms standard K-Means.
Robust Subspace Clustering With Complex Noise
• Computer Science
IEEE Transactions on Image Processing
• 2015
Experimental results on three commonly used data sets show that the proposed novel optimization model for robust subspace clustering outperforms state-of-the-art subspace clusters methods.
A closed form solution to robust subspace estimation and clustering
• Computer Science, Mathematics
CVPR 2011
• 2011
This work uses an augmented Lagrangian optimization framework, which requires a combination of the proposed polynomial thresholding operator with the more traditional shrinkage-thresholding operator, to solve the problem of fitting one or more subspace to a collection of data points drawn from the subspaces and corrupted by noise/outliers.
Robust Principal Component Analysis with Complex Noise
• Computer Science, Geology
ICML
• 2014
This work proposes a generative RPCA model under the Bayesian framework by modeling data noise as a mixture of Gaussians (MoG), a universal approximator to continuous distributions and thus the model is able to fit a wide range of noises such as Laplacian, Gaussian, sparse noises and any combinations of them.
Robust Kernel Low-Rank Representation
• Computer Science
IEEE Transactions on Neural Networks and Learning Systems
• 2016
This work proposes the robust kernel LRR (RKLRR) approach, and develops an efficient optimization algorithm to solve it based on the alternating direction method, and shows that both the subproblems in the optimization algorithm can be efficiently and exactly solved.
Learning Structured Low-Rank Representation via Matrix Factorization
• Computer Science
AISTATS
• 2016
This paper proposes to learn structured LRR by factorizing the nuclear norm regularized matrix, which leads to the proposed non-convex formulation NLRR, a general framework for unifying a variety of popular algorithms including LRR, dictionary learning, robust principal component analysis, sparse subspace clustering, etc.