# Exactly Robust Kernel Principal Component Analysis

arXiv: https://arxiv.org/abs/1802.10558 · HTML: https://mlsanity.com/paper/1802.10558/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Feb 2018.

## Built on by (most cited first, 7 of 7)

- [Robust and Explainable Autoencoders for Unsupervised Time Series Outlier Detection---Extended Version](https://mlsanity.com/paper/2204.03341/) (2022)
- [Deep Orthogonal Hypersphere Compression for Anomaly Detection](https://mlsanity.com/paper/2302.06430/) (2023)
- [Subject Information Extraction for Novelty Detection with Domain Shifts](https://mlsanity.com/paper/2504.21247/) (2025)
- [Robust Principal Component Analysis: A Median of Means Approach](https://mlsanity.com/paper/2102.03403/) (2021)
- [Coarse to Fine Two-Stage Approach to Robust Tensor Completion of Visual Data](https://mlsanity.com/paper/2106.10422/) (2021)
- [Extending Kernel PCA through Dualization: Sparsity, Robustness and Fast Algorithms](https://mlsanity.com/paper/2306.05815/) (2023)
- [Rethinking PCA Through Duality](https://mlsanity.com/paper/2510.18130/) (2025)

## Abstract (arXiv)

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. Comparative studies in noise removal and robust subspace clustering corroborate the effectiveness and superiority of RKPCA.