Outlier-aware Tensor Robust Principal Component Analysis with Self-guided Data Augmentation

2025/04/25 by Yangyang Xu, Xu, Yangyang, Kexin Li +5
Computer Science · Engineering · Mathematics · #15A69 #65K10 #Block (permutation group theory) #Computer Vision and Pattern Recognition (cs.CV) #Convergence (economics) #Coordinate descent #FOS: Computer and information sciences #FOS: Mathematics #Face and Expression Recognition #G.1.6 #Gradient descent #I.4.5 #Machine Learning (cs.LG) #Numerical Analysis (math.NA) #Outlier #Principal component analysis #Robust principal component analysis #Sparse and Compressive Sensing Techniques #Tensor (intrinsic definition) #Tensor decomposition and applications #Weighting

paper · pdf · doi:10.48550/arxiv.2504.18323

openalex publication_date 2025/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Tensor Robust Principal Component Analysis (TRPCA) is a fundamental technique for decomposing multi-dimensional data into a low-rank tensor and an outlier tensor, yet existing methods relying on sparse outlier assumptions often fail under structured corruptions. In this paper, we propose a self-guided data augmentation approach that employs adaptive weighting to suppress outlier influence, reformulating the original TRPCA problem into a standard Tensor Principal Component Analysis (TPCA) problem. The proposed model involves an optimization-driven weighting scheme that dynamically identifies and downweights outlier contributions during tensor augmentation. We develop an efficient proximal block coordinate descent algorithm with closed-form updates to solve the resulting optimization problem, ensuring computational efficiency. Theoretical convergence is guaranteed through a framework combining block coordinate descent with majorization-minimization principles. Numerical experiments on synthetic and real-world datasets, including face recovery, background subtraction, and hyperspectral denoising, demonstrate that our method effectively handles various corruption patterns. The results show the improvements in both accuracy and computational efficiency compared to state-of-the-art methods.

Citations

• Learning Spatial-Temporal Regularized Tensor Sparse RPCA for Background Subtraction
• Guaranteed Tensor Recovery Fused Low-rankness and Smoothness
• Fast and Provable Tensor Robust Principal Component Analysis via Scaled Gradient Descent
• Generalized Low-rank plus Sparse Tensor Estimation by Fast Riemannian Optimization
• Tensor Robust Principal Component Analysis with a New Tensor Nuclear Norm
• Tensor Ring Decomposition
• Tensor Robust Principal Component Analysis: Exact Recovery of Corrupted Low-Rank Tensors via Convex Optimization
• A Unified Convergence Analysis of Block Successive Minimization Methods for Nonsmooth Optimization
• Tensor Decompositions and Applications
• Image quality assessment: from error visibility to structural similarity
• Principal Component Analysis of Three-Mode Data by Means of Alternating Least Squares Algorithms
• Analysis of Individual Differences in Multidimensional Scaling Via an N-way Generalization of “Eckart-Young” Decomposition
• Some Mathematical Notes on Three-Mode Factor Analysis

Related

• Fast and Provable Tensor Robust Principal Component Analysis via Scaled Gradient Descent
• Robust Multilinear Principal Component Analysis
• Deep Unfolded Tensor Robust PCA with Self-supervised Learning
• Global Weighted Tensor Nuclear Norm for Tensor Robust Principal Component Analysis
• Tensor Robust PCA with Nonconvex and Nonlocal Regularization