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

• URL: http://arxiv.org/abs/2504.18323v1
• Date: Fri, 25 Apr 2025 13:03:35 GMT
• Title: Outlier-aware Tensor Robust Principal Component Analysis with Self-guided Data Augmentation
• Authors: Yangyang Xu, Kexin Li, Li Yang, You-Wei Wen,
• Abstract summary: We propose a self-guided data augmentation approach that employs adaptive weighting to suppress outlier influence.<n>We show the improvements in both accuracy and computational efficiency compared to state-of-the-art methods.
• Score: 21.981038455329013
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

Related papers

• Robust PCA Based on Adaptive Weighted Least Squares and Low-Rank Matrix Factorization [2.983818075226378]
  We propose a novel RPCA model that integrates adaptive weight factor update during initial component instability.<n>Our method outperforms existing non-inspired regularization approaches, offering superior performance and efficiency.
  arXiv  Detail & Related papers  (2024-12-19T08:31:42Z)
• Causal Context Adjustment Loss for Learned Image Compression [72.7300229848778]
  In recent years, learned image compression (LIC) technologies have surpassed conventional methods notably in terms of rate-distortion (RD) performance. Most present techniques are VAE-based with an autoregressive entropy model, which obviously promotes the RD performance by utilizing the decoded causal context. In this paper, we make the first attempt in investigating the way to explicitly adjust the causal context with our proposed Causal Context Adjustment loss.
  arXiv  Detail & Related papers  (2024-10-07T09:08:32Z)
• Stable Nonconvex-Nonconcave Training via Linear Interpolation [51.668052890249726]
  This paper presents a theoretical analysis of linearahead as a principled method for stabilizing (large-scale) neural network training. We argue that instabilities in the optimization process are often caused by the nonmonotonicity of the loss landscape and show how linear can help by leveraging the theory of nonexpansive operators.
  arXiv  Detail & Related papers  (2023-10-20T12:45:12Z)
• An Optimization-based Deep Equilibrium Model for Hyperspectral Image Deconvolution with Convergence Guarantees [71.57324258813675]
  We propose a novel methodology for addressing the hyperspectral image deconvolution problem. A new optimization problem is formulated, leveraging a learnable regularizer in the form of a neural network. The derived iterative solver is then expressed as a fixed-point calculation problem within the Deep Equilibrium framework.
  arXiv  Detail & Related papers  (2023-06-10T08:25:16Z)
• End-to-End Meta-Bayesian Optimisation with Transformer Neural Processes [52.818579746354665]
  This paper proposes the first end-to-end differentiable meta-BO framework that generalises neural processes to learn acquisition functions via transformer architectures. We enable this end-to-end framework with reinforcement learning (RL) to tackle the lack of labelled acquisition data.
  arXiv  Detail & Related papers  (2023-05-25T10:58:46Z)
• Scalable and Robust Tensor Ring Decomposition for Large-scale Data [12.02023514105999]
  We propose a scalable and robust TR decomposition algorithm capable of handling large-scale tensor data with missing entries and gross corruptions. We first develop a novel auto-weighted steepest descent method that can adaptively fill the missing entries and identify the outliers during the decomposition process.
  arXiv  Detail & Related papers  (2023-05-15T22:08:47Z)
• Fast Learnings of Coupled Nonnegative Tensor Decomposition Using Optimal Gradient and Low-rank Approximation [7.265645216663691]
  We introduce a novel coupled nonnegative CANDECOMP/PARAFAC decomposition algorithm optimized by the alternating gradient method (CoNCPD-APG) By integrating low-rank approximation with the proposed CoNCPD-APG method, the proposed algorithm can significantly decrease the computational burden without compromising decomposition quality.
  arXiv  Detail & Related papers  (2023-02-10T08:49:36Z)
• Fast and Provable Tensor Robust Principal Component Analysis via Scaled Gradient Descent [30.299284742925852]
  This paper tackles tensor robust principal component analysis (RPCA) It aims to recover a low-rank tensor from its observations contaminated by sparse corruptions. We show that the proposed algorithm achieves better and more scalable performance than state-of-the-art matrix and tensor RPCA algorithms.
  arXiv  Detail & Related papers  (2022-06-18T04:01:32Z)
• Deep Equilibrium Assisted Block Sparse Coding of Inter-dependent Signals: Application to Hyperspectral Imaging [71.57324258813675]
  A dataset of inter-dependent signals is defined as a matrix whose columns demonstrate strong dependencies. A neural network is employed to act as structure prior and reveal the underlying signal interdependencies. Deep unrolling and Deep equilibrium based algorithms are developed, forming highly interpretable and concise deep-learning-based architectures.
  arXiv  Detail & Related papers  (2022-03-29T21:00:39Z)
• Multiplicative noise and heavy tails in stochastic optimization [62.993432503309485]
  empirical optimization is central to modern machine learning, but its role in its success is still unclear. We show that it commonly arises in parameters of discrete multiplicative noise due to variance. A detailed analysis is conducted in which we describe on key factors, including recent step size, and data, all exhibit similar results on state-of-the-art neural network models.
  arXiv  Detail & Related papers  (2020-06-11T09:58:01Z)
• A Unified Framework for Coupled Tensor Completion [42.19293115131073]
  Coupled tensor decomposition reveals the joint data structure by incorporating priori knowledge that come from the latent coupled factors. The TR has powerful expression ability and achieves success in some multi-dimensional data processing applications. The proposed method is validated on numerical experiments on synthetic data, and experimental results on real-world data demonstrate its superiority over the state-of-the-art methods in terms of recovery accuracy.
  arXiv  Detail & Related papers  (2020-01-09T02:15:46Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.