Matrix recovery with implicitly low-rank data

Xie, Xingyu; Wu, Jian; Liu, Guangcan; Wang, Jun

doi:10.1016/j.neucom.2019.01.030

Cited by 9 publications

(1 citation statement)

References 24 publications

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“…Low-rank matrix recovery is important in many fields, such as image processing and computer vision [1][2][3], pattern recognition and machine learning [4][5][6] and many other applications [7][8][9]. Due to the sensor or environmental reasons, the observations used in these fields are readily corrupted by noise or outliers, and so the given data matrix Y can be decomposed into low-rank and sparse components.…”

Section: Introductionmentioning

confidence: 99%

Low-Rank Matrix Recovery from Noise via an MDL Framework-Based Atomic Norm

Qin

Xian

Yang

et al. 2020

Sensors

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The recovery of the underlying low-rank structure of clean data corrupted with sparse noise/outliers is attracting increasing interest. However, in many low-level vision problems, the exact target rank of the underlying structure and the particular locations and values of the sparse outliers are not known. Thus, the conventional methods cannot separate the low-rank and sparse components completely, especially in the case of gross outliers or deficient observations. Therefore, in this study, we employ the minimum description length (MDL) principle and atomic norm for low-rank matrix recovery to overcome these limitations. First, we employ the atomic norm to find all the candidate atoms of low-rank and sparse terms, and then we minimize the description length of the model in order to select the appropriate atoms of low-rank and the sparse matrices, respectively. Our experimental analyses show that the proposed approach can obtain a higher success rate than the state-of-the-art methods, even when the number of observations is limited or the corruption ratio is high. Experimental results utilizing synthetic data and real sensing applications (high dynamic range imaging, background modeling, removing noise and shadows) demonstrate the effectiveness, robustness and efficiency of the proposed method.

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Section: Introductionmentioning

confidence: 99%

Low-Rank Matrix Recovery from Noise via an MDL Framework-Based Atomic Norm

Qin

Xian

Yang

et al. 2020

Sensors

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SSCNet: learning-based subspace clustering

Xie,

Wu,

Liu

et al. 2024

Vis. Intell.

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Sparse subspace clustering (SSC), a seminal clustering method, has demonstrated remarkable performance by effectively solving the data sparsity problem. However, it is not without its limitations. Key among these is the difficulty of incremental learning with the original SSC, accompanied by a computationally demanding recalculation process that constrains its scalability to large datasets. Moreover, the conventional SSC framework considers dictionary construction, affinity matrix learning and clustering as separate stages, potentially leading to suboptimal dictionaries and affinity matrices for clustering. To address these challenges, we present a novel clustering approach, called SSCNet, which leverages differentiable programming. Specifically, we redefine and generalize the optimization procedure of the linearized alternating direction method of multipliers (ADMM), framing it as a multi-block deep neural network, where each block corresponds to a linearized ADMM iteration step. This reformulation is used to address the SSC problem. We then use a shallow spectral embedding network as an unambiguous and differentiable module to approximate the eigenvalue decomposition. Finally, we incorporate a self-supervised structure to mitigate the non-differentiability inherent in k-means to achieve the final clustering results. In essence, we assign unique objectives to different modules and jointly optimize all module parameters using stochastic gradient descent. Due to the high efficiency of the optimization process, SSCNet can be easily applied to large-scale datasets. Experimental evaluations on several benchmarks confirm that our method outperforms traditional state-of-the-art approaches.

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