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<p>In recent years, tensor learning based multi-view subspace clustering (TLMSC) methods have been raised wide attention. Generally, TLMSC methods use low-rank representations to capture the relationship between the data and apply tensor rank functions for biased estimation. However, these methods treat the different singular values with the averaging regularization, which leads to the insufficient utilization of matrix prior information. Furthermore, these methods usually only consider one of Laplacian noise or Gaussian noise, which cannot well represent the noise information in the data and affect the clustering performance. To solve the above problems, we propose a novel TLMSC method, i.e., nonconvex low-rank tensor approximation with denoising model for multi-view subspace clustering (NLTDC), which not only removes Laplacian noise and Gaussian noise simultaneously but also considers the different contributions of singular values. Specifically, we first preserve the local information of the view by manifold learning. Then, we model the noise by using Laplacian noise (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(l_1\)</EquationSource> </InlineEquation>-norm for the loss) and Gaussian noise(<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(l_{2,1}\)</EquationSource> </InlineEquation>-norm for the loss) in the matrices, which thinking both types of noise simultaneously facilitate the recovery of clean tensors and obtain more accurate tensor subspace structures. Furthermore, to fully utilize the prior information of the matrix, we use the weighted tensor Schatten <i>p</i>-norm to assign reasonable weights to singular values. In addition, we design an optimization strategy utilizing the alternating direction method of multipliers (ADMM). Experiments on five commonly used datasets show that our proposed algorithm has better performance.</p>

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Nonconvex low-rank tensor approximation with denoising model for multi-view subspace clustering

  • 期刊论文

  • 发表日期：

    2025年10月27日

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  • Yong Wang,
  • Ao Li,
  • Guifu Lu,
  • Weiping Ding,
  • Huadong Zhou

摘要

In recent years, tensor learning based multi-view subspace clustering (TLMSC) methods have been raised wide attention. Generally, TLMSC methods use low-rank representations to capture the relationship between the data and apply tensor rank functions for biased estimation. However, these methods treat the different singular values with the averaging regularization, which leads to the insufficient utilization of matrix prior information. Furthermore, these methods usually only consider one of Laplacian noise or Gaussian noise, which cannot well represent the noise information in the data and affect the clustering performance. To solve the above problems, we propose a novel TLMSC method, i.e., nonconvex low-rank tensor approximation with denoising model for multi-view subspace clustering (NLTDC), which not only removes Laplacian noise and Gaussian noise simultaneously but also considers the different contributions of singular values. Specifically, we first preserve the local information of the view by manifold learning. Then, we model the noise by using Laplacian noise ( \(l_1\) -norm for the loss) and Gaussian noise( \(l_{2,1}\) -norm for the loss) in the matrices, which thinking both types of noise simultaneously facilitate the recovery of clean tensors and obtain more accurate tensor subspace structures. Furthermore, to fully utilize the prior information of the matrix, we use the weighted tensor Schatten p-norm to assign reasonable weights to singular values. In addition, we design an optimization strategy utilizing the alternating direction method of multipliers (ADMM). Experiments on five commonly used datasets show that our proposed algorithm has better performance.