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<p>The Support Matrix Machine (SMM) has become a prominent model in matrix classification, seamlessly integrating into the ”Loss + Penalty” regularization framework to balance model complexity and classification accuracy. Traditional SMMs often employ the hinge loss function, which is nondifferentiable, leading to significant computational complexity in the optimization process. To address this issue, we introduce a novel differentiable alternative called the Adaptively Robust Smoothed Support Matrix Machine (ARSSMM). Our method employs adaptively robust principal component analysis by imposing the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\gamma \)</EquationSource> </InlineEquation>-norm on the low-rank matrix and the <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(l_1\)</EquationSource> </InlineEquation> norm on the sparse matrix. This approach not only mitigates the degradation in classification performance due to data corruption but also achieves more efficient estimation, especially when there are substantial disparities among the singular values of the low-rank matrix. To fully leverage the potential of ARSSMM, we have developed an effective optimization algorithm tailored to its unique structure, ensuring both efficiency and global convergence. We demonstrate the effectiveness of our model through promising experimental results on synthetic datasets under various settings, as well as on two real-world datasets.</p>

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Adaptively robust classification via smoothed support matrix machine

  • 期刊论文

  • 发表日期：

    2025年11月22日

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  • Kunjie Gao,
  • Zihao Song,
  • Tengteng Xu,
  • Weihua Zhao,
  • Xiangjian Xu

摘要

The Support Matrix Machine (SMM) has become a prominent model in matrix classification, seamlessly integrating into the ”Loss + Penalty” regularization framework to balance model complexity and classification accuracy. Traditional SMMs often employ the hinge loss function, which is nondifferentiable, leading to significant computational complexity in the optimization process. To address this issue, we introduce a novel differentiable alternative called the Adaptively Robust Smoothed Support Matrix Machine (ARSSMM). Our method employs adaptively robust principal component analysis by imposing the \(\gamma \) -norm on the low-rank matrix and the \(l_1\) norm on the sparse matrix. This approach not only mitigates the degradation in classification performance due to data corruption but also achieves more efficient estimation, especially when there are substantial disparities among the singular values of the low-rank matrix. To fully leverage the potential of ARSSMM, we have developed an effective optimization algorithm tailored to its unique structure, ensuring both efficiency and global convergence. We demonstrate the effectiveness of our model through promising experimental results on synthetic datasets under various settings, as well as on two real-world datasets.