提出一种更鲁棒的低维结构学习模型，能适应多种噪声类型。
Robust Subspace-Constrained Quadratic Models for Low-Dimensional Structure Learning
- 基于二次矩阵分解框架，引入子空间约束提升模型稳定性。
- 在重尾和轻尾噪声下均表现优异，重建精度显著优于现有方法。
- 适合处理含复杂噪声的高维数据，如生物或金融信号分析。
本文提出一种鲁棒的子空间约束二次模型（SCQM），用于从高维数据中学习低维结构。在子空间约束二次矩阵分解（SQMF）框架基础上，该模型可兼容广义高斯和径向拉普拉斯等多类噪声分布，从而在重尾与轻尾噪声下均保持可靠性能，显著提升不同数据场景下的鲁棒性。为高效求解由此带来的非凸优化问题，我们设计了一种基于梯度且带有回溯线搜索策略的算法，确保收敛稳定高效。此外，还对ℓₚᵖ和ℓ₂损失函数进行了敏感性分析，揭示其在不同噪声特性下的差异行为。大量数值实验验证了理论分析，并表明所提方法在鲁棒性和重构精度上持续优于现有方法。
原文摘要 · Abstract (English)
In this paper, we propose a robust subspace-constrained quadratic model (SCQM) for learning low-dimensional structure from high-dimensional data. Building upon the subspace-constrained quadratic matrix factorization (SQMF) framework, the proposed model accommodates a broad class of noise distributions, including generalized Gaussian and radial Laplace models. This generalization enables reliable performance under both heavy-tailed and light-tailed noise, thereby substantially enhancing robustness across diverse data regimes. To efficiently address the resulting nonconvex optimization problem, we develop a gradient-based algorithm equipped with a backtracking line-search strategy that ensures stable and efficient convergence. In addition, we present a sensitivity analysis of the $\ell_p^p$ and $\ell_2$ loss functions, elucidating their distinct behaviors under varying noise characteristics. Extensive numerical experiments corroborate the theoretical analysis and demonstrate that the proposed approach consistently outperforms existing methods in terms of robustness and reconstruction accuracy.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。