发表机构
University of Kentucky（肯塔基大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出基于幂次范数比正则化的SNMF模型，结合DCA与ADMM算法求解，在锚点识别和分类任务上性能优于或媲美现有方法，计算效率具竞争力。
AI 中文摘要
可分非负矩阵分解（SNMF）因能生成基于部分的、可解释的分解结果，已广泛应用于非负数据的低秩表示与聚类，尤其与图聚类和社区检测密切相关。为提升学习到的因子的稀疏性与可识别性，我们提出一种基于幂次范数比正则项的ℓ₁^p/ℓ₂正则化SNMF模型。该模型非凸且非光滑，给优化带来重大挑战。为解决此问题，我们开发了基于凸差分算法（DCA）和乘子交替方向法（ADMM）的高效算法，所提方法利用与幂次范数项相关的闭式邻近算子，将原问题分解为易处理的子问题。我们证明了DCA方案的下降性与极限临界性，以及ADMM方案在标准假设下的收敛性。在合成数据集和手势分类任务上的大量数值实验表明，与现有SNMF方法相比，所提方法在锚点识别和分类准确率上达到了有竞争力或更优的性能，同时保持了有竞争力的计算效率。
英文摘要
Separable nonnegative matrix factorization (SNMF) has been widely used for low-rank representation and clustering of nonnegative data, owing to its ability to produce part-based and interpretable decompositions. In particular, SNMF is closely related to graph clustering and community detection. To enhance sparsity and identifiability of the learned factors, we propose an $\ell_1^p/\ell_2$-regularized SNMF model based on a powered ratio-of-norms regularizer. The resulting formulation is nonconvex and nonsmooth, which poses significant challenges for optimization. To address this, we develop efficient algorithms based on the difference-of-convex function algorithm (DCA) and the alternating direction method of multipliers (ADMM). The proposed methods decompose the original problem into tractable subproblems, leveraging closed-form proximal operators associated with the powered norm terms. We establish descent and limiting criticality properties for the DCA scheme and convergence under standard assumptions for the ADMM scheme. Extensive numerical experiments on synthetic datasets and hand gesture classification tasks demonstrate that the proposed approach achieves competitive or improved performance in anchor identification and classification accuracy compared with existing SNMF methods, while maintaining competitive computational efficiency.
