提出自适应稀疏性约束的低秩子空间聚类方法，提升聚类精度。
Data-Adaptive Low-Rank Sparse Subspace Clustering
- 设计数据自适应的S0/L0近似替代函数，增强稀疏性建模能力。
- 在三个标准数据集上优于Sp/Lp（p∈{0,1/2,2/3,1}）约束的LRSSC方法。
- 理论证明全局收敛至驻点，适用于高维结构化数据聚类。
基于自表达模型的低秩稀疏子空间聚类（LRSSC）算法能有效捕捉数据的全局与局部结构。然而，现有方法主要依赖于与Sp/Lp（p ∈ {0, 1/2, 2/3, 1}）范数相关的近似算子，缺乏数据自适应性。本文提出一种结合数据自适应替代函数的LRSSC算法，该函数用于逼近S0/L0准范数。当解析表达式不可得时，提供数值求解方案。所提算法在近似映射框架下构建，并给出其全局收敛至驻点的理论证明。在三个知名数据集上评估性能，对比了受Sp/Lp（p ∈ {0, 1/2, 2/3, 1}）约束的各类LRSSC算法，验证了其优越性。
原文摘要 · Abstract (English)
Low-rank sparse subspace clustering (LRSSC) algorithms built on self-expressive model effectively capture both the global and local structure of the data. However, existing solutions, primarily based on proximal operators associated with Sp/Lp , p e {0, 1/2, 2/3, 1}, norms are not data-adaptive. In this work, we propose an LRSSC algorithm incorporating a data-adaptive surrogate for the S0/L0 quasi-norm. We provide a numerical solution for the corresponding proximal operator in cases where an analytical expression is unavailable. The proposed LRSSC algorithm is formulated within the proximal mapping framework, and we present theoretical proof of its global convergence toward a stationary point. We evaluate the performance of the proposed method on three well known datasets, comparing it against LRSSC algorithms constrained by Sp/Lp, p e {0, 1/2, 2/3, 1}, norms.
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