提出自适应张量低秩模型，提升图像聚类抗噪能力
Data-Adaptive Transformed Bilateral Tensor Low-Rank Representation for Clustering
- 通过学习任意酉变换实现数据自适应核范数
- 融合双边结构捕捉样本与特征的局部相关性
- 结合l1/2和Frobenius正则项应对复杂现实噪声
张量低秩表示（TLRR）在图像聚类中表现优异，但现有方法多依赖固定变换，对噪声鲁棒性差。本文提出新型变换双侧张量低秩表示模型TBTLRR，通过学习任意酉变换引入数据自适应张量核范数，更有效捕捉全局相关性；同时利用潜在张量数据的双边结构，挖掘图像样本与特征间的局部相关性；此外，集成l1/2-范数与Frobenius范数正则项，更好处理真实场景中的复杂噪声。为求解该非凸模型，提出基于交替方向乘子法（ADMM）的高效优化算法，并提供理论收敛性证明。大量实验验证其优于当前最优方法。代码将发布于https://github.com/xianchaoxiu/TBTLRR。
原文摘要 · Abstract (English)
Tensor low-rank representation (TLRR) has demonstrated significant success in image clustering. However, most existing methods rely on fixed transformations and suffer from poor robustness to noise. In this paper, we propose a novel transformed bilateral tensor low-rank representation model called TBTLRR, which introduces a data-adaptive tensor nuclear norm by learning arbitrary unitary transforms, allowing for more effective capture of global correlations. In addition, by leveraging the bilateral structure of latent tensor data, TBTLRR is able to exploit local correlations between image samples and features. Furthermore, TBTLRR integrates the $\ell_{1/2}$-norm and Frobenius norm regularization terms for better dealing with complex noise in real-world scenarios. To solve the proposed nonconvex model, we develop an efficient optimization algorithm inspired by the alternating direction method of multipliers (ADMM) and provide theoretical convergence. Extensive experiments validate its superiority over the state-of-the-art methods in clustering. The code will be available at https://github.com/xianchaoxiu/TBTLRR.
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