Abstract Inspired by the temporal subspace clustering (TSC) method and low-rank matrix approximation constraint, a new model is proposed termed as temporal plus low-rank subspace clustering (TLRSC) by utilizing both the local and global structural information. On one hand, to solve the drawback that the nuclear norm-based constraint usually results in a suboptimal solution, we incorporate certain nonconvex surrogates into our model, which approximates the low-rank constraint closely and holds the potential for the convexity of the whole cost function. On the other hand, to ensure fast convergence, we propose an efficient iteratively reweighted singular value minimization (IRSVD) algorithm under the majorization-minimization framework. Moreover, we show that for the weighted low-rank constraint, a cutoff can be derived to automatically threshold the singular values computed from the proximal operator. This guarantees the thresholding operation can be reduced to that of two smaller matrices. Accordingly, an efficient singular value thresholding scheme is proposed for acceleration. Comprehensive experiments are conducted on several public available datasets for quantitative evaluation. Results demonstrate the efficacy and efficiency of TLRSC compared with several state-of-the-art methods.

中文翻译：

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时间子空间聚类的增强低秩约束及其加速方案

摘要 受时间子空间聚类（TSC）方法和低秩矩阵近似约束的启发，提出了一种利用局部和全局结构信息的时间加低秩子空间聚类（TLRSC）模型。一方面，为了解决基于核范数的约束通常会导致次优解决方案的缺点，我们将某些非凸代理纳入我们的模型，它非常接近低秩约束并保持整个成本的凸性的潜力功能。另一方面，为了确保快速收敛，我们在主最小化框架下提出了一种高效的迭代重新加权奇异值最小化（IRSVD）算法。此外，我们表明，对于加权低秩约束，可以导出一个截止值来自动阈值从近端算子计算的奇异值。这保证了阈值操作可以减少到两个较小矩阵的操作。因此，提出了一种用于加速的有效奇异值阈值方案。对几个公开可用的数据集进行了综合实验以进行定量评估。结果表明，与几种最先进的方法相比，TLRSC 的功效和效率。