Enhanced Low-rank Constraint for Temporal Subspace Clustering and Its Acceleration Scheme

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.