Sparse Subspace Clustering via Two-Step Reweighted L1-Minimization: Algorithm and Provable Neighbor Recovery Rates

Sparse subspace clustering (SSC) relies on sparse regression for accurate neighbor identification. Inspired by recent progress in compressive sensing, this paper proposes a new scheme SSC via two-step reweighted $\ell _{1} $ -minimization, which also generalizes -minimization algorithm introduced E. J. Candès et al. [ xmlns:xlink="http://www.w3.org/1999/xlink">The Annals of Statistics , vol. 42, no. 2, pp. 669–699, 2014] without incurring extra algorithmic complexity. To fully exploit the prior information offered computed representation vector first step, our approach places weight each component vector, and solves weighted LASSO second step. We propose data weighting rule suitable enhancing identification accuracy. Then, under formulation dual problem LASSO, we study depth theoretical recovery rates proposed scheme. Specifically, an interesting connection between locations nonzeros optimal solution to indexes active constraints is established. Afterwards, semi-random model, analytic probability lower/upper bounds various events are derived. Our results confirm that, with aid if enough, higher can produce many correct neighbors few incorrect as compared weighting. Computer simulations provided validate evidence effectiveness approach.