Robust sequential subspace clustering via ℓ1-norm temporal graph

Abstract

Subspace clustering (SC) has been widely applied to segment data drawn from multiple subspaces. However, for sequential data, a main challenge in subspace clustering is to exploit temporal information. In this paper, we propose a novel robust sequential subspace clustering approach with a ℓ1-norm temporal graph. The ℓ1-norm temporal graph is designed to encode the temporal information underlying in sequential data. By using the ℓ2 norm, it can enforce well temporal similarity of neighboring frames with a sample-dependent weight, and mitigate the effect of noises and outliers on subspace clustering because large errors mixed in the real data can be suppressed. Under assumption of data self-expression, our clustering model is put forward by further integrating the classical Sparse Subspace Clustering and the ℓ1-norm Temporal Graph (SSC-L1TG). To solve the proposed model, we introduce a new efficient proximity algorithm. At each iteration, the sub-problem is solved by proximal minimization with closed-form solution. In contrast to the alternating direction method of multipliers (ADMM) employed in most existing clustering approaches without convergence guarantee, the proposed SSC-L1TG is guaranteed to converge to the desired optimal solution. Experimental results on both synthetic and real data demonstrate the efficacy of our method and its superior performance over the state-of-the-art methods.