One-step temporal subspace clustering with structured sparsity and indicator graph-Laplacian regularization

Subspace clustering (SC) is a powerful technique for effectively segmenting data residing in multiple subspaces. However, traditional SC methods often fall short in accurately clustering temporal data due to their limited ability to capture temporal dependencies. These methods typically adopt a two-step framework: first, an affinity matrix is learned from the data; second, spectral clustering is performed using the affinity matrix to construct the indicator matrix for achieving the final segmentation. This disjointed process neglects the interdependence between the affinity matrix and the cluster assignments, and hence fails to fully exploit the temporal smoothness inherent in sequential data, where neighboring samples are usually similar. To address these limitations, we propose a novel one-step temporal subspace clustering method that integrates Structured Sparsity and Indicator graph-Laplacian regularization, termed SSIL. Our approach improves upon existing temporal SC techniques in two key aspects. First, we introduce a temporal Indicator Graph-Laplacian (IL) regularization directly on the indicator matrix, which promotes temporal smoothness and enhances alignment between the clustering result and ground truth. Second, we incorporate Structured Sparsity (SS) to jointly learn the affinity and indicator matrices within a unified optimization framework. We further develop an efficient optimization algorithm to alternatingly solve the affinity and indicator matrices. Extensive experiments on six benchmark datasets, particularly on motion capture data, demonstrate the effectiveness of our method and its superior performance compared to several state-of-the-art approaches.