Learning Robust Graph Regularisation for Subspace Clustering

Various subspace clustering methods have benefited from introducing a graph regularisation term in their objective functions. In this work, we identify two critical limitations of the graph regularisation term employed in existing subspace clustering models and provide solutions for both of them. First, the squared l2-norm used in the existing term is replaced by a l1-norm term to make the regularisation term more robust against outlying data samples and noise. Solving l1 optimisation problems is notoriously expensive and a new formulation and an efficient algorithm are provided to make our model tractable. Second, instead of assuming that the graph topology and weights are known a priori and fixed during learning, we propose to learn the graph and integrate the graph learning into the proposed l1-norm graph regularised optimisation problem. Extensive experiments conducted on five benchmark datasets show that the proposed robust subspace clustering method significantly outperforms the state-of-the-art.