Multi-view low-rank sparse subspace clustering

•A multi-view low-rank plus sparse subspace clustering algorithm is proposed.•Agreements are enforced between representations of the pairs of views or towards a common centroid.•Constrained convex optimization problem is for each view solved using alternating direction method of multipliers.•By solving related problem in reproducing kernel Hilbert space, kernel extension of the algorithm is derived.•Experimental results demonstrate that the proposed algorithm outperforms state-of-the-art multi-view subspace clustering algorithms.

Most existing approaches address multi-view subspace clustering problem by constructing the affinity matrix on each view separately and afterwards propose how to extend spectral clustering algorithm to handle multi-view data. This paper presents an approach to multi-view subspace clustering that learns a joint subspace representation by constructing affinity matrix shared among all views. Relying on the importance of both low-rank and sparsity constraints in the construction of the affinity matrix, we introduce the objective that balances between the agreement across different views, while at the same time encourages sparsity and low-rankness of the solution. Related low-rank and sparsity constrained optimization problem is for each view solved using the alternating direction method of multipliers. Furthermore, we extend our approach to cluster data drawn from nonlinear subspaces by solving the corresponding problem in a reproducing kernel Hilbert space. The proposed algorithm outperforms state-of-the-art multi-view subspace clustering algorithms on one synthetic and four real-world datasets.