Outlier-Robust Multi-View Subspace Clustering with Prior Constraints

Data may have multiple modalities, known as multi-view data. With the assumption that multi-view data often lie on a latent subspace, multi-view subspace clustering finds the underlying subspace by leveraging multiple views and clusters the data accordingly. Due to inevitable system errors, multi-view data may contain outliers and it may not therefore strictly follow subspace structure. Besides, prior information such as pairwise constraints describing relations between data instances is often available. These constraints provide a valuable guide on learning. Unfortunately, standard multi-view subspace clustering methods do not simultaneously exploit high order correlations among views and prior constraints with low computational complexity. In this paper, we propose a novel Robust Multi-View Subspace Clustering method, named as RMVSC, which is capable of taking advantage of high order correlations among views and prior constraints for outlier-robust multi-view subspace clustering with low computational complexity. The key idea is to use a low-rank tensor along with a constraint to integrate information from views and prior constraints for more comprehensive learning. We regard underlying clean subspace of singular vectors of views (leveraging views) which also represent projection coefficient of cluster membership vectors in data space (utilizing prior constraints) as a tensor. By decomposing singular vector of each view into its underlying clean subspace and a structured-sparse error (outlier) term, we characterize outliers explicitly. To solve the challenging optimization problem, we develop an algorithm based on Augmented Lagrangian Multiplier. Experimental results on real-world datasets show the superiority of the proposed method and its robustness against outliers.