On Reliable Multi-View Affinity Learning for Subspace Clustering

Abstract

In multi-view subspace clustering, the low-rankness of the stacked self-representation tensor is widely accepted to capture the high-order cross-view correlation. However, using the nuclear norm as a convex surrogate of the rank function, the self-representation tensor exhibits strong connectivity with dense coefficients. When noise exists in the data, the generated affinity matrix may be unreliable for subspace clustering as it retains the connections across inter-cluster samples due to the lack of sparsity. Since both the connectivity and sparsity of the self-representation coefficients are curial for subspace clustering, we propose a Reliable Multi-View Affinity Learning (RMVAL) method so as to optimize both properties in a single model. Specifically, RMVAL employs the low-rank tensor constraint to yield a well-connected yet dense solution, and purifies the densely connected self-representation tensor by preserving only the connections in local neighborhoods using the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$l_1$</tex-math></inline-formula> -norm regularization. This way, the strong connections on the self-representation tensor are retained and the trivial coefficients corresponding to the inter-cluster connections are suppressed, leading to a “clean” self-representation tensor and also a reliable affinity matrix. We propose an efficient algorithm to solve RMVAL using the alternating direction method of multipliers. Extensive experiments on benchmark databases have demonstrated the superiority of RMVAL.