Facilitated low-rank multi-view subspace clustering

Abstract

Low-rank multi-view subspace clustering has recently attracted increasing attention in the multi-view learning research. Despite significant progress, most existing approaches still suffer from two issues. First, they mostly focus on exploiting the low-rank consistency across multiple views, but often ignore the low-rank structure within each view. Second, they often encounter the expensive time overhead, typically owing to the costs of matrix inversion and singular value decomposition (SVD) at each iteration. In light of this, we propose an efficient and effective approach termed Facilitated Low-rank Multi-view Subspace Clustering (FLMSC) in this paper. In terms of efficiency, our approach factorizes the view-specific representation matrix into two small factor matrices, i.e., an orthogonal dictionary and a latent representation, which mitigates the computation cost of solving SVD problems. In terms of effectiveness, our approach preserves the latent low-rank structure within each view, while at the same time encourages the structural consistency across different views by imposing an agreement term. Based on this, our approach can fully explore the underlying subspace structure of multiple views, so as to better serve for the following spectral clustering. Besides, a facilitated iterative algorithm is developed for the resultant optimization problem, upon which the matrix inversion operation is substantially accelerated during iterations. Experimental results on a variety of multi-view data sets demonstrate the effectiveness and efficiency of our approach. The source code and data sets are available at: https://www.researchgate.net/publication/365349930_FLMSC_v1.