Efficient Anchor Graph Factorization for Multi-View Clustering
Jing Li, Qianqian Wang, Ming Yang, Quanxue Gao, Xinbo Gao
Abstract
Due to the excellent interpretability of non-negative matrix factorization (NMF), NMF-based multi-view clustering has attracted much attention for multi-media data analysis and processing. However, the existing clustering methods leverage NMF to cluster data matrix, resulting in high computational complexity. Moreover, they are sub-optimal to exploit the complementary information between views because they all measure the between-views error pixel by pixel. To tackle this problem, inspired by orthogonal NMF and anchor graph, we present an efficient anchor graph factorization model with orthogonal, non-negative, and tensor low-rank constraints. We use an anchor graph instead of a data matrix to get an indicator matrix without post-processing, which remarkably reduces the computational complexity. To exploit the between-views complementary information well, we introduce tensor Schatten <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$p$</tex-math></inline-formula> -norm regularization on the third tensor, composed of soft label matrices of views. The solution can be obtained by iteratively optimizing four decoupled sub-problems, which can be solved more efficiently with good convergence. Through experimental results on the six multi-view datasets, our approach ensures the enhancement of clustering performance while improving efficiency.