Rank-<i>r</i> Discrete Matrix Factorization for Anchor Graph Clustering
Jingjing Xue, Feiping Nie, Rong Wang, Xuelong Li
Abstract
Considering many graph clustering methods are with quadratic or cubic time complexity and need post-processing to obtain the discrete solution. Combining with the anchor graph, we study a novel graph clustering model called Rank- <inline-formula><tex-math notation="LaTeX">$r$</tex-math></inline-formula> Discrete Matrix Factorization (DMF-RR), which is linear time complexity, and motivated by nonnegative matrix factorization (NMF). Instead of constraining the factor matrices of NMF to be nonnegative as many existed methods, we constrain them to indicator matrices. Thus, DMF-RR can obtain the discrete solution by directly solving the original problem without post-processing. Furthermore, considering the greater similarity between samples of the same category, an anchor graph is constructed as an input to capture essential clustering structure by utilizing the duality information between samples and anchors. Subsequently, an efficient and simple algorithm is proposed due to the nature of indicator matrices. Extensive experiments performed on synthetic and real-world datasets demonstrate the superiority of DMF-RR.