Multi-order graph based clustering via dynamical low rank tensor approximation

Nian Wang, Zhigao Cui, Aihua Li, Yuanliang Xue, Rong Wang, Feiping Nie

Abstract: Graph based clustering involves learning a proximity matrix with explicit clustering structure. However, since the limited link inputs and insufficient graph fusion, current works always obtain poor graphs with suboptimal clustering results. To solve the problem, in this paper, we propose a novel multi-order graph based clustering model via dynamic low-rank tensor approximation (MCDLT). Firstly, we use high-order proximity to enrich the link relations for graph inputs. Then a graph selection mechanism and low rank tensor approximation method are used to dynamically learn the consistent information from the complex links in various-order graphs. Finally, we propose a doubly stochastic graph fusion method to directly learn a symmetrical graph that provides clustering results by its connectivity. A novel Augmented Lagrangian Multiplier (ALM) based method is proposed for the sub-problem of doubly stochastic constraints. Experiments shows that our method learns a graph with clearer data structure, achieving SOTA clustering performance and obtaining the GroundTruth for JAFFE data set. Code will be published at https://github.com/NianWang-HJJGCDX/MCDLT.git.