Spectral clustering based on hypergraph and self-re-presentation

Yonggang Li, Shichao Zhang, Debo Cheng, Wei He, Guoqiu Wen, Qing Xie

Abstract: Traditional spectral clustering methods cluster data samples with pairwise relationships usually illustrated as graphs. However, the relationships among the data in real life are much more complex than pairwise. Merely representing the complex relationships into pairwise will result in loss of information which is helpful for improving clustering results. Moreover, the data in real life are often with noise and outliers. Therefore, to solve the problems mentioned above, we introduce hypergraph to fully consider the complex relationships of the data and use the self-representation based row sparse ℓ 2,1-norm to weaken the effect of the noise. The main contribution of this work is to integrate self-representation and hypergraph together and extend graph based spectral clustering to hypergraph. After that, we propose the spectral hypergraph clustering method named Spectral Clustering based on Hypergraph and Self-representation (HGSR). Finally, we put forward an efficient optimal method to solve the proposed problem. Experiment results showed that our method prominently outperforms the graph based methods.