Spectral clustering based on hypergraph and self-re-presentation Yonggang Li 1 & Shichao Zhang 1 & Debo Cheng 1 & Wei He 1 & Guoqiu Wen 1 & Qing Xie 2 Received: 15 May 2016 /Revised: 14 September 2016 /Accepted: 3 November 2016 # Springer Science+Business Media New York 2016 Abstract Traditional spectral clustering methods cluster data samples with pairwise relation- ships 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 relation- ships 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 promi- nently outperforms the graph based methods. Keywords Spectral clustering . Hypergraph . Row-sparse . Self-representation . Hypergraph Laplacian 1 Introduction Clustering is a fundamental issue in many aspects of computer vision and machine learning [11]. The main focus of it is to cluster data so that the data in same cluster could reveal consistent relationships, while objects which do not pertain to the same cluster should not Multimed Tools Appl DOI 10.1007/s11042-016-4131-6 * Shichao Zhang mtlyg2@sina.com 1 Guangxi Key Lab of Multi-source Information Mining & Security, Guangxi Normal University, Guilin, Guangxi 541004, China 2 Wuhan University of Technology, Wuhan, Hubei 430070, China