基于超图和样本自表征的谱聚类算法

Hypergraph and self-representation for spectral clustering

针对传统谱聚类算法仅考虑数据点对点间的相互关系而未考虑数据间可能隐藏的复杂的相关性的问题,提出一种基于超图和自表征的谱聚类方法。首先,建立数据的超图,得到超图的拉普拉斯矩阵表示;然后利用l_(2,1)-范数对样本进行行稀疏自表征,同时融入超图来描述数据间多层次的相互关系;最后,利用生成的自表征系数进行谱聚类。利用基于超图的样本自表征技术考虑了样本之间复杂的相关性。通过在Hopkins155等数据集上的实验表明,在聚类错误率评判标准下,算法优于现有基于普通图的谱聚类算法SSC、SRC等。

To solve the issue that the traditional spectral clustering methods constructed the similarity matrix by only considering the pairwise relationship of the data but ignoring the complicated correlations among samples, this paper put forward a hypergraph and self-representation based spectral Clustering method, called hypergraph and self-representation for spectral clustering （HGSR）. Firstly, the algorithm constructed a hypergraph which fully considered the relations of samples to output the hypergraph Laplacian matrix. Secondly, it conducted row sparse self-representation for all samples by utilizing an l2.1-norm regu- larizer, and also put hypergraph Laplacian into the regulation to guarantee the local structure of each sample. In this way, simi- lar samples were clustered into same cluster. At last, it obtained an affinity matrix for conducting spectral clustering. By utilizing the hypergraph based self-representation, it considered the complicate relationships between the samples. The experimental resuits of Hopkins155 dataset and some image datasets show that the proposed method outperforms the LSR, SSC and LRR, in terms of the subspace clustering error.