Spectral clustering is a powerful tool for unsupervised data analysis. In this paper, we propose a context-aware hypergraph similarity measure (CAHSM), which leads to robust spectral clustering in the case of noisy data. We construct three types of hypergraph---the pairwise hypergraph, the k-nearest-neighbor (kNN) hypergraph, and the high-order over-clustering hypergraph. The pairwise hypergraph captures the pairwise similarity of data points; the kNN hypergraph captures the neighborhood of each point; and the clustering hypergraph encodes high-order contexts within the dataset. By combining the affinity information from these three hypergraphs, the CAHSM algorithm is able to explore the intrinsic topological information of the dataset. Therefore, data clustering using CAHSM tends to be more robust. Considering the intra-cluster compactness and the inter-cluster separability of vertices, we further design a discriminative hypergraph partitioning criterion (DHPC). Using both CAHSM and DHPC, a robust spectral clustering algorithm is developed. Theoretical analysis and experimental evaluation demonstrate the effectiveness and robustness of the proposed algorithm.

本文提出了一种上下文感知的超图相似度测量方法和一种基于此的健壮谱聚类算法，该算法可以处理有噪声的数据并且结合了三种超图处理方法：成对超图、k近邻超图和超分类超图，同时使用判别式超图分割准则进行聚类。实验表明，该算法具备高效性和鲁棒性。

上下文感知的超图构建方法用于稳健的谱聚类