  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.
