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Subspace clustering methods have become a powerful tool to cluster hyperspectral imaging (HSI) data as they ensure theoretical guarantees and empirical success. However, existing methods explore subspace representation in the Euclidean space, and thus, failing to exploit the high-order relationship and long-range interdependences. This article presents a simple yet effective method, to extend subspace clustering into the non-Euclidean domain entitled hypergraph convolutional subspace clustering (HGCSC). Instead of treating HSI as Euclidean data only, we represent all the intraclass relations as hyperedges in a hypergraph. With this representation, we can recast the classic self-expression as a hypergraph convolutional self-representation model. To explore the long-range neighboring relation, we introduce a multihop hypergraph convolution process into the method by collapsing the repeated multiplications into a single matrix. HGCSC adopts the Frobenius norm to ensure a closed-form solution. We assess the performance of HGCSC on five real HSI datasets and show that HGCSC significantly outperforms competitors in terms of clustering accuracy.

Hypergraph Convolutional Subspace Clustering With Multihop Aggregation for Hyperspectral Image