  Hyperspectral image (HSI) clustering is a challenging task due to the high
complexity of HSI data. Subspace clustering has been proven to be powerful for
exploiting the intrinsic relationship between data points. Despite the
impressive performance in the HSI clustering, traditional subspace clustering
methods often ignore the inherent structural information among data. In this
paper, we revisit the subspace clustering with graph convolution and present a
novel subspace clustering framework called Graph Convolutional Subspace
Clustering (GCSC) for robust HSI clustering. Specifically, the framework
recasts the self-expressiveness property of the data into the non-Euclidean
domain, which results in a more robust graph embedding dictionary. We show that
traditional subspace clustering models are the special forms of our framework
with the Euclidean data. Basing on the framework, we further propose two novel
subspace clustering models by using the Frobenius norm, namely Efficient GCSC
(EGCSC) and Efficient Kernel GCSC (EKGCSC). Both models have a globally optimal
closed-form solution, which makes them easier to implement, train, and apply in
practice. Extensive experiments on three popular HSI datasets demonstrate that
EGCSC and EKGCSC can achieve state-of-the-art clustering performance and
dramatically outperforms many existing methods with significant margins.
