Graph Convolutional Subspace Clustering: A Robust Subspace Clustering Framework for Hyperspectral Image

Abstract

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