Self-Supervised Learning of Discriminative Spatial–Spectral Features for Hyperspectral Images Clustering

Abstract

Deep subspace clustering methods have demonstrated its outstanding capability for hyperspectral image (HSI) clustering. However, there is a lack of explicit supervision to ensure that low-dimensional spatial–spectral features learned from high-dimensional HSI cubes have good subspace structures. In this letter, we propose a cascade residual capsule network (CRCN) for extracting deep spatial–spectral features and introduce the coding rate reduction (CRR) to measure the compactness of learned spatial–spectral features. We exploit the difference between the coding rate of all features and the sum of that of features of each category as loss function, which provides explicit supervision for learning invariant spatial–spectral features to HSI cube flips and rotations and facilitate the subsequent HSI clustering. To learn features that are discriminative to diverse spatial context information on land-cover objects of the same category, we add a regularization term to the loss function, which is a brink loss between the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${l_{2}}$ </tex-math></inline-formula> -norm of active vectors of class capsules in the proposed CRCN and the assigned labels. Experimental results on three benchmark HSI datasets demonstrate the effectiveness of the proposed method, which achieves superiority performance over several state-of-the-art HSI clustering methods.