Adaptive Mask Sampling and Manifold to Euclidean Subspace Learning with Distance Covariance Representation for Hyperspectral Image Classification

For the abundant spectral and spatial information recorded in hyperspectral images (HSIs), fully exploring spectral-spatial relationships has attracted widespread attention in hyperspectral image classification (HSIC) community. However, there are still some intractable obstructs. For one thing, in the patch-based processing pattern, some spatial neighbor pixels are often inconsistent with the central pixel in land-cover class. For another thing, linear and nonlinear correlations between different spectral bands are vital yet tough for representing and excavating. To overcome these mentioned issues, an adaptive mask sampling and manifold to Euclidean subspace learning (AMS-M2ESL) framework is proposed for HSIC. Specifically, an adaptive mask based intra-patch sampling (AMIPS) module is firstly formulated for intra-patch sampling in an adaptive mask manner based on central spectral vector oriented spatial relationships. Subsequently, based on distance covariance descriptor, a dual channel distance covariance representation (DC-DCR) module is proposed for modeling unified spectral-spatial feature representations and exploring spectral-spatial relationships, especially linear and nonlinear interdependence in spectral domain. Furthermore, considering that distance covariance matrix lies on the symmetric positive definite (SPD) manifold, we implement a manifold to Euclidean subspace learning (M2ESL) module respecting Riemannian geometry of SPD manifold for high-level spectral-spatial feature learning. Additionally, we introduce an approximate matrix square-root (ASQRT) layer for efficient Euclidean subspace projection. Extensive experimental results on three popular HSI data sets with limited training samples demonstrate the superior performance of the proposed method compared with other state-of-the-art methods. The source code is available at https://github.com/lms-07/AMS-M2ESL.