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

Abstract

For the abundant spectral and spatial information recorded in hyperspectral images (HSIs), fully exploring spectral–spatial relationships has attracted widespread attention in the HSI 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 the Euclidean subspace learning (AMS-M2ESL) framework is proposed for HSIC. Specifically, an adaptive mask-based intrapatch sampling (AMIPS) module is first formulated for intrapatch sampling in an adaptive mask manner based on central spectral vector-oriented spatial relationships. Subsequently, based on the 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 the spectral domain. Furthermore, considering that the distance covariance matrix lies on the symmetric positive definite (SPD) manifold, we implement an M2ESL module respecting the Riemannian geometry of the 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 datasets 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.