A Nonlinear Weighted Graph Convolution Network Based on Manifold Geometric Regularization for Hyperspectral Image Classification

Extracting spatial–spectral joint features has become a critical approach for improving model classification performance in the field of hyperspectral image classification (HSIC). However, existing methods fail to fully exploit nonlinear spatial–spectral information. Unlike traditional convolutional neural networks (CNNs), graph convolutional networks (GCNs) can extract nonlinear spatial information. Nevertheless, both methods lack an accurate measurement of local neighborhood information, leading to blurred classification boundaries for ground objects. Additionally, the high-dimensional nature of hyperspectral data results in poor generalization and redundant information of trained models. To address these three issues, a nonlinear weighted graph convolution network based on manifold geometric regularization (MGR-NWGCN) method is devised for HSIC. Specifically, a nonlinear weighted graph convolution network (NWGCN) module is designed, which utilizes a graph-in-graph structure based on cosine similarity-based normalized weighted graph convolution to extract nonlinear spatial–spectral information. Then, the manifold curvature regularization (C-MGR) module is implemented to improve the accuracy of similarity measurement and to enhance the generalization ability of the model, which constrains the model to form flatter feature manifold surfaces. Finally, the manifold intrinsic dimensionality regularization (ID-MGR) module is developed with the aim of eliminating redundant information, which embeds noise onto the surface of a low-dimensional manifold. The superior classification performance and robustness of the proposed MGR-NWGCN method are validated through extensive experiments on four datasets, with comparisons conducted against nine methods.