The graph embedding (GE) methods have been widely applied for dimensionality reduction of hyperspectral imagery (HSI). However, a major challenge of GE is how to choose the proper neighbors for graph construction and explore the spatial information of HSI data. In this paper, we proposed an unsupervised dimensionality reduction algorithm called spatial-spectral manifold reconstruction preserving embedding (SSMRPE) for HSI classification. At first, a weighted mean filter (WMF) is employed to preprocess the image, which aims to reduce the influence of background noise. According to the spatial consistency property of HSI, SSMRPE utilizes a new spatial-spectral combined distance (SSCD) to fuse the spatial structure and spectral information for selecting effective spatial-spectral neighbors of HSI pixels. Then, it explores the spatial relationship between each point and its neighbors to adjust the reconstruction weights to improve the efficiency of manifold reconstruction. As a result, the proposed method can extract the discriminant features and subsequently improve the classification performance of HSI. The experimental results on the PaviaU and Salinas hyperspectral data sets indicate that SSMRPE can achieve better classification results in comparison with some state-of-the-art methods.

Marginal Fisher analysis (MFA) exploits the margin criterion to compact the intraclass data and separate the interclass data, and it is very useful to analyze the high-dimensional data. However, MFA just considers the structure relationships of neighbor points, and it cannot effectively represent the intrinsic structure of hyperspectral imagery (HSI) that possesses many homogenous areas. In this paper, we propose a new dimensionality reduction (DR) method, termed local geometric structure Fisher analysis (LGSFA), for HSI classification. Firstly, LGSFA uses the intraclass neighbor points of each point to compute its reconstruction point. Then, an intrinsic graph and a penalty graph are constructed to reveal the intraclass and interclass properties of hyperspectral data. Finally, the neighbor points and corresponding intraclass reconstruction points are used to enhance the intraclass-manifold compactness and the interclass-manifold separability. LGSFA can effectively reveal the intrinsic manifold structure and obtain the discriminating features of HSI data for classification. Experiments on the Salinas, Indian Pines, and Urban data sets show that the proposed LGSFA algorithm achieves the best classification results than other state-of-the-art methods.

Recently, the sparse representation (SR)-based graph embedding method has been extensively used in feature extraction (FE) tasks, but it is hard to reveal the complex manifold structure and multivariate relationship of samples in the hyperspectral image (HSI). Meanwhile, the small size sample problem in HSI data also limits the performance of the traditional SR approach. To tackle this problem, this article develops a new semisupervised FE algorithm called a geodesic-based sparse manifold hypergraph (GSMH). The presented method first utilizes the geodesic distance to measure the nonlinear similarity between samples lying on manifold space and further constructs the manifold neighborhood of each sample. Then, a geodesic-based neighborhood SR (GNSR) model is designed to explore the multivariate sparse correlations of different manifold neighborhoods. Considering the multivariate sparse manifold correlations among samples, a pair of semisupervised hypergraphs (HGs) is constructed to effectively incorporate the labeled and unlabeled training information in the embedding process and obtain the nonlinear discriminative feature representation for HSI. Experimental results on three HSI datasets indicate that the proposed method not only achieves satisfying FE performance with limited labeled training samples but also shows superiority compared with other state-of-the-art methods.

Sparse representation-based graph embedding methods have been successfully applied to dimensionality reduction (DR) in recent years. However, these approaches usually become problematic in the presence of the hyperspectral image (HSI) that contains complex nonlinear manifold structure. Inspired by recent progress in manifold learning and hypergraph framework, a novel DR method named local constraint-based sparse manifold hypergraph learning (LC-SMHL) algorithm is proposed to discover the manifold-based sparse structure and the multivariate discriminant sparse relationship of HSI, simultaneously. The proposed method first designs a new sparse representation (SR) model named local constrained sparse manifold coding (LCSMC) by fusing local constraint and manifold reconstruction. Then, two manifold-based sparse hypergraphs are constructed with sparse coefficients and label information. Based on these hypergraphs, LC-SMHL learns an optimal projection for mapping data into low-dimensional space in which embedding features not only discover the manifold structure and sparse relationship of original data but also possess strong discriminant power for HSI classification. Experimental results on three real HSI data sets demonstrate that the proposed LC-SMHL method achieves better performance in comparison with some state-of-the-art DR methods.

Hyperspectral image (HSI) generally contains a complex manifold structure and strong sparse correlation in its nonlinear high-dimensional data space. However, the existing manifold learning and sparse learning methods usually consider the manifold structure and sparse relationship separately rather than combining manifold and sparse properties to discover the intrinsic information in the original data. To simultaneously reveal the complex sparse relation and manifold structure of HSI, a novel feature extraction (FE) method, called local manifold-based sparse discriminant learning (LMSDL), has been proposed on the basis of manifold learning and sparse representation (SR). The LMSDL method first designs a new sparse optimization model called local manifold-based SR (LMSR) to reveal the local manifold-based sparse structure of data. Then, two geometrical sparse graphs are constructed to represent the discriminant relationship between samples and the geometrical and sparse neighbors. An objective function is constructed via geometrical sparse graphs and reconstruction points to learn a projection matrix for FE. The LMSDL effectively reveals the complex sparse relation and manifold structure in high-dimensional data, and it enhances the representation ability of extracted features for HSI classification significantly. The experimental results on the three real HSI datasets show that the proposed LMSDL algorithm possesses better performance in comparison with some state-of-the-art FE methods.

In this paper, we designed an adaptive residual convolutional neural network (ARCNN) that takes raw hyperspectral image (HSI) cubes as input data for land cover classification. In this network, spectral and spatial feature extraction blocks are explored to learn discriminative features from abundant spectral information and spatial contexts in HSI, respectively. The proposed ARCNN is an end-to-end deep learning framework that alleviates the declining-accuracy phenomenon of deep learning models, and it also ranks the correlation and importance of each band in HSI. Furthermore, the residual blocks connect every other 3-D convolutional layer by using identity mapping, which facilitates the backpropagation of gradients. In order to address the common issue of imbalance between high dimensionality and limited availability of training samples for HSI classification, attention mechanism and feature fusion block are investigated to improve the performance of the ARCNN. Finally, some strategies, batch normalization and dropout are imposed on every convolutional layer to regularize the learning process. Therefore, the ARCNN method brings benefits to extract discriminative features, and it is easier to avoid over-fitting and achieves better performance. Experimental results on three public HSI data sets demonstrate the effectiveness of ARCNN over some state-of-the-art methods.