Hyperspectral image (HSI) clustering is a challenging task due to the high complexity of HSI data. Subspace clustering has been proven to be powerful for exploiting the intrinsic relationship between data points. Despite the impressive performance in the HSI clustering, traditional subspace clustering methods often ignore the inherent structural information among data. In this article, we revisit the subspace clustering with graph convolution and present a novel subspace clustering framework called graph convolutional subspace clustering (GCSC) for robust HSI clustering. Specifically, the framework recasts the self-expressiveness property of the data into the non-Euclidean domain, which results in a more robust graph embedding dictionary. We show that traditional subspace clustering models are the special forms of our framework with the Euclidean data. On the basis of the framework, we further propose two novel subspace clustering models by using the Frobenius norm, namely efficient GCSC (EGCSC) and efficient kernel GCSC (EKGCSC). Each model has a globally optimal closed-form solution, making it easier to implement, train, and apply in practice. Extensive experiments strongly evidence that EGCSC and EKGCSC dramatically outperform current models on three popular HSI data sets consistently.

Autoencoder (AE) is an unsupervised neural network framework for efficient and effective feature extraction. Most AE-based methods do not consider spatial information and band correlations for hyperspectral image (HSI) analysis. In addition, graph-based AE methods often learn discriminative representations with the assumption that connected samples share the same label and they can not directly embed the geometric structure into feature extraction. To address these issues, in this paper, we propose a dual graph autoencoder (DGAE) to learn discriminative representations for HSIs. Utilizing the relationships of pair-wise pixels within homogenous regions and pair-wise spectral bands, DGAE first constructs the superpixel-based similarity graph with spatial information and band-based similarity graph to characterize the geometric structures of HSIs. With the developed dual graph convolution, more discriminative feature representations are learnt from the hidden layer via the encoder-decoder structure of DGAE. The main advantage of DGAE is that it fully exploits both the geometric structures of pixels with spatial information and spectral bands to promote nonlinear feature extraction of HSIs. Experiments on HSI datasets show the superiority of the proposed DGAE over the state-of-the-art methods. The source code of DGAE is available at https://github.com/ZhangYongshan/DGAE.

As the most classical unsupervised dimension reduction algorithm, principal component analysis (PCA) has been widely used in hyperspectral images (HSIs) preprocessing and analysis tasks. Recently proposed superpixelwise PCA (SuperPCA) has shown promising accuracy where superpixels segmentation technique was first used to segment an HSI to various homogeneous regions and then PCA was adopted in each superpixel block to extract the local features. However, the local features could be ineffective due to the neglect of global information especially in some small homogeneous regions and/or in some large homogeneous regions with mixed ground truth objects. In this article, a novel spectral–spatial and SuperPCA (S ³ -PCA) is proposed to learn the effective and low-dimensional features of HSIs. Inspired by SuperPCA we further adopt superpixels-based local reconstruction to filter the HSIs and use the PCA-based global features as the supplement of local features. It turns out that the global–local and spectral–spatial features can be well exploited. Specifically, each pixel of an HSI is reconstructed by the nearest neighbors’ pixels in the same superpixel block, which could eliminate the noise and enhance the spatial information adaptively. After the local reconstruction-based data preprocessing, PCA is performed on each region and the entire HSI to obtain local and global features, respectively. Then we simply concatenate them to get the global–local and spectral–spatial features for HSIs classification. The experimental results on two HSIs data sets demonstrate the superiority of the proposed method over the state-of-the-art methods. The source code of the proposed model is available at https://github.com/XinweiJiang/S3-PCA .

Unsupervised band selection is an essential step in preprocessing hyperspectral images (HSIs) to select informative bands. Most existing methods exploit the spatial information from the entire HSI while ignoring the difference between diverse homogeneous regions. Moreover, traditional methods utilize the limited size of data for model training that may result in degraded generalization performance. In this article, we propose a marginalized graph self-representation (MGSR) method for unsupervised hyperspectral band selection. To explore the spatial information from diverse homogenous regions, MGSR generates the segmentations of an HSI by superpixel segmentation and records the relationships between adjacent pixels of the same segmentation in a structural graph. Meanwhile, to improve the generalization and robustness, infinite corrupted samples are obtained from the original pixels by introducing noises in spectral bands for model training. To solve the proposed formulation, we design an alternating optimization algorithm to marginalize out the corruption and search for the optimal solution. Experimental studies on HSI datasets demonstrate the effectiveness of the proposed MGSR and the superiority over the state-of-the-art methods. The source code is available at https://github.com/ZhangYongshan/MGSR .

Deep neural networks have gained increasing interest in hyperspectral image (HSI) processing. However, prior arts often neglect the high-order correlation among data points, failing to capture intraclass variations. In this letter, we present a unified neural network framework, termed as hypergraph-structured autoencoder (HyperAE), to leverage the high-order relationship among data and learn robust deep representation for downstream tasks. Technically, the proposed method adopts a deep autoencoder regularized by hypergraph structure as the backbone network, which is jointly trained with a task-specific branch, resulting in a multitask architecture. We separately combine the subspace clustering model and the softmax classifier into the HyperAE to deal with HSI unsupervised and semisupervised classification problems. Benefiting from the hypergraph, HyperAE endows traditional networks with the capacity of preserving the high-order structured information. We evaluate the proposed methods on three benchmarking HSI data sets, demonstrating that the proposed HyperAE dramatically outperforms many existing methods with significant margins in both unsupervised and semisupervised HSI classification problems.

Unsupervised band selection aims to select informative spectral bands to preprocess hyperspectral images (HSIs) without using labels. Traditional band selection methods only work well on Euclidean data, but ignore structural information of pixels and spectral bands. Moreover, they treat each HSI as a whole to exploit latent spatial information while ignoring the difference in spatial distribution between diverse homogeneous regions. In this article, we propose a robust dual graph self-representation (RDGSR) method for unsupervised band selection. RDGSR uses a superpixel segmentation technique to generate homogenous regions of each HSI to extract spatial information. Based on the segmentation result, the superpixel-based similarity graph and band-based similarity graph are constructed from HSIs to record spatial and structural information. With this knowledge, the dual graph convolution is developed and the $\ell _{2,1}$ -norm is introduced in the loss function and regularization term to eliminate the noise in rows for robust and effective band selection. The novelty of RDGSR is the joint utilization of the geometric structure of pixels with spatial consistency and the geometric structure of spectral bands to enhance the performance of band selection in a robust $\ell _{2,1}$ -norm manner. An iterative optimization algorithm is designed to solve the proposed formulation. Substantial experiments on HSI datasets are conducted to verify the superiority of the proposed RDGSR over the state-of-the-art methods. The source code is available at https://github.com/ZhangYongshan/RDGSR .