Landmark-Based Large-Scale Sparse Subspace Clustering Method for Hyperspectral Images

Deep subspace clustering methods have demonstrated its outstanding capability for hyperspectral image (HSI) clustering. However, there is a lack of explicit supervision to ensure that low-dimensional spatial–spectral features learned from high-dimensional HSI cubes have good subspace structures. In this letter, we propose a cascade residual capsule network (CRCN) for extracting deep spatial–spectral features and introduce the coding rate reduction (CRR) to measure the compactness of learned spatial–spectral features. We exploit the difference between the coding rate of all features and the sum of that of features of each category as loss function, which provides explicit supervision for learning invariant spatial–spectral features to HSI cube flips and rotations and facilitate the subsequent HSI clustering. To learn features that are discriminative to diverse spatial context information on land-cover objects of the same category, we add a regularization term to the loss function, which is a brink loss between the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${l_{2}}$ </tex-math></inline-formula> -norm of active vectors of class capsules in the proposed CRCN and the assigned labels. Experimental results on three benchmark HSI datasets demonstrate the effectiveness of the proposed method, which achieves superiority performance over several state-of-the-art HSI clustering methods.

Graph Regularized Residual Subspace Clustering Network for hyperspectral image clustering

Clustering large hyperspectral images (HSIs) is a very challenging problem because large HSIs have high dimensionality, large spectral variability, and large computational and memory consumption. Recently, sparse subspace clustering (SSC) has achieved remarkable success in HSI clustering. However, most SSC-based methods suffer from the following bottlenecks for large HSIs: 1) high computational consumption and memory space during the construction of the similarity matrix and decomposition of the graph Laplacian matrix and 2) failure to capture the relationships among dictionary atoms, sparse coefficients, and hyperspectral pixels. To address these challenges, we propose a novel algorithm that extends SSC to cocluster large HSIs, called bipartite graph partition with graph nonnegative matrix factorization (BGP-GNMF). Specifically, to fully explore the characteristics of the spectral and spatial contexts in HSIs, we propose a novel superpixel and pixel coclustering framework with bipartite graph partitioning in the joint sparse representation domain, where superpixel-based dictionary atoms are defined as disjoint vertex sets of the bipartite graph and the joint sparsity representation is mapped into the adjacency matrix of the undirected bipartite graph. To overcome the challenges of high computational consumption and large memory space for large HSIs, the bipartite graph partition with orthonormal constrained nonnegative matrix factorization is proposed to simultaneously cluster the structured dictionary atoms and hyperspectral pixels with an indicator matrix. Finally, to exploit the intrinsic geometry of HSIs, we incorporate manifold regularization into the bipartite graph partition to improve final clustering accuracy. The effectiveness and efficiency of the proposed method are verified on three classical HSIs, and the experimental results illustrate the superiority of the proposed method compared with other state-of-the-art HSI clustering methods.

Hyperspectral image (HSI) clustering has been widely used in the field of remote sensing. However, most traditional clustering algorithms are not suitable for dealing with large-scale HSI due to their low clustering performance and high computational complexity. In this letter, we propose a novel fuzzy clustering algorithm, called fuzzy embedded clustering based on the bipartite graph (FECBG), to efficiently deal with large-scale HSI clustering problems. First, we propose the FECBG method that incorporates fuzzy clustering with the nonnegative regularization term based on the bipartite graph into a unified model, which has good clustering performance and reduces the sensitivity of fuzzy clustering to the initial cluster centers. Second, we adopt the fast spectral embedded method to obtain the low-dimensional representation of HSI data, to reduce the computational complexity. At last, we add the nonnegative regularization term based on the bipartite graph to fuzzy clustering, to constrain the solution space of the fuzzy membership matrix. Experimental results on several HSI data sets have demonstrated the efficiency and effectiveness of the proposed FECBG algorithm.

Subspace clustering methods with sparsity prior, such as Sparse Subspace Clustering (SSC) [1], are effective in partitioning the data that lie in a union of subspaces. Most of those methods require certain assumptions, e.g. independence or disjointness, on the subspaces. These assumptions are not guaranteed to hold in practice and they limit the application of existing sparse subspace clustering methods. In this paper, we propose \(\ell ^{0}\)-induced sparse subspace clustering (\(\ell ^{0}\)-SSC). In contrast to the required assumptions, such as independence or disjointness, on subspaces for most existing sparse subspace clustering methods, we prove that subspace-sparse representation, a key element in subspace clustering, can be obtained by \(\ell ^{0}\)-SSC for arbitrary distinct underlying subspaces almost surely under the mild i.i.d. assumption on the data generation. We also present the “no free lunch” theorem that obtaining the subspace representation under our general assumptions can not be much computationally cheaper than solving the corresponding \(\ell ^{0}\) problem of \(\ell ^{0}\)-SSC. We develop a novel approximate algorithm named Approximate \(\ell ^{0}\)-SSC (\(\hbox {A}\ell ^{0}\)-SSC) that employs proximal gradient descent to obtain a sub-optimal solution to the optimization problem of \(\ell ^{0}\)-SSC with theoretical guarantee, and the sub-optimal solution is used to build a sparse similarity matrix for clustering. Extensive experimental results on various data sets demonstrate the superiority of \(\hbox {A}\ell ^{0}\)-SSC compared to other competing clustering methods.

Hyperspectral image clustering is usually used for unsupervised learning in different applications. However, the traditional clustering methods have not been considered the complex relationships among neighbouring pixels. The Albedo and Shading elements can define pixel values in the HyperSpectral Images (HSIs). In HSIs, features are different from each other because of their natural physical characteristics and the physical nature of different image features can be described by the Albedo element. Therefore, in this paper, we generate the natural Albedo feature of the HSIs by applying Albedo recovery step to exploit main information from HSIs. Then, we utilized the Fuzzy C-means clustering method to cluster the natural Albedo dataset. In this paper, we propose a novel accurate Albedo Recovery based Fuzzy C-Means (ARFCM) method to cluster HSIs. In the dataset, each feature vector is processed by the Albedo recovery step to create a new feature vector. This new feature vector can describe the dataset better than the original one. Comparing clustering methods as one of the powerful clustering algorithms are widely used in the remote sensing fields of studying. The experiments conducted on several benchmark datasets demonstrated that the proposed clustering method achieves higher performance than other methods and present the efficiency and effectiveness of the proposed method. The results of experiments over different HSI datasets indicated that the proposed method could produce reliable and suitable results compared to the other methods. This shows the robustness of the proposed ARFCM algorithm over the various HSI datasets. Other methods may provide a good response in a given dataset and do not perform well in the other data. Consequently, the ARFCM method, regardless of the study area characteristics and the sensor features, always renders remarkable clustering accuracy.

Robust techniques such as sparse subspace clustering (SSC) have been recently developed for hyperspectral images (HSIs) based on the assumption that pixels belonging to the same land-cover class approximately lie in the same subspace. In order to account for the spatial information contained in HSIs, SSC models incorporating spatial information have become very popular. However, such models are often based on a local averaging constraint, which does not allow for a detailed exploration of the spatial information, thus limiting their discriminative capability and preventing the spatial homogeneity of the clustering results. To address these relevant issues, in this letter, we develop a new and effective $\ell _{2} $ -norm regularized SSC algorithm which adds a four-neighborhood $\ell _{2} $ -norm regularizer into the classical SSC model, thus taking full advantage of the spatial-spectral information contained in HSIs. The experimental results confirm the potential of including the spatial information (through the newly added $\ell _{2} $ -norm regularization term) in the SSC framework, which leads to a significant improvement in the clustering accuracy of SSC when applied to HSIs.

Due to the difficulty of labeling a large number of training samples of a hyperspectral image (HSI), unsupervised clustering methods have drawn great attention. The recently proposed broad learning (BL) can implement both linear and nonlinear mappings. However, the original BL is a supervised model. In this letter, a novel method named unsupervised BL (UBL) is introduced for HSI clustering. First, a graph-regularized sparse autoencoder is performed on the input and mapped feature of UBL in order to maintain the intrinsic manifold structure of origin HSI. Then, the objective function of UBL composed of an $l_{2}$ -norm of output-layer weights and a graph regularization term is designed, which can be easily solved by choosing eigenvectors corresponding to the smallest eigenvalues. Finally, the HSI clustering results can be obtained by applying spectral clustering on the output of UBL. Experiments on three popular real HSI data sets demonstrate that, compared with several competitive methods, UBL can achieve better clustering performance.

Data clustering is an important research topic in data mining and signal processing communications. In all the data clustering methods, the subspace spectral clustering methods based on self expression model, e.g., the Sparse Subspace Clustering (SSC) and the Low Rank Representation (LRR) methods, have attracted a lot of attention and shown good performance. The key step of SSC and LRR is to construct a proper affinity or similarity matrix of data for spectral clustering. Recently, Laplacian graph constraint was introduced into the basic SSC and LRR and obtained considerable improvement. However, the current graph construction methods do not well exploit and reveal the non-linear properties of the clustering data, which is common for high dimensional data. In this paper, we introduce the classic manifold learning method, the Local Linear Embedding (LLE), to learn the non-linear structure underlying the data and use the learned local geometry of manifold as a regularization for SSC and LRR, which results the proposed LLE-SSC and LLE-LRR clustering methods. Additionally, to solve the complex optimization problem involved in the proposed models, an efficient algorithm is also proposed. We test the proposed data clustering methods on several types of public databases. The experimental results show that our methods outperform typical subspace clustering methods with Laplacian graph constraint.

Hyperspectral image (HSI) clustering groups pixels into clusters without labeled data, which is an important yet challenging task. For large-scale HSIs, most methods rely on superpixel segmentation and perform superpixel-level clustering based on graph neural networks (GNNs). However, existing GNNs cannot fully exploit the spectral information of the input HSI, and the inaccurate superpixel topological graph may lead to the confusion of different class semantics during information aggregation. To address these challenges, we first propose a structural-spectral graph convolutional operator (SSGCO) tailored for graph-structured HSI superpixels to improve their representation quality through the co-extraction of spatial and spectral features. Second, we propose an evidence-guided adaptive edge learning (EGAEL) module that adaptively predicts and refines edge weights in the superpixel topological graph. We integrate the proposed method into a contrastive learning framework to achieve clustering, where representation learning and clustering are simultaneously conducted. Experiments demonstrate that the proposed method improves clustering accuracy by 2.61%, 6.06%, 4.96% and 3.15% over the best compared methods on four HSI datasets. Our code is available at https://github.com/jhqi/SSGCO-EGAEL.

We propose a method for the unsupervised clustering of hyperspectral images based on spatially regularized spectral clustering with ultrametric path distances. The proposed method efficiently combines data density and spectral-spatial geometry to distinguish between material classes in the data, without the need for training labels. The proposed method is efficient, with quasilinear scaling in the number of data points, and enjoys robust theoretical performance guarantees. Extensive experiments on synthetic and real HSI data demonstrate its strong performance compared to benchmark and state-of-the-art methods. Indeed, the proposed method not only achieves excellent labeling accuracy, but also efficiently estimates the number of clusters. Thus, unlike almost all existing hyperspectral clustering methods, the proposed algorithm is essentially parameter-free.

Hyperspectral image (HSI) clustering is a challenging task due to the complex spatial-spectral structure and high-dimensional property in HSI data. In this letter, a novel clustering information-constrained 3D U-Net subspace clustering network is proposed for HSI clustering. Considering the spatial-spectral information, the proposed network takes the 3D pixel cubes around the pixels as the input. Based on the 3D pixel cubes, a 3D U-Net subspace clustering network is introduced to extract spatial-spectral features from 3D pixel cubes and learn self-representation subspace property among pixels. In order to learn features more suitable for clustering, a clustering information constraint is introduced to explore useful information gain in the existing clustering result. Experiments conducted on three public HSI datasets illustrate the superior performance of the proposed method.

Spectral image clustering is an unsupervised classification method which identifies distributions of pixels using spectral information without requiring a previous training stage. The sparse subspace clustering-based methods (SSC) assume that hyperspectral images lie in the union of multiple low-dimensional subspaces. Using this, SSC groups spectral signatures in different subspaces, expressing each spectral signature as a sparse linear combination of all pixels, ensuring that the non-zero elements belong to the same class. Although these methods have shown good accuracy for unsupervised classification of hyperspectral images, the computational complexity becomes intractable as the number of pixels increases, i.e. when the spatial dimension of the image is large. For this reason, this paper proposes to reduce the number of pixels to be classified in the hyperspectral image, and later, the clustering results for the missing pixels are obtained by exploiting the spatial information. Specifically, this work proposes two methodologies to remove the pixels, the first one is based on spatial blue noise distribution which reduces the probability to remove cluster of neighboring pixels, and the second is a sub-sampling procedure that eliminates every two contiguous pixels, preserving the spatial structure of the scene. The performance of the proposed spectral image clustering framework is evaluated in three datasets showing that a similar accuracy is obtained when up to 50% of the pixels are removed, in addition, it is up to 7.9 times faster compared to the classification of the data sets without incomplete pixels.

Hyperspectral image (HSI) clustering has attracted a great deal of attention, owing to lower cost and higher application prospects. Deep subspace clustering has been proved to be an effective method to explore the sample relationship of HSI clustering. However, due to the complex distribution of HSI data, the problem of data cluster overlap occurs frequently. In the actual sample distribution, a sample may belong to multiple subspaces. The complex sample distribution brings challenges to subspace clustering. In this letter, we propose a deep mutual information subspace clustering network (DMISC) to find a more intuitive feature space for non-linear subspace clustering. Technically, we maximize the mutual information between the samples and their generated features to enlarge the inter-class dispersion and intra-class compactness. The deep subspace method can find a more suitable non-linear intrinsic relationship, benefitting from the generated feature distribution. We evaluate DMISC on four HSI data sets and compare the performances with 12 popular clustering methods. The experiment results demonstrate our method outperforms many prior unsupervised methods.

This paper studies the subspace segmentation problem. Given a set of data points drawn from a union of subspaces, the goal is to partition them into their underlying subspaces they were drawn from. The spectral clustering method is used as the framework. It requires to find an affinity matrix which is close to block diagonal, with nonzero entries corresponding to the data point pairs from the same subspace. In this work, we argue that both sparsity and the grouping effect are important for subspace segmentation. A sparse affinity matrix tends to be block diagonal, with less connections between data points from different subspaces. The grouping effect ensures that the highly corrected data which are usually from the same subspace can be grouped together. Sparse Subspace Clustering (SSC), by using $\ell^1$-minimization, encourages sparsity for data selection, but it lacks of the grouping effect. On the contrary, Low-Rank Representation (LRR), by rank minimization, and Least Squares Regression (LSR), by $\ell^2$-regularization, exhibit strong grouping effect, but they are short in subset selection. Thus the obtained affinity matrix is usually very sparse by SSC, yet very dense by LRR and LSR. In this work, we propose the Correlation Adaptive Subspace Segmentation (CASS) method by using trace Lasso. CASS is a data correlation dependent method which simultaneously performs automatic data selection and groups correlated data together. It can be regarded as a method which adaptively balances SSC and LSR. Both theoretical and experimental results show the effectiveness of CASS.