Scalable Context-Preserving Model-Aware Deep Clustering for Hyperspectral Images

In the last few years, great efforts have been made to extend the linear projection technique (LPT) for multidimensional data (i.e., tensor), generally referred to as the multilinear projection technique (MPT). The vectorized nature of LPT requires high-dimensional data to be converted into vector, and hence may lose spatial neighborhood information of raw data. MPT well addresses this problem by encoding multidimensional data as general tensors of a second or even higher order. In this paper, we propose a novel multilinear projection technique, called multilinear spatial discriminant analysis (MSDA), to identify the underlying manifold of high-order tensor data. MSDA considers both the nonlocal structure and the local structure of data in the transform domain, seeking to learn the projection matrices from all directions of tensor data that simultaneously maximize the nonlocal structure and minimize the local structure. Different from multilinear principal component analysis (MPCA) that aims to preserve the global structure and tensor locality preserving projection (TLPP) that is in favor of preserving the local structure, MSDA seeks a tradeoff between the nonlocal (global) and local structures so as to drive its discriminant information from the range of the non-local structure and the range of the local structure. This spatial discriminant characteristic makes MSDA have more powerful manifold preserving ability than TLPP and MPCA. Theoretical analysis shows that traditional MPTs, such as multilinear linear discriminant analysis, TLPP, MPCA, and tensor maximum margin criterion, could be derived from the MSDA model by setting different graphs and constraints. Extensive experiments on face databases (ORL, CMU PIE, and the extended Yale-B) and the Weizmann action database demonstrate the effectiveness of the proposed MSDA method.

High-dimensional data is usually drawn from the union of multiple low-dimensional subspaces. The task of subspace clustering is to cluster high-dimensional data into their corresponding subspace. Subspace clustering algorithm based on spectral clustering is one of the important methods of subspace clustering. This method is proposed by the spectral clustering framework. This type of method is usually divided into two steps, namely learning the affinity matrix and obtaining the segmentation matrix by spectral clustering. However, the results obtained this way are often sub-optimal. Meanwhile many state-of-the-art algorithms do not consider consistency of correlation data, resulting in the affinity matrix either too dense to make the algorithm contain a lot of erroneous information, or too sparse to make the algorithm lose correlation information. In this paper, we propose Correlation Structured Low-Rank Subspace Clustering (CSLRSC). The CSLRSC is based on the model of low rank representation by adding new $l_{1}$ norm to solve the problem that the affinity matrix established by the previous method is too dense. Adding the structured norm to the model can integrate affinity matrix learning and spectral clustering into one step to obtain an approximate optimal solution of the algorithm. The experimental results that we obtain on Extended Yale B face dataset, MINIST hand-write dataset, and ORL dataset show that our algorithm is superior to others.

Subspace clustering refers to the problem of clustering high-dimensional data into a union of low-dimensional subspaces. Current subspace clustering approaches are usually based on a two-stage framework. In the first stage, an affinity matrix is generated from data. In the second one, spectral clustering is applied on the affinity matrix. However, the affinity matrix produced by two-stage methods cannot fully reveal the similarity between data points from the same subspace, resulting in inaccurate clustering. Besides, most approaches fail to solve large-scale clustering problems due to poor efficiency. In this paper, we first propose a new scalable sparse method called Iterative Maximum Correlation (IMC) to learn the affinity matrix from data. Then we develop Piecewise Correlation Estimation (PCE) to densify the intra-subspace similarity produced by IMC. Finally we extend our work into a Sparse-Dense Subspace Clustering (SDSC) framework with a dense stage to optimize the affinity matrix for two-stage methods. We show that IMC is efficient for large-scale tasks, and PCE ensures better performance for IMC. We show the universality of our SDSC framework for current two-stage methods as well. Experiments on benchmark data sets demonstrate the effectiveness of our approaches.

Unsupervised image segmentation is a challenge task, since a high-quality segmented image should perceive not only local object structures but also certain semantics without any annotations. In this paper, we propose a novel encoder-decoder pixel clustering framework with dual constraints to incorporate local structure and global semantic information for guiding pixel feature learning in a self-supervised manner. On one hand, a Local Structure Constraint (LStC) is constructed based on fine-grained superpixels, which improves the boundary perception of pixel features by keeping intra-superpixel feature consistency and largening inter-superpixel feature distance. On the other hand, a new Global Semantic Constraint (GSeC) is proposed via adapting the mutual information maximization technique to the single-image setting, and it strengthens the global semantic perception of pixel features and thus improves the segmenting integrity of objects. Finally, based on the learned pixel features, a smoothing component is employed to achieve semantically meaningful pixel clustering. The experimental evaluation on BSDS500 and PASCAL Context datasets show the superiority of our method on region and boundary qualities.

Subspace clustering methods based on data self-expression have become very popular for learning from data that lie in a union of low-dimensional linear subspaces. However, the applicability of subspace clustering has been limited because practical visual data in raw form do not necessarily lie in such linear subspaces. On the other hand, while Convolutional Neural Network (ConvNet) has been demonstrated to be a powerful tool for extracting discriminative features from visual data, training such a ConvNet usually requires a large amount of labeled data, which are unavailable in subspace clustering applications. To achieve simultaneous feature learning and subspace clustering, we propose an end-to-end trainable framework, called Self-Supervised Convolutional Subspace Clustering Network (S$^2$ConvSCN), that combines a ConvNet module (for feature learning), a self-expression module (for subspace clustering) and a spectral clustering module (for self-supervision) into a joint optimization framework. Particularly, we introduce a dual self-supervision that exploits the output of spectral clustering to supervise the training of the feature learning module (via a classification loss) and the self-expression module (via a spectral clustering loss). Our experiments on four benchmark datasets show the effectiveness of the dual self-supervision and demonstrate superior performance of our proposed approach.

This paper presents a novel clustering method, named Laplacian regularized deep subspace clustering (LRDSC), for unsupervised hyperspectral image (HSI) classification. We introduce the Laplacian regularization into the subspace clustering to consider the manifold structure reflecting geometric information. To enable the subspace clustering, which works in linear space, to deal with the complicated HSI data with nonlinear characteristics, we combine the subspace clustering as a self-expressive layer with deep convolutional auto-encoder. Furthermore, the 3-D convolutions and deconvolutions with skip connections are utilized to make full extraction of the spectral-spatial information and full use of the historical feature maps produced by the network. We compare the results of the proposed method with six existing cluster methods on four real hyperspectral data sets, showing that the proposed method is able to achieve state-of-the-art performance.

Graph Regularized Residual Subspace Clustering Network for hyperspectral image clustering

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) denoising is an effective image processing technology to improve the quality of HSI. By exploiting the spectral-spatial characteristics of HSI, this paper proposes a HSI denoising method based on the Graph-structured Low Rank model and Non-Local constraint (GLRNL). Graph-structured low rank model can reveal the spectral similarity in HSI and preserve the distribution characteristics of spectral bands. The graph structure is used to ensure that the denoised HSI has similar spectral characteristics as the real HSI, and reduce the spectral distortions. Moreover, the non-local constraint in GLRNL adopts the spatial-spectral self-similarity and provides an effective side prior information for low rank calculation. Comparing with some traditional low rank and sparse model based HSI denoising methods, the proposed method achieves the competitive results on different simulated and real HSI data with various types of noise.

High-dimensional data often lie in low-dimensional subspaces instead of the whole space. Subspace clustering is a problem to analyze data that are from multiple low-dimensional subspaces and cluster them into the corresponding subspaces. In this work, we propose a $(k,k)$-sparse matrix factorization method for subspace clustering. In this method, data itself is considered as the 'dictionary', and each data point is represented as a linear combination of the basis of its cluster in the dictionary. Thus, the coefficient matrix is low-rank and sparse. With an appropriate permutation, it is also blockwise with each block corresponding to a cluster. With an assumption that each block is no more than $k$-by-$k$ in matrix recovery, we seek a low-rank and $(k,k)$-sparse coefficient matrix, which will be used for the construction of affinity matrix in spectral clustering. The advantage of our proposed method is that we recover a coefficient matrix with $(k,k)$-sparse and low-rank simultaneously, which is better fit for subspace clustering. Numerical results illustrate the effectiveness that it is better than SSC and LRR in real-world classification problems such as face clustering and motion segmentation.

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.

Layered silicates have important applications as host materials, supports for catalysis, and zeolite precursors. However, their local structures are often challenging to establish due to disorder of the sheet assemblies. We present a new protocol that combines long- and short-range structural constraints from diffraction and solid-state NMR techniques, respectively, to determine the molecular structure of layered silicates in the presence of various extents of stacking disorder. Solid-state 29Si NMR data are largely insensitive to the incomplete extent of three-dimensional (3D) crystallinity that limits the interpretation of diffraction data alone to the identification of possible unit cells and space groups. State-of-the-art NMR crystallography techniques consequently provide a simplified view of materials from which candidate framework structures can be built and evaluated based on local structural constraints, including interatomic distances, Si site numbers and multiplicities, and Si–O–Si connectivities, and refined using density functional theory. This protocol was applied to a new layered silicate material named CLS-1, of composition [Si5O11H][C9N2H15]·1.9(H2O), synthesized by using a fluoride-based protocol and cationic alkylaminopyridinium as a structure-directing agent (SDA). Despite the intrinsic complexity and partial ordering of the intersheet arrangements and organic–inorganic interactions, this led to the identification of a single space group that is compatible with both NMR and diffraction data, from which the silicate framework structure could be established,. The remarkable similarities between the layered framework structures of CLS-1, HUS-2 (Tsunoji et al. J. Mater. Chem. 2012, 22, 13682), and another layered silicate material with a radically different morphology and extent of stacking order and interlayer dynamics, established by using a similar approach (Brouwer et al. J. Am. Chem. Soc. 2013, 135, 5641), point to the remarkable robustness of this previously unknown silicate framework type.

A robust adaptive clustering analysis method for automatic identification of clusters

Nonlinear subspace clustering for image clustering

Subspace clustering is an effective algorithm refer to the problem which separate the data lying on a union of subspaces. Usually the algorithm consists of two steps. First, an affinity matrix is calculated from the self-representation of the data. Second, spectral clustering is used to cluster the data by the affinity matrix. The paper introduces a new method based on the sparse subspace clustering. The new method used a new objective which considered both the sparseness and grouping effect. And the affinity matrix which is calculated from the self-representation of the data is furthered optimized. It proved to be more efficient than existing subspace clustering methods.