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It is hard to construct an optimal classifier for high-dimensional imbalanced data, on which the performance of classifiers is seriously affected and becomes poor. Although many approaches, such as resampling, cost-sensitive, and ensemble learning methods, have been proposed to deal with the skewed data, they are constrained by high-dimensional data with noise and redundancy. In this study, we propose an adaptive subspace optimization ensemble method (ASOEM) for high-dimensional imbalanced data classification to overcome the above limitations. To construct accurate and diverse base classifiers, a novel adaptive subspace optimization (ASO) method based on adaptive subspace generation (ASG) process and rotated subspace optimization (RSO) process is designed to generate multiple robust and discriminative subspaces. Then a resampling scheme is applied on the optimized subspace to build a class-balanced data for each base classifier. To verify the effectiveness, our ASOEM is implemented based on different resampling strategies on 24 real-world high-dimensional imbalanced datasets. Experimental results demonstrate that our proposed methods outperform other mainstream imbalance learning approaches and classifier ensemble methods.

Learning-to-learn, a progressive speedup of learning while solving a series of similar problems, represents a core process of knowledge acquisition that draws attention in both neuroscience and artificial intelligence. To investigate its underlying brain mechanism, we trained a recurrent neural network model on arbitrary sensorimotor mappings known to depend on the prefrontal cortex. The network displayed an exponential time course of accelerated learning. The neural substrate of a schema emerges within a low-dimensional subspace of population activity; its reuse in new problems facilitates learning by limiting connection weight changes. Our work highlights the weight-driven modifications of the vector field, which determines the population trajectory of a recurrent network and behavior. Such plasticity is especially important for preserving and reusing the learnt schema in spite of undesirable changes of the vector field due to the transition to learning a new problem; the accumulated changes across problems account for the learning-to-learn dynamics.

Partial multilabel learning (PML) aims to learn from training data, where each instance is associated with a set of candidate labels, among which only a part is correct. The common strategy to deal with such a problem is disambiguation, that is, identifying the ground-truth labels from the given candidate labels. However, the existing PML approaches always focus on leveraging the instance relationship to disambiguate the given noisy label space, while the potentially useful information in label space is not effectively explored. Meanwhile, the existence of noise and outliers in training data also makes the disambiguation operation less reliable, which inevitably decreases the robustness of the learned model. In this article, we propose a prior label knowledge regularized self-representation PML approach, called PAKS, where the self-representation scheme and prior label knowledge are jointly incorporated into a unified framework. Specifically, we introduce a self-representation model with a low-rank constraint, which aims to learn the subspace representations of distinct instances and explore the high-order underlying correlation among different instances. Meanwhile, we incorporate prior label knowledge into the above self-representation model, where the prior label knowledge is regarded as the complement of features to obtain an accurate self-representation matrix. The core of PAKS is to take advantage of the data membership preference, which is derived from the prior label knowledge, to purify the discovered membership of the data and accordingly obtain more representative feature subspace for model induction. Enormous experiments on both synthetic and real-world datasets show that our proposed approach can achieve superior or comparable performance to state-of-the-art approaches.

Multiview subspace clustering (MVSC) leverages the complementary information among different views of multiview data and seeks a consensus subspace clustering result better than that using any individual view. Though proved effective in some cases, existing MVSC methods often obtain unsatisfactory results since they perform subspace analysis with raw features that are often of high dimensions and contain noises. To remedy this, we propose a self-guided deep multiview subspace clustering (SDMSC) model that performs joint deep feature embedding and subspace analysis. SDMSC comprehensively explores multiview data and strives to obtain a consensus data affinity relationship agreed by features from not only all views but also all intermediate embedding spaces. With more constraints being cast, the desirable data affinity relationship is supposed to be more reliably recovered. Besides, to secure effective deep feature embedding without label supervision, we propose to use the data affinity relationship obtained with raw features as the supervision signals to self-guide the embedding process. With this strategy, the risk that our deep clustering model being trapped in bad local minima is reduced, bringing us satisfactory clustering results in a higher possibility. The experiments on seven widely used datasets show the proposed method significantly outperforms the state-of-the-art clustering methods. Our code is available at https://github.com/kailigo/dmvsc.git.

Feature selection has attracted a lot of attention in obtaining discriminative and non-redundant features from high-dimension data. Compared with traditional filter and wrapper methods, embedded methods can obtain a more informative feature subset by fully considering the importance of features in the classification tasks. However, the existing embedded methods emphasize the above importance of features and mostly ignore the correlation between the features, which leads to retain the correlated and redundant features with similar scores in the feature subset. To solve the problem, we propose a novel supervised embedded feature selection framework, called feature selection under global redundancy minimization in orthogonal regression (GRMOR). The proposed framework can effectively recognize redundant features from a global view of redundancy among the features. We also incorporate the large margin constraint into GRMOR for robust multi-class classification. Compared with the traditional embedded methods based on least square regression, the proposed framework utilizes orthogonal regression to preserve more discriminative information in the subspace, which can help accurately rank the importance of features in the classification tasks. Experimental results on twelve public datasets demonstrate that the proposed framework can obtain superior classification performance and redundancy removal performance than twelve other feature selection methods.

Facing with rapidly increasing demands for analyzing high-order data or multiway data, feature-extracting methods become imperative for analysis and processing. The traditional feature-extracting methods, however, either need to overly vectorize the data and smash the original structure hidden in data, such as PCA and PCA-like methods, which is unfavorable to the data recovery, or cannot eliminate the redundant information very well, such as tucker decomposition (TD) and TD-like methods. To overcome these limitations, we propose a more flexible and more powerful tool, called the multiview principal components analysis (Multiview-PCA) in this article. By segmenting a random tensor into equal-sized subarrays called sections and maximizing variations caused by orthogonal projections of these sections, the Multiview-PCA finds principal components in a parsimonious and flexible way. In so doing, two new operations on tensors, the S -direction inner/outer product, are introduced to formulate tensor projection and recovery. With different segmentation ways characterized by section depth and direction, the Multiview-PCA can be implemented many times in different ways, which defines the sequential and global Multiview-PCA, respectively. These multiple Multiview-PCA take the PCA and PCA-like, and TD and TD-like as the special cases, which correspond to the deepest section depth and the shallowest section depth, respectively. We propose an adaptive depth and direction selection algorithm for the implementation of Multiview-PCA. The Multiview-PCA is then tested in terms of subspace recovery ability, compression ability, and feature extraction performance when applied to a set of artificial data, surveillance videos, and hyperspectral imaging data. All numerical results support the flexibility, effectiveness, and usefulness of Multiview-PCA.

Linear discriminant analysis (LDA) is a classical statistical machine-learning method, which aims to find a linear data transformation increasing class discrimination in an optimal discriminant subspace. Traditional LDA sets assumptions related to the Gaussian class distributions and single-label data annotations. In this article, we propose a new variant of LDA to be used in multilabel classification tasks for dimensionality reduction on original data to enhance the subsequent performance of any multilabel classifier. A probabilistic class saliency estimation approach is introduced for computing saliency-based weights for all instances. We use the weights to redefine the between-class and within-class scatter matrices needed for calculating the projection matrix. We formulate six different variants of the proposed saliency-based multilabel LDA (SMLDA) based on different prior information on the importance of each instance for their class(es) extracted from labels and features. Our experiments show that the proposed SMLDA leads to performance improvements in various multilabel classification problems compared to several competing dimensionality reduction methods. publishedVersion

Sharp speed variation leads to a shift of sample distribution domain, which poses a challenge for vibration-based rolling bearing fault diagnosis. Furthermore, the overfitting effects inflicted on the intelligent diagnosis model due to insufficient data will hinder the performance significantly. In this work, a Subspace Network with Shared Representation learning (SNSR) based on meta-learning is constructed for fault diagnosis under speed transient conditions with few samples. Firstly, shared representation learning based on the cross mutual information estimation is designed to promote the encoder to learn the domain invariant features. Meanwhile, we developed non-parameterized adaptive weight allocation to optimize the estimation of the discriminator. Then, the subspace classifiers in the meta-learning paradigm are employed to force the encoder to learn the discriminative features. Finally, the shared representation learning is embedded into the meta-learning and a cross co-training mechanism is designed for optimization. Thus the fusion framework is endowed with the capacity of learning distinguishable and domain invariant features simultaneously for diagnosis under speed transient conditions with few samples. Comparative experiments on two case studies of bearing fault diagnosis validated the superior performance of the proposed method, with an accuracy of 97.72% and 96.46% in 7-way and 9-way learning respectively.

Due to the shortage of COVID-19 viral testing kits, radiology is used to complement the screening process. Deep learning methods are promising in automatically detecting COVID-19 disease in chest x-ray images. Most of these works first train a Convolutional Neural Network (CNN) on an existing large-scale chest x-ray image dataset and then fine-tune the model on the newly collected COVID-19 chest x-ray dataset, often at a much smaller scale. However, simple fine-tuning may lead to poor performance due to two issues, firstly the large domain shift present in chest x-ray datasets and secondly the relatively small scale of the COVID-19 chest x-ray dataset. In an attempt to address these issues, we formulate the problem of COVID-19 chest x-ray image classification in a semi-supervised open set domain adaptation setting and propose a novel domain adaptation method, Semi-supervised Open set Domain Adversarial network (SODA). SODA is designed to align the data distributions across different domains in the general domain space and also in the common subspace of source and target data. In our experiments, SODA achieves a leading classification performance compared with recent state-of-the-art models in separating COVID-19 with common pneumonia. We also present results showing that SODA produces better pathology localizations.

Lately, variational autoencoder (VAE) has arisen as one of the most prevalent methods for unsupervised learning of intricate distributions. Despite being successful in deep feature extraction and uncertain data modelling, it still suffers from the instability and reconstruction error due to random sampling in the latent subspace representation of original input space. In this paper, to deal with those limitations, constrained VAE (CVAE) is proposed by utilizing input sample information. Enthused by parallel interaction mechanism between the ventral and dorsal stream of human brain in object recognition, parallel interaction spatial-temporal CVAE (PIST-CVAE) is proposed to extract spatial and temporal features from input samples. Lower dimensional nonlinear features extracted from PIST-CVAE are used to build the soft sensor. The effectiveness of CVAE and PIST-CVAE is demonstrated in an industrial case study, a polyester polymerization process.

We propose a novel structured analysis-synthesis dictionary pair learning method for efficient representation and image classification, referred to as relaxed block-diagonal dictionary pair learning with a locality constraint (RBD-DPL). RBD-DPL aims to learn relaxed block-diagonal representations of the input data to enhance the discriminability of both analysis and synthesis dictionaries by dynamically optimizing the block-diagonal components of representation, while the off-block-diagonal counterparts are set to zero. In this way, the learned synthesis subdictionary is allowed to be more flexible in reconstructing the samples from the same class, and the analysis dictionary effectively transforms the original samples into a relaxed coefficient subspace, which is closely associated with the label information. Besides, we incorporate a locality-constraint term as a complement of the relaxation learning to enhance the locality of the analytical encoding so that the learned representation exhibits high intraclass similarity. A linear classifier is trained in the learned relaxed representation space for consistent classification. RBD-DPL is computationally efficient because it avoids both the use of class-specific complementary data matrices to learn discriminative analysis dictionary, as well as the time-consuming l₁/l₀-norm sparse reconstruction process. The experimental results demonstrate that our RBD-DPL achieves at least comparable or better recognition performance than the state-of-the-art algorithms. Moreover, both the training and testing time are significantly reduced, which verifies the efficiency of our method. The MATLAB code of the proposed RBD-DPL is available at https://github.com/chenzhe207/RBD-DPL.

Linear discriminant analysis (LDA) is a well-known technique for supervised dimensionality reduction and has been extensively applied in many real-world applications. LDA assumes that the samples are Gaussian distributed, and the local data distribution is consistent with the global distribution. However, real-world data seldom satisfy this assumption. To handle the data with complex distributions, some methods emphasize the local geometrical structure and perform discriminant analysis between neighbors. But the neighboring relationship tends to be affected by the noise in the input space. In this research, we propose a new supervised dimensionality reduction method, namely, locality adaptive discriminant analysis (LADA). In order to directly process the data with matrix representation, such as images, the 2-D LADA (2DLADA) is also developed. The proposed methods have the following salient properties: 1) they find the principle projection directions without imposing any assumption on the data distribution; 2) they explore the data relationship in the desired subspace, which contains less noise; and 3) they find the local data relationship automatically without the efforts for tuning parameters. The performance of dimensionality reduction shows the superiorities of the proposed methods over the state of the art.

Evolutionary multitasking (EMT) with the ability to tackle multiple different tasks has attracted more and more attention. The transferred knowledge among tasks can simultaneously improve the solving efficiency of all optimization problems in the evolutionary process. However, if the way of knowledge transfer is inappropriate, the negative knowledge transfer will make a bad effect on the performance of EMT algorithms. It is worth studying that how to promote the positive knowledge transfer across tasks. In this paper, a multiobjective multitasking algorithm named EMT-DAVT is introduced. The proposed algorithm contains two components, namely subspace distribution alignment (DA) strategy and decision variable transfer (VT) mechanism. In DA strategy, a learned mapping matrix is utilized to align the distributions in the subspaces and reduces the divergence between subpopulations belonging to different tasks. Then, VT mechanism is implemented which can further promote the positive information transfer. The two proposed strategies interact with each other to improve the knowledge transfer. Finally, the search engine is designed to balance exploration and exploitation. The experimental results on the multiobjective multitasking test suites demonstrate that EMT-DAVT outperforms other classical multiobjective multitasking evolutionary algorithms.

This paper considers a problem of estimating brain effective connectivity from EEG signals using a Granger causality (GC) concept characterized on state-space models. We propose a state-space model for explaining coupled dynamics of the source and EEG signals where EEG is a linear combination of sources according to the characteristics of volume conduction. Our formulation has a sparsity prior on the source output matrix that can further classify active and inactive sources. The scheme is comprised of two main steps: model estimation and model inference to estimate brain connectivity. The model estimation consists of performing a subspace identification and the active source selection based on a group-norm regularized least-squares. The model inference relies on the concept of state-space GC that requires solving a discrete-time Riccati equation for the covariance of estimation error. We verify the performance on simulated data sets that represent realistic human brain activities under several conditions including percentages of active sources, a number of EEG electrodes and the location of active sources. The performance of estimating brain networks is compared with a two-stage approach using source reconstruction algorithms and VAR-based Granger analysis. Our method achieved better performances than the two-stage approach under the assumptions that the true source dynamics are sparse and generated from state-space models. The method is applied to a real EEG SSVEP data set and we found that the temporal lobe played a role of a mediator of connections between temporal and occipital areas, which agreed with findings in previous studies.

Frequency selective surface (FSS) is critical for electromagnetic (EM) radiation protection due to its high spatial filtering performance, especially for active FSS. Recently, artificial neural network (ANN) has shown great potential in solving EM inverse problems and rapid industrial design. In such an inverse model with ANN, it establishes the relationship between the given inputs of S-parameters and the desired structure parameters or material parameters. However, faced with applications where S-parameters vary in a large frequency range with different curve shapes, such as multi-band microwave devices, equal interval sampling may result in high dimensional inputs and will require more complicated neural network. In this work, we present a Fourier subspace-based deep learning method (FS-BDLM) for FSS inverse design, where the dimension of the input is largely reduced by using Fourier subspace to represent the most salient features of the desired S-parameter performance. Compared with existing deep learning methods, the proposed technique makes inverse neural models more compact and more stable to noise contaminations. The validation of the proposed FS-BDLM is conducted both numerically and experimentally through two dual-passband FSS design examples, where the well-designed FSS is fabricated to validate the technique.

Currently, visual-tactile fusion learning for robotic object recognition has achieved appealing performance, due to the fact that visual and tactile data can offer complementary information. However: 1) the distinct gap between vision and touch makes it difficult to fully explore the complementary information, which would further lead to performance degradation and 2) most of the existing visual-tactile fused learning methods assume that visual and tactile data are complete, which is often difficult to be satisfied in many real-world applications. In this article, we propose a partial visual-tactile fused (PVTF) framework for robotic object recognition to address these challenges. Specifically, we first employ two modality-specific (MS) encoders to encode partial visual-tactile data into two incomplete subspaces (i.e., visual subspace and tactile subspace). Then, a modality gap mitigated (MGM) network is adopted to discover modality-invariant high-level label information, which is utilized to generate gap loss and further help updating the MS encoders for relatively consistent visual and tactile subspaces generation. In this way, the huge gap between vision and touch is mitigated, which would further contribute to mine the complementary visual-tactile information. Finally, to achieve data completeness and complementary visual-tactile information exploration simultaneously, a cycle subspace leaning technique is proposed to project the incomplete subspaces into a complete subspace by fully exploiting all the obtainable samples, where complete latent representations with maximum complementary information can be learned. A lot of comparative experiments conducted on three visual-tactile datasets validate the advantage of the proposed PVTF framework, by comparing with state-of-the-art baselines.

Neighborhood reconstruction is proved effective for dimensionality reduction because of the preservation of manifold structure. Conventional neighborhood preserving embedding (NPE) method first learns the affinity relationship or reconstruction relationship in the original space, and then learns the projection matrix to preserve the learned local information in low-dimensional space. However, the pre-learned manifold information may be inaccurate due to the noises and irrelevant features in real-world data. The performance of dimensionality reduction would be influenced as well. Besides, NPE and its variants only aim to preserve the local reconstruction relationship but ignore the fuzzy membership relationship between samples and cluster prototypes. To address these issues, we propose an adaptive neighborhood preserving discriminant projection model, where sparse reconstruction coefficients are updated in the process of dimensionality reduction to eliminate the influence of noises and irrelevant features. Meanwhile, we also learn the fuzzy membership relationships between data points and cluster prototypes to gather the samples belonging to the same class together in low-dimensional space. Neighborhood reconstruction learning and clustering are seamlessly connected in the learned subspace. To solve this model, an iterative algorithm is developed. The experimental results of recognition accuracy show the superiorities of the proposed methods over the state-of-the-arts.

Supervised dimensionality reduction for sequence data learns a transformation that maps the observations in sequences onto a low-dimensional subspace by maximizing the separability of sequences in different classes. It is typically more challenging than conventional dimensionality reduction for static data, because measuring the separability of sequences involves non-linear procedures to manipulate the temporal structures. In this paper, we propose a linear method, called order-preserving Wasserstein discriminant analysis (OWDA), and its deep extension, namely DeepOWDA, to learn linear and non-linear discriminative subspace for sequence data, respectively. We construct novel separability measures between sequence classes based on the order-preserving Wasserstein (OPW) distance to capture the essential differences among their temporal structures. Specifically, for each class, we extract the OPW barycenter and construct the intra-class scatter as the dispersion of the training sequences around the barycenter. The inter-class distance is measured as the OPW distance between the corresponding barycenters. We learn the linear and non-linear transformations by maximizing the inter-class distance and minimizing the intra-class scatter. In this way, the proposed OWDA and DeepOWDA are able to concentrate on the distinctive differences among classes by lifting the geometric relations with temporal constraints. Experiments on four 3D action recognition datasets show the effectiveness of OWDA and DeepOWDA.

In real-world applications, complete or incomplete multi-view data are common, which leads to the problem of generalized multi-view clustering. Recently, researchers attempt to learn the latent representation in the common subspace from heterogeneous data, which usually suffers from feature degeneration. Moreover, there are limited efforts on simultaneously revealing the underlying subspace structure and exploring the complementary information from incomplete multiple views. In this paper, we introduce a novel Generalized Multi-view Collaborative Subspace Clustering (GMCSC) framework to address the above issues, in which consensus subspace structure of all views and embedding subspaces for each view are jointly learned to benefit each other. Specifically, we develop a novel collaborative subspace learning strategy based on self-representation learning, which provides a brand-new way of pursuing the complete subspace structure directly from multi-view data. Furthermore, we explore complementary information by enforcing the consistency across different views and preserving the view-specific information of each view, which can alleviate the problem of feature degeneration and enhance the reasonability of using a consensus representation for multiple views. Experimental results on six benchmark datasets demonstrate that the proposed method can significantly outperform the state-of-the-art algorithms.

Human action recognition which recognizes human actions in a video is a fundamental task in computer vision field. Although multiple existing methods with single-view or multi-view have been presented for human action recognition, these recognition approaches cannot be extended into new action recognition or action classification tasks, as well as discover underlying correlations among different views. To tackle the above problem, this paper proposes a new lifelong multi-view subspace learning framework for continuous human action recognition, which could exploit the complementary information amongst different views from a lifelong learning perspective. More specifically, a set of view-specific libraries is established to gradually store the useful information within multiple views. As a new action recognition task comes, we decompose the model parameters into a set of embedded parameters over view-specific libraries. A latent representation subspace is constructed via encouraging it to be close to different view-specific libraries, which can leverage the high-order correlations among different views and further avoid partial information for action recognition task. Meanwhile, we propose to employ an alternating direction strategy to optimize our proposed method. Empirical studies on real-world multi-view action recognition datasets have shown that our proposed framework attains the superior recognition performance and saves the computational time when continually learning new action recognition tasks.

Surrogate-based-constrained optimization for some optimization problems involving computationally expensive objective functions and constraints is still a great challenge in the optimization field. Its difficulties are of two primary types. One is how to handle the constraints, especially, equality constraints; another is how to sample a good point to improve the prediction of the surrogates in the feasible region. Overcoming these difficulties requires a reliable constraint-handling method and an efficient infill-sampling strategy. To perform inequality- and equality-constrained optimization of expensive black-box systems, this work proposes a hybrid surrogate-based-constrained optimization method (HSBCO), and the main innovation is that a new constraint-handling method is proposed to map the feasible region into the origin of the Euclidean subspace. Thus, if the constraint violation of an infeasible solution is large, then it is far from the origin in the Euclidean subspace. Therefore, all constraints of the problem can be transformed into an equivalent equality constraint, and the distance between an infeasible point and the origin in the Euclidean subspace represents the constraint violation of the infeasible solution. Based on the distance, the objective function of the problem can be penalized by a Gaussian penalty function, and the original constrained optimization problem becomes an unconstrained optimization problem. Thus, the feasible solutions of the original minimization problem always have a lower objective function value than any infeasible solution in the penalized objective space. To improve the optimization performance, kriging-based efficient global optimization (EGO) is used to find a locally optimal solution in the first phase of HSBCO, and starting from this locally optimal solution, RBF-model-based global search and local search strategies are introduced to seek global optimal solutions. Such a hybrid optimization strategy can help the optimization process converge to the global optimal solution within a given maximum number of function evaluations, as demonstrated in the experimental results on 23 test problems. The method is shown to achieve the global optimum more closely and efficiently than other leading methods.

This article presents a novel discriminative subspace-learning-based unsupervised domain adaptation (DA) method for the gas sensor drift problem. Many existing subspace learning approaches assume that the gas sensor data follow a certain distribution such as Gaussian, which often does not exist in real-world applications. In this article, we address this issue by proposing a novel discriminative subspace learning method for DA with neighborhood preserving (DANP). We introduce two novel terms, including the intraclass graph term and the interclass graph term, to embed the graphs into DA. Besides, most existing methods ignore the influence of the subspace learning on the classifier design. To tackle this issue, we present a novel classifier design method (DANP+) that incorporates the DA ability of the subspace into the learning of the classifier. The weighting function is introduced to assign different weights to different dimensions of the subspace. We have verified the effectiveness of the proposed methods by conducting experiments on two public gas sensor datasets in comparison with the state-of-the-art DA methods.

In this article, considering the supervised dimensionality reduction, we first propose a model, called infinite Bayesian max-margin linear discriminant projection (iMMLDP), by assembling a set of local regions, where we make use of Bayesian nonparametric priors to handle the model selection problem, for example, the underlying number of local regions. In each local region, our model jointly learns a discriminative subspace and the corresponding classifier. Under this framework, iMMLDP combines dimensionality reduction, clustering, and classification in a principled way. Moreover, to deal with more complex data, for example, a local nonlinear separable structure, we extend the linear projection to a nonlinear case based on the kernel trick and develop an infinite kernel max-margin discriminant projection (iKMMDP) model. Thanks to the conjugate property, the parameters in these two models can be inferred efficiently via the Gibbs sampler. Finally, we implement our models on synthesized and real-world data, including multimodally distributed datasets and measured radar image data, to validate their efficiency and effectiveness.

Multiview subspace learning has attracted much attention due to the efficacy of exploring the information on multiview features. Most existing methods perform data reconstruction on the original feature space and thus are vulnerable to noisy data. In this article, we propose a novel multiview subspace learning method, called multiview consensus structure discovery (MvCSD). Specifically, we learn the low-dimensional subspaces corresponding to different views and simultaneously pursue the structure consensus over subspace clustering for multiple views. In such a way, latent subspaces from different views regularize each other toward a common consensus that reveals the underlying cluster structure. Compared to existing methods, MvCSD leverages the consensus structure derived from the subspaces of diverse views to better exploit the intrinsic complementary information that well reflects the essence of data. Accordingly, the proposed MvCSD is capable of producing a more robust and accurate representation structure which is crucial for multiview subspace learning. The proposed method can be optimized effectively, with theoretical convergence guarantee, by alternatively iterating the argument Lagrangian multiplier algorithm and the eigendecomposition. Extensive experiments on diverse datasets demonstrate the advantages of our method over the state-of-the-art methods.

The exploration of single cell RNA-sequencing (scRNA-seq) technology generates a new perspective to analyze biological problems. One of the major applications of scRNA-seq data is to discover subtypes of cells by cell clustering. Nevertheless, it is challengeable for traditional methods to handle scRNA-seq data with high level of technical noise and notorious dropouts. To better analyze single cell data, a novel scRNA-seq data analysis model called Maximum correntropy criterion based Non-negative and Low Rank Representation (MccNLRR) is introduced. Specifically, the maximum correntropy criterion, as an effective loss function, is more robust to the high noise and large outliers existed in the data. Moreover, the low rank representation is proven to be a powerful tool for capturing the global and local structures of data. Therefore, some important information, such as the similarity of cells in the subspace, is also extracted by it. Then, an iterative algorithm on the basis of the half-quadratic optimization and alternating direction method is developed to settle the complex optimization problem. Before the experiment, we also analyze the convergence and robustness of MccNLRR. At last, the results of cell clustering, visualization analysis, and gene markers selection on scRNA-seq data reveal that MccNLRR method can distinguish cell subtypes accurately and robustly.

To realize fault identification of unlabeled data and improve model generalization capability, domain adaptation has been increasingly applied to intelligent fault diagnosis of machinery. Nevertheless, traditional domain adaptation diagnosis models generally constrain different domains to have the same label space, which is not always hold in complex industrial scenarios. Consequently, a more practical scenario, i.e. partial-set transfer diagnosis (PSTD), is explored in this work, where the target label space is a subspace of source domain. A multi-weight domain adversarial network (MWDAN) is proposed to solve this issue, in which class-level and instance-level weighted mechanisms are jointly designed to quantify the transferability and importance of data example. Based on the proposed strategy, the positive transfer between shared classes is promoted while the negative effect caused by outlier classes is circumvented. As a result, MWDAN can learn discriminative representations for accurate fault diagnosis in target domain. Extensive experiments constructed on two mechanical systems demonstrate the outstanding performance of MWDAN.

Domain adaptation, which transfers the knowledge from label-rich source domain to unlabeled target domains, is a challenging task in machine learning. The prior domain adaptation methods focus on pairwise adaptation assumption with a single source and a single target domain, while little work concerns the scenario of one source domain and multiple target domains. Applying pairwise adaptation methods to this setting may be suboptimal, as they fail to consider the semantic association among multiple target domains. In this work we propose a deep semantic information propagation approach in the novel context of multiple unlabeled target domains and one labeled source domain. Our model aims to learn a unified subspace common for all domains with a heterogeneous graph attention network, where the transductive ability of the graph attention network can conduct semantic propagation of the related samples among multiple domains. In particular, the attention mechanism is applied to optimize the relationships of multiple domain samples for better semantic transfer. Then, the pseudo labels of the target domains predicted by the graph attention network are utilized to learn domain-invariant representations by aligning labeled source centroid and pseudo-labeled target centroid. We test our approach on four challenging public datasets, and it outperforms several popular domain adaptation methods.

We show that the classification performance of graph convolutional networks (GCNs) is related to the alignment between features, graph, and ground truth, which we quantify using a subspace alignment measure (SAM) corresponding to the Frobenius norm of the matrix of pairwise chordal distances between three subspaces associated with features, graph, and ground truth. The proposed measure is based on the principal angles between subspaces and has both spectral and geometrical interpretations. We showcase the relationship between the SAM and the classification performance through the study of limiting cases of GCNs and systematic randomizations of both features and graph structure applied to a constructive example and several examples of citation networks of different origins. The analysis also reveals the relative importance of the graph and features for classification purposes., Comment: Published in IEEE Transactions on Neural Networks and Learning Systems; Date of Publication: 11 January 2021

Locality-preserving projection (LPP) has been widely used in feature extraction. However, LPP does not use data category information and uses the 2 L -norm for distance measurement, which is highly sensitive to outliers. In this paper, we consider the LPP weight matrix from a supervised perspective and combine the low-rank regression method to propose a new model to discover and extract features. By using the L2,1-norm to constrain the loss function and the regression matrix, not only is the sensitivity to outliers reduced but the low-rank condition of the regression matrix is also restricted. Then, we propose a solution to the optimization problem. Finally, we apply the method to a series of face databases, handwriting digital datasets and palmprint datasets to test the performance, and the experimental results show that this method is effective compared with some existing methods.

In this paper, we proposed a more robust supervised hashing framework based on the Cauchy loss function and Supervised Discrete Hashing (SDH) called Robust Supervised Discrete Hashing (RSDH), which can learn a robust subspace consisted of binary codes. The Cauchy loss is used to measure the error between the label matrix and the product of the decomposed matrices. RSDH can not only reduce the outliers and noise of the hashing codes, but also achieve the more satisfactory retrieval effect. Image retrieval experiments demonstrate that RSDH performs better than the other hashing methods.

In contrast to the traditional single-tasking evolutionary algorithms, evolutionary multitasking (EMT) travels in the search space of multiple optimization tasks simultaneously. Through sharing knowledge across the tasks, EMT is able to enhance solving the optimization tasks. However, if knowledge transfer is not properly carried out, the performance of EMT might become unsatisfactory. To address this issue and improve the quality of knowledge transfer among the tasks, a novel multiobjective EMT algorithm based on subspace alignment and self-adaptive differential evolution (DE), namely, MOMFEA-SADE, is proposed in this article. Particularly, a mapping matrix obtained by subspace learning is used to transform the search space of the population and reduce the probability of negative knowledge transfer between tasks. In addition, DE characterized by a self-adaptive trial vector generation strategy is introduced to generate promising solutions based on previous experiences. The experimental results on multiobjective multi/many-tasking optimization test suites show that MOMFEA-SADE is superior or comparable to other state-of-the-art EMT algorithms. MOMFEA-SADE also won the Competition on Evolutionary Multitask Optimization (the multitask multiobjective optimization track) within IEEE 2019 Congress on Evolutionary Computation.

Fuzzy K-Means (FKM) clustering is of great importance for analyzing unlabeled data. FKM algorithms assign each data point to multiple clusters with some degree of certainty measured by the membership function. In these methods, the fuzzy membership degree matrix is obtained based on the calculation of the distance between data points in the original space. However, this operation may lead to suboptimal results because of the influence of noises and redundant features. Besides, some FKM clustering methods ignore the importance of the weighting exponent. In this paper, we propose a novel FKM method called Fuzzy K-Means Clustering With Discriminative Embedding. Within this method, we simultaneously conduct dimensionality reduction along with fuzzy membership degree learning. To retain most information in the embedding subspace and improve the robustness of this method, principal component analysis is incorporated into our framework. An iterative optimization algorithm is proposed to solve the model. To validate the efficacy of the proposed method, we perform comprehensive analyses, including convergence behavior, parameter determination and computational complexity. Moreover, we also match a appropriate weighting exponent for each data set. Experimental results on benchmark data sets show that the proposed method is more discriminative and effective for clustering tasks.

Deep learning has great potential for accurate detection and classification of diseases with medical imaging data, but the performance is often limited by the number of training datasets and memory requirements. In addition, many deep learning models are considered a "black-box," thereby often limiting their adoption in clinical applications. To address this, we present a successive subspace learning model, termed VoxelHop, for accurate classification of Amyotrophic Lateral Sclerosis (ALS) using T2-weighted structural MRI data. Compared with popular convolutional neural network (CNN) architectures, VoxelHop has modular and transparent structures with fewer parameters without any backpropagation, so it is well-suited to small dataset size and 3D imaging data. Our VoxelHop has four key components, including (1) sequential expansion of near-to-far neighborhood for multi-channel 3D data; (2) subspace approximation for unsupervised dimension reduction; (3) label-assisted regression for supervised dimension reduction; and (4) concatenation of features and classification between controls and patients. Our experimental results demonstrate that our framework using a total of 20 controls and 26 patients achieves an accuracy of 93.48 % and an AUC score of 0.9394 in differentiating patients from controls, even with a relatively small number of datasets, showing its robustness and effectiveness. Our thorough evaluations also show its validity and superiority to the state-of-the-art 3D CNN classification approaches. Our framework can easily be generalized to other classification tasks using different imaging modalities.

Subspace clustering has been extensively studied from the hypothesis-and-test, algebraic, and spectral clustering-based perspectives. Most assume that only a single type/class of subspace is present. Generalizations to multiple types are non-trivial, plagued by challenges such as choice of types and numbers of models, sampling imbalance and parameter tuning. In many real world problems, data may not lie perfectly on a linear subspace and hand designed linear subspace models may not fit into these situations. In this work, we formulate the multi-type subspace clustering problem as one of learning non-linear subspace filters via deep multi-layer perceptrons (mlps). The response to the learnt subspace filters serve as the feature embedding that is clustering-friendly, i.e., points of the same clusters will be embedded closer together through the network. For inference, we apply K-means to the network output to cluster the data. Experiments are carried out on synthetic data and real world motion segmentation problems, producing state-of-the-art results.

This paper introduces a pose error compensation method performed in joint space to improve both position and orientation accuracy of industrial robots. Joint space division is proposed to achieve dimension reduction to reduce the workload of pose error sampling. The six-dimensional joint space is divided into two three-dimensional subspaces by the wrist center. Each subspace is discretized by a sequence of grid elements of which grid vertices are considered as sample points. Based on point set registration, two spatial databases of pose errors are built in the two subspaces respectively using a laser tracker. For a given robot posture, the pose errors generated in the two subspaces can be separately estimated using spatial interpolation based on inverse distance weighting algorithm. Formed by the estimated values, two transformation error matrices are introduced to compensate for the pose errors of the two subspaces. A Comau NJ370–3.0 manipulator was employed as an experimental platform to evaluate the effectiveness of the proposed method. Experimental results demonstrated the maximum position error was reduced by 96.06% to below 0.334 mm, and the maximum orientation errors have decreased to below 0.027° after compensation was performed.

Regression-based methods have been widely applied in face identification, which attempts to approximately represent a query sample as a linear combination of all training samples. Recently, a matrix regression model based on nuclear norm has been proposed and shown strong robustness to structural noises. However, it may ignore two important issues: the label information and local relationship of data. In this article, a novel robust representation method called locality-constrained discriminative matrix regression (LDMR) is proposed, which takes label information and locality structure into account. Instead of focusing on the representation coefficients, LDMR directly imposes constraints on representation components by fully considering the label information, which has a closer connection to identification process. The locality structure characterized by subspace distances is used to learn class weights, and the correct class is forced to make more contribution to representation. Furthermore, the class weights are also incorporated into a competitive constraint on the representation components, which reduces the pairwise correlations between different classes and enhances the competitive relationships among all classes. An iterative optimization algorithm is presented to solve LDMR. Experiments on several benchmark data sets demonstrate that LDMR outperforms some state-of-the-art regression-based methods.

Domain adaptation aims to exploit domain-invariant features by aligning the cross-domain distributions in the manifold subspace for applying the classifier trained on the source domain to the target domain. However, two limitations may still deteriorate their performances: (1) the influences of noisy or irrelevant features in the original feature space are ignored, which may unexpectedly hurt the classification of target samples; (2) the graph constructed directly in the original data space cannot accurately capture the inherent local manifold structures of high-dimensional data due to the curse of dimensionality, which may seriously mislead the transferable features learning. In this paper, we propose a novel approach to address these problems, referred to as joint Adaptive Dual Graph and Feature Selection for domain adaptation (ADGFS). Specifically, feature selection can characterize the relative importance of different features through a scaling factor, which enables ADGFS to not only reduce the impacts of noisy or irrelevant features on knowledge transfer but also learn informative domain-invariant features. Meanwhile, ADGFS adaptively optimizes the dual graph by learning the similarity matrices of both instance-level and feature-level graphs in the projected low-dimensional manifold subspace rather than the original high-dimensional space, such that the intrinsic local manifold structures of data can be captured precisely. Moreover, ADGFS simultaneously aligns the marginal and conditional probability distributions in the nonnegative matrix factorization framework to narrow the distribution discrepancies between the two different domains, which can adequately transfer knowledge from the source domain to the target domain. Comprehensive experiments on four benchmark datasets can demonstrate that the effectiveness of the proposed approach in cross-domain image classification.

In this paper, to bridge the gap between the traditional model-based methods and data-driven deep learning schemes, we propose a physical model-inspired deep unrolling network for solving nonlinear inverse scattering problems, termed PM-Net. The proposed end-to-end network is formed by two consequent steps. First, an augmented Lagrangian method is introduced to transform a constrained objective function to be an unconstrained optimization. In addition, it is further decomposed into four quasi-linear subproblems. Second, we unfold the iterative scheme into a layer-wise deep neural network. Each subproblem is mapped into a module of the deep unrolling network. In PM-Net, these variables including the weight, the regularization of contrast and other parameters are learned and updated alternately by corresponding network layers. PM-Net effectively combines neural network with the knowledge of underlying physics as well as traditional techniques. Unlike existing networks, PM-Net explicitly exploits contrast source and contrast modules. Compared to traditional iterative methods, the performance of PM-Net is comparable or even better than subspace-based optimization method in the high noise level circumstance. Compared to state-of-the-art learning approaches, not only less network parameters need to be learned, but also better performance is achieved by PM-Net.

Terahertz (0.1-10 THz) wireless communications are expected to meet 100+ Gbps data rates for 6G communications. Being able to combat the distance limitation with reduced hardware complexity, ultra-massive multiple-input multiple-output (UM-MIMO) systems with hybrid dynamic array-of-subarrays (DAoSA) beamforming are a promising technology for THz wireless communications. However, fundamental challenges in THz DAoSA systems include millidegree-level three-dimensional direction-of-arrival (DoA) estimation and millisecond-level beam tracking with reduced pilot overhead. To address these challenges, an off-grid subspace-based DAoSA-MUSIC and a deep convolutional neural network (DCNN) methods are proposed for DoA estimation. Furthermore, by exploiting the temporal correlations of the channel variation, an augmented DAoSA-MUSIC-T and a convolutional long short-term memory (ConvLSTM) solutions are further developed to realize DoA tracking. Extensive simulations and comparisons on the proposed subspace- and deep-learning-based algorithms are conducted. Results show that both DAoSA-MUSIC and DCNN achieve super-resolution DoA estimation and outperform existing solutions, while DCNN performs better than DAoSA-MUSIC at a high signal-to-noise ratio. Moreover, DAoSA-MUSIC-T and ConvLSTM can capture fleeting DoA variation with an accuracy of 0.1° within milliseconds, and reduce 50% pilot overhead. Compared to DAoSA-MUSIC-T, ConvLSTM can tolerate large angle variation and remain robust over a long duration.

Hyperspectral images (HSIs) exist in directional stripes commonly due to the failure of pushbroom acquisition. These stripes are not only vertically and horizontally oriented but also tend to be oblique. Furthermore, they can also be aperiodic and heavy. To address this problem, we propose a hyperspectral destriping algorithm, namely, GF-destriping. Taking advantage of the high sparsity and strong directionality of stripes in HSIs, Gabor filters are used to detect the stripes band by band first, and then, an advanced inpainting method, FastHyIn, is used to recover to the striped image. The numerical experiments on simulated data and real data sets show that our proposed algorithm is efficient and superior to state-of-the-art HSI destriping algorithms.

The clutter encountered in ground-penetrating radar (GPR) systems seriously affects the performance of the subsurface target detection methods. A new clutter removal method based on convolutional autoencoders (CAEs) is introduced. The raw GPR image is encoded via successive convolution and pooling layers and then decoded to provide the clutter-free GPR image. The loss function is defined in terms of the reference clutter-free target image and the decoder output is optimized to learn the weight coefficients from the raw data. The method is compared to the conventional subspace methods, recently proposed nonnegative matrix factorization, as well as low-rank and sparse decomposition (LRSD) methods and dictionary separation-based morphological component analysis. CAE and its deeper version deep CAE (DCAE) are trained by several scenarios generated by the electromagnetic simulation tool gprMax. Simulation results demonstrate the effectiveness of the proposed method for challenging scenarios. While for real GPR image, the simulated data trained networks remain slightly behind the LRSD methods for the dry case, nonetheless, they outperform the aforementioned processing techniques for the more challenging wet case.

Graph-based methods have achieved impressive performance on semisupervised classification (SSC). Traditional graph-based methods have two main drawbacks. First, the graph is predefined before training a classifier, which does not leverage the interactions between the classifier training and similarity matrix learning. Second, when handling high-dimensional data with noisy or redundant features, the graph constructed in the original input space is actually unsuitable and may lead to poor performance. In this article, we propose an SSC method with novel graph construction (SSC-NGC), in which the similarity matrix is optimized in both label space and an additional subspace to get a better and more robust result than in original data space. Furthermore, to obtain a high-quality subspace, we learn the projection matrix of the additional subspace by preserving the local and global structure of the data. Finally, we intergrade the classifier training, the graph construction, and the subspace learning into a unified framework. With this framework, the classifier parameters, similarity matrix, and projection matrix of subspace are adaptively learned in an iterative scheme to obtain an optimal joint result. We conduct extensive comparative experiments against state-of-the-art methods over multiple real-world data sets. Experimental results demonstrate the superiority of the proposed method over other state-of-the-art algorithms.

Several algorithms for nuclear power plant (NPP) break event detection, isolation, localization, and size estimation are proposed. A break event can be promptly detected and isolated after its occurrence by simultaneously monitoring changes in the sensing readings and by employing an interquartile range-based isolation scheme. By considering the multi-sensor data block of a break to be rank-one, it can be located as the position whose lead field vector is most orthogonal to the noise subspace of that data block using the Multiple Signal Classification (MUSIC) algorithm. Owing to the flexibility of deep neural networks in selecting the best regression model for the available data, we can estimate the break size using multiple-sensor recordings of the break regardless of the sensor types. The efficacy of the proposed algorithms was evaluated using the data generated by Maanshan NPP simulator. The experimental results demonstrated that the MUSIC method could distinguish two near breaks. However, if the two breaks were close and of small sizes, the MUSIC method might wrongly locate them. The break sizes estimated by the proposed deep learning model were close to their actual values, but relative errors of more than 8% were seen while estimating small breaks’ sizes.

The high spectral resolution of hyperspectral images (HSIs) generally comes at the expense of low spatial resolution, which hinders the application of HSIs. Fusing an HSI and a multispectral image (MSI) from different sensors to get an image with high spatial and spectral resolution is an economic and effective approach, but localized spatial and spectral changes between images acquired at different time instants can have negative impacts on the fusion results, which has rarely been considered in many fusion methods. In this paper, we propose a novel group sparsity constrained fusion method to fuse hyperspectral and multispectral images based on the matrix factorization. Specifically, we imposed l2,1 norm on the residual term of the MSI to account for the localized inter-image changes occurring during the acquisition of the hyperspectral and multispectral images. Further, by exploiting the plug-and-play framework, we plugged a state-of-the-art denoiser, namely BM3D, as the prior of the subspace coefficients. We refer to the proposed fusion method as group sparsity constrained fusion method (GSFus). We performed fusion experiments on two kinds of datasets, i.e. with and without obvious localized changes between the HSIs and MSIs, and a full resolution data set. Extensive experiments in comparison with seven state-of-the-art fusion methods suggest that the proposed fusion method is more effective on fusing hyperspectral and multispectral images than the competitors.

The holographic subsurface radar (HSR) is recognized as an effective remote sensing modality for the detection of shallowly buried objects with a high-resolution image in plain view. However, subsurface detection with HSR is prone to be impaired by clutter contamination, which often obscures the target response. In this letter, a novel clutter mitigation method combining singular value decomposition (SVD) and response cross correlation analysis is presented. The proposed method first applies SVD to decompose the radar data matrix to a number of singular components. Furthermore, the signal cross correlation characteristics are analyzed to demonstrate that the variance of left singular vectors is directly proportional to the target proportion in radar data. Then, target and clutter subspaces can be identified by maximizing the defined weighted target-to-clutter ratio (WTCR). Results of numerical simulation and laboratory experiments corroborate the effectiveness of the proposed method in reducing clutter while preserving the target image.

Hyperspectral image (HSI) classification is a current research hotspot. Most existing methods usually export discriminative features with low-quality distribution and low information utilization, which may induce classification performance degeneration. To remedy such deficiencies, we propose a diagonalized low-rank learning (DLRL) model for HSI classification in this study. Specifically, a classwise regularization is used to capture the classwise block-diagonal structure of low-rank representation, which can further cluster the represented HSI pixels from one class into the same subspace and extract features with well-ordered distribution. Such a regularization assists to easily and correctly classify HSIs. In addition, we combine sparsity and collaboration to extract more discriminative features for guaranteeing high information utilization, i.e., a tradeoff of sparsity and collaboration is sought to acquire both correlations among HSI pixels and characteristics of each pixel. By this way, rich information in the HSI can be fully used for good feature extraction. Further, the estimated feature representation is used as an input to the support vector machine (SVM) classifier for HSI classification. Extensive experiments have been done to validate that the proposed DLRL method achieves much classification performance in contrast to several state-of-the-art algorithms.

Teleoperation is a valuable tool for robotic manipulators in highly unstructured environments. However, finding an intuitive mapping between a human hand and a non-anthropomorphic robot hand can be difficult, due to the hands' dissimilar kinematics. In this paper, we seek to create a mapping between the human hand and a fully actuated, non-anthropomorphic robot hand that is intuitive enough to enable effective real-time teleoperation, even for novice users. To accomplish this, we propose a low-dimensional teleoperation subspace which can be used as an intermediary for mapping between hand pose spaces. We present two different methods to define the teleoperation subspace: an empirical definition, which requires a person to define hand motions in an intuitive, hand-specific way, and an algorithmic definition, which is kinematically independent, and uses objects to define the subspace. We use each of these definitions to create a teleoperation mapping for different hands. One of the main contributions of this paper is the validation of both the empirical and algorithmic mappings with teleoperation experiments controlled by ten novices and performed on two kinematically distinct hands. The experiments show that the proposed subspace is relevant to teleoperation, intuitive enough to enable control by novices, and can generalize to non-anthropomorphic hands with different kinematics., 14 pages, 6 tables, 8 figures, accepted October 2020 IEEE T-ASE

Recently, graph-based discriminant analysis has drawn much attention in representing a high-dimensional hyperspectral data set using a low-dimensional subspace by defining high-dimensional data structure on a graph. Obtaining optimal representation coefficients for classification purposes are the key in such methods. A closed form solution can be found to solve the problem related to collaborative representation using labeled samples, which offers computational efficiency. There exists an unsupervised approach of collaboration preserving graph embedding (CPGE) for dimensionality reduction (DR), and its performance is further enhanced by imposing locality-preserving constraint in the method called collaboration-competition preserving graph embedding (CCPGE). In this letter, we introduce spatial-aware collaboration-competitive preserving graph embedding with Tikhonov (SaCCPGT) by imposing a spatial regularization term in the objective function of CCPGE with Tikhonov regularization. In this way, spectral and spatial information can be utilized in a closed form solution in the proposed method. Experimental results on different hyperspectral data sets demonstrate the superior performance of the proposed SaCCPGT in comparison to state-of-the-art graph-based discriminant analysis approaches for DR.

Sparse subspace clustering (SSC) is a representative data clustering paradigm that has been broadly applied in the unsupervised classification of hyperspectral images (HSIs). Existing SSC methods usually produce a subspace affinity matrix between representations of hyperspectral pixels first, followed by spectral clustering for the affinity matrix. To this end, the separated framework fails to exploit the dualities contained in both features and pixels or higher order entities at the same time, and thus, it is difficult to compute coclusters simultaneously. In addition, SSC methods often require expensive computational consumption and memory capacity to approximate the spectral decomposition of the affinity matrix, thus hindering the applicability of SSC methods for large HSIs. To overcome these limitations, we propose a novel graph convolutional sparse subspace coclustering (GCSSC) model with nonnegative orthogonal factorization for large HSIs in which affinity matrix learning and spectral coclustering are integrated into a unified optimizing model to obtain the optimal clustering results. Specifically, to form a more compact self-representation, the superpixel-based adaptive dictionary construction strategy is proposed instead of the global dictionary to precisely represent the pixels. To explore the spatial-contextual and spectral neighboring characteristics between dictionary atoms, graph convolution is incorporated into the dictionary atoms to aggregate the local neighborhood information, and the affinity matrix in the proposed coclustering framework is constructed under a joint sparsity constrained representation model. To reduce high computational consumption and memory capacity, a nonnegative orthogonal factorization constraint is proposed to offer an alternative spectral clustering for hyperspectral pixels and dictionary atoms simultaneously. The clustering performance of the proposed method is evaluated for three classical HSIs, and the experimental results illustrate that the proposed method is memory and computationally efficient and outperforms the state-of-the-art HSI clustering methods.