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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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

To generate a high-spatial-resolution hyperspectral (HHS) image from a high-spatial-resolution multispectral (HMS) image, both spatial information and spectral information should be considered simultaneously if we want to build a more accurate mapping from HMS to HHS. To this end, a spectral and spatial jointed spectral super-resolution method is proposed in this letter using an end-to-end learning strategy for each subspace with the cluster-based multibranch backpropagation neural network (BPNN). More specifically, in addition to the spectra similarity, a modified superpixel segmentation is introduced to jointly take spatial contextual information into account, and a new framework with it is given. Comparisons on the Columbia University Automated Vision Environment (CAVE) data set show that our proposed method outperforms other relative state-of-the-art methods more than 0.3 in the root mean squared error (RMSE) and more than 1.0 in the spectral angle mapper (SAM) index. Especially, an exemplary application is demonstrated using the synchronized observation data collected by the multispectral and hyperspectral sensors mounted on the HJ-1A satellite at the same time.

Deep multiview clustering methods have achieved remarkable performance. However, all of them failed to consider the difficulty labels (uncertainty of ground truth for training samples) over multiview samples, which may result in a nonideal clustering network for getting stuck into poor local optima during the training process; worse still, the difficulty labels from the multiview samples are always inconsistent, and such a fact makes it even more challenging to handle. In this article, we propose a novel deep adversarial inconsistent cognitive sampling (DAICS) method for multiview progressive subspace clustering. A multiview binary classification (easy or difficult) loss and a feature similarity loss are proposed to jointly learn a binary classifier and a deep consistent feature embedding network, throughout an adversarial minimax game over difficulty labels of multiview consistent samples. We develop a multiview cognitive sampling strategy to select the input samples from easy to difficult for multiview clustering network training. However, the distributions of easy and difficult samples are mixed together, hence not trivial to achieve the goal. To resolve it, we define a sampling probability with a theoretical guarantee. Based on that, a golden section mechanism is further designed to generate a sample set boundary to progressively select the samples with varied difficulty labels via a gate unit, which is utilized to jointly learn a multiview common progressive subspace and clustering network for more efficient clustering. Experimental results on four real-world datasets demonstrate the superiority of DAICS over state-of-the-art methods.

Various palmprint recognition methods have been proposed and applied in security, particularly authentication. However, improving the performance of palmprint recognition with insufficient training samples per person is still a challenging task. The undersampling problem limits the application and popularization of palmprint recognition. In this article, by regularly sampling different local regions of the palmprint image, we learn complete and discriminative convolution features by using deep convolutional neural networks (DCNNs). With this powerful palmprint description, a joint constrained least-square regression (JCLSR) framework, which performs representation for each local region of the same palmprint image requiring all regular local regions of the palmprint image to have similar projected target matrices, is presented to exploit the commonality of different patches. The proposed method can well solve the undersampling classification problem in palmprint recognition. Experiments were conducted on the IITD, CASIA, noisy IITD, and PolyU multispectral palmprint databases. It can be seen from the experimental results that the proposed JCLSR consistently outperformed the classical palmprint recognition methods and some subspace learning-based methods for palmprint recognition.

In multi-label learning, feature selection is a topical issue for addressing high-dimension data. However, most of existing methods adopt imperfect labels to perform feature selection. Although some graph-based multi-label feature selection methods are proposed to deal with the problem, they adopt the fixed graph Laplacian matrix so that the performances of these models are under-performing. To this end, this paper proposes a Dynamic Subspace dual-graph regularized Multi-label Feature Selection method named DSMFS. DSMFS decomposes the original label space into a low-dimensional subspace, and then both the dynamic label-level subspace graph and the feature-level graph are used to obtain a high-quality label subspace to conduct feature selection process. Seven state-of-the-art methods are compared to the proposed method on twelve multi-label benchmark data sets in the experiments. Experimental results demonstrate the superiority of DSMFS.

Due to the difficulty and time-consuming of labeling ground truth map in practical situations, unsupervised multiple change detection (MCD) for multispectral images (MSIs) have attracted much attention in recent years. One possible strategy to obtain multiple changes is to assign labels to the binary change result. However, some methods are difficult to obtain the accurate binary result because of the complexity of backgrounds; moreover, assigning labels is also a challenge owing to the limitation of the number of spectral channels in MSIs. Therefore, we propose a novel unsupervised MCD framework based on auto-updating multitemporal matrix factorization (AMMF) and spatiospectral channel augmentation (SSCA). In AMMF, the accurate binary change result can be detected based on joint matrix factorization, during which the distribution and subspace information of each temporal image are regularized to encode the spatiotemporal correlation. In SSCA, some novel augmentation strategies are introduced to increase the number of channels in MSIs to form the normalized high-dimensional maps for each temporal image based on nonlinear operations and convolutional sparse analysis, respectively. MCD can be achieved by integrating the binary change result and directional information that can be calculated by high-dimensional maps of different temporal images. Experiments are conducted on two real MSIs, indicating that the proposed framework performs well in detecting multiple changes.

Factors such as insufficient training samples, high-dimensional data features, and unbalanced data classes can degrade the accuracy of hyperspectral classification. To this end, this paper proposes an iterative spatial-spectral training sample augmentation (ITSA) algorithm and a new classification model incorporating maximum marginal projection (ITSA-MMP). First, ITSA iteratively augments samples by a similar region clustering strategy (SRCS) integrating spatial-spectral metric. Then, box-plot for representative sample selection (BPRSS) is adopted to screen optimal samples for the final augmented sample set (ASS). Next, based on the ASS, MMP projects the hyperspectral image into a low-dimensional subspace to explore the local structure of the data manifold and improve the inter-class separability of the data. Finally, the MMP-reduced data is classified by support vector machine. Experiments on two real hyperspectral datasets validate that ITSA-MMP can effectively increase the training sample set especially for small initial sample set and unbalanced dataset, and obtain a higher classification accuracy.

The Random Subspace Method (RSM) is an ensemble procedure in which each constituent learner is constructed using a randomly chosen subset of the data features. Regression trees are ideal candidate learners in RSM ensembles. By constructing trees upon different feature subsets, RSM reduces correlation between trees resulting in a stronger ensemble. Furthermore, it lessens computational burden by only considering a subset of the features when building each tree. Despite its apparent advantages, RSM has a notable drawback. In some instances a randomly chosen subspace may lack informative features. This is especially true in situations in which the number of truly informative variables is small relative to the total number of variables. Trees that are constructed using feature subsets lacking informative features can be damaging to the ensemble. Here we present Grafted Random Subspaces (GRS) and Vanishing Random Subspaces (VRS), two novel ensemble procedures designed to remedy the aforementioned drawback by reusing information across trees. Both techniques borrow from RSM by growing individual trees on randomly selected feature subsets. For each tree in a GRS ensemble, the most important variable is identified and guaranteed inclusion into the next q feature subsets. This allows GRS to recycle a promising feature from one tree across several successive trees, effectively grafting the variable into the next q active subsets. In the VRS procedure the least important feature is guaranteed exclusion from the next q feature subsets. This creates a more enriched pool of candidate variables from which the successive feature subsets are drawn.

Noise in hyperspectral images (HSIs) may degrade the HSI classification result. Robust principal component analysis (RPCA) is an excellent method to obtain low-rank (LR) representation of data and is widely used in image denoising and also in HSI classification. However, data are drawn as a union from multiple subspaces in HSIs, so LR subspace estimation (LRSE) is necessary when using RPCA, which is complicated and time-consuming. To solve this problem, this letter proposes a novel LR-based method for HSI classification called two-branch network combined with RPCA, which combines RPCA with a neural network. Specifically, both the LR component and the sparse component are preserved and used for feature extraction in two independent convolutional branches. This way, we can avoid information loss without using accurate LRSE. A concatenate operation and a pointwise convolution are then adopted to realize the feature fusion. Finally, fused features are constructed to indicate the ground truth of each pixel in the classification process. The proposed method constructs a convenient model for HSI classification by discarding the LRSE and combining denoising, feature extraction, feature fusion, and classification into an end-to-end network. The experimental results on three data sets demonstrate that the proposed method outperforms many state-of-the-art methods including ones based on LR representation and ones based on deep learning. In addition, it maintains good classification performance for the cases of small samples and class imbalance.

Effectively recognizing different sceneries with complex backgrounds and varied lighting conditions plays an important role in modern AI systems. Competitive performance has recently been achieved by the deep scene categorization models. However, these models implicitly hypothesize that the image-level labels are 100% correct, which is too restrictive. Practically, the image-level labels for massive-scale scenery sets are usually calculated by external predictors such as ImageNet-CN. These labels can easily become contaminated because no predictors are completely accurate. This article proposes a new deep architecture that calculates scene categories by hierarchically deriving stable templates, which are discovered using a generative model. Specifically, we first construct a semantic space by incorporating image-level labels using subspace embedding. Afterward, it is noticeable that in the semantic space, the superpixel distributions from identically labeled images remain unchanged, regardless of the image-level label noises. On the basis of this observation, a probabilistic generative model learns the stable templates for each scene category. To deeply represent each scenery category, a novel aggregation network is developed to statistically concatenate the CNN features learned from scene annotations predicted by HSA. Finally, the learned deep representations are integrated into an image kernel, which is subsequently incorporated into a multiclass SVM for distinguishing scene categories. Thorough experiments have shown the performance of our method. As a byproduct, an empirical study of 33 SIFT-flow categories shows that the learned stable templates remain almost unchanged under a nearly 36% image label contamination rate.

Recent years have witnessed the rapid development of face image hallucination techniques. However, the previous face hallucination methods are unsupervised and ignore the label information of training samples, leading to undesirable results. This article proposes a locality-constrained and category embedding representation (LCER) method to super-resolve face image in a supervised manner by embedding the label information in data representation. The proposed LCER incorporates the locality prior and category information into one unified framework, which aims to learn both the advantages of locality in preserving the true typologic structure of data manifold and the discriminability in exposing the class subspace information. Such strategy allows the LCER not only to preserve more sharpen image details but also to guarantee the face structure pattern be transferred mainly from the same subject in super-resolution reconstruction. Extensive experiments were conducted to evaluate the proposed LCER, and the comparative results demonstrate that it achieved superior face hallucination performance in both the quantitative measurements and visual impressions compared to several state-of-the-art.

Chemometric multivariate analysis based on low-dimensional linear and bilinear data modelling is presented as a fast and interpretable alternative to more fancy “AI” for practical use of Big Data streams from hyperspectral “video” cameras. The purpose of the present illustration is to find, quantify and understand the various known and unknown factors affecting the process of drying moist wood. It involves an “interpretable machine learning” that analyses more than 350 million absorbance spectra, requiring 418 GB of data storage, without the use of black box operations. The 159-channel high-resolution hyperspectral wood “video” in the 500–1005 nm range was reduced to five known and four unknown variation components of physical and chemical nature, each with its spectral, spatial and temporal parameters quantified. Together, this 9-dimensional linear model explained more than 99.98% of the total input variance.

Due to sensor drift, instrumental variation, or change of measurement object, the distributions of the datasets (domains) acquired by the sensors are often different. A domain adaptive framework called MCSP-SSS is proposed to reduce the distribution discrepancy across domains for high-accuracy sensor data classification. The framework consists of two key parts: Multi-Constraint Subspace Projection (MCSP) and Source Sample Selection (SSS). MCSP is a subspace-projection-based approach, which introduces four constraints to get an optimized projection matrix: Principal Component Analysis (PCA) is used to reduce the redundancy of features; Mean Distribution Discrepancy (MDD) is applied to minimize the difference between source and target data; Hilbert-Schmidt Independence Criterion (HSIC) is adopted to maximizing the dependence between features and labels; A so-called weighted-within-class scatter matrix is introduced to minimize the within-class variance to avoid samples with different labels to overlap in the subspace. SSS is designed to remove the outliers in projected source samples so as to reduce distribution discrepancy between the source and target samples projected by MCSP. Experimental results show that our framework can achieve the best accuracies in all classification tasks in comparison with other state-of-the-art approaches. The accuracy of MCSP-SSS is 3.57 percentage points (pps) higher on average than that of the second best approach for single-source domain adaptation, and 7.00 pps for multi-source domain adaptation. Source code is available at https://github.com/threedteam/tsc_subspace_projection .

Multi-label transfer learning aiming to learn robust classifiers for the target domain by leveraging knowledge from a source domain has been received considerable attention recently. The core part of such research is similarity measurement. Nevertheless, the existing similarity measurement functions of probability distributions are still too simple to fully describe the similarity of probability distributions.. In order to address this problem, we propose a Multi-label Transfer Learning Via Latent Graph Alignment (G-MLTL). G-MLTL uses subspace learning to make the feature distribution of the target domain consistent with the source domain. At the same time, G-MLTL decomposes the label matrix to ensure data points sharing the same labels to have identical latent semantic representation in the new reconstruction space. The proposed G-MLTL also focuses on directly utilizing Latent Graph Alignment to guide the knowledge transfer process. Extensive experiments demonstrate that G-MLTL significantly outperforms the existing multi-label transfer learning methods. Especially when the number of labels is more than four, the mean Average Precision of G-MLTL is higher than the baseline algorithm by 2.1-10.5%.

As a powerful coding strategy for superpixels in synthetic aperture radar (SAR) images, Fisher vector (FV) lies in a low-dimensional subspace and can be sparsely represented as a linear combination of training samples. The existing ship detection methods based on FVs often consider the Euclidean distances between target FVs and clutter FVs, where the subspace features of FVs are generally not exploited. In this article, we propose a new ship detection algorithm based on nonnegative sparse locality-representation (NSLR) to exploit the subspace features of FVs. The proposed NSLR method is based on the assumption that FVs of superpixels in SAR images are sparsely represented by the dictionary of background sea clutter only under a null hypothesis. In addition, we propose two FV-based filters to enhance the robustness of our newly developed NSLR to heterogeneous sea clutter environments by further exploiting the intrinsic features of ship targets in terms of intensity and spatiality. The experimental results based on Gaofen-3 SAR images demonstrate that the proposed NSLR detection method provides higher target-to-clutter contrast and achieves better detection performance than other commonly used ship detection algorithms.

Kinship verification using single image of a person is a challenging task for real-world applications. In this paper, we propose a novel robust discriminative feature subspace analysis (RDFSA) method to address single sample per person (SSPP) problem in kinship verification. The proposed RDFSA method takes advantages of facial symmetry and patch-based analysis to extract discriminative features for kinship verification. Each face image is firstly divided into two halves about bilateral symmetry axis, and each halved face is then partitioned into equal sized non-overlapping patches. Multiple image-sets are formed by grouping these patches according to their positions at each halved face. Then, an SSPP is formulated as an RDFSA problem and a feature subspace is learned by maximizing inter-class separation and minimizing intra-class variance for different patches in each image-set. For a given test image pair, similarity is computed for each feature subspace and majority voting strategy is employed to determine if a given image pair is kin related or not. Proposed RDFSA method is extensively evaluated on different publicly available kinship datasets to validate kinship accuracy. Experimental results show that RDFSA achieves competitive accuracy on all kinship datasets while performing kinship verification under unconstrained environment.

Superpixel segmentation aims at dividing the input image into some representative regions containing pixels with similar and consistent intrinsic properties, without any prior knowledge about the shape and size of each superpixel. In this paper, to alleviate the limitation of superpixel segmentation applied in practical industrial tasks that detailed boundaries are difficult to be kept, we regard each representative region with independent semantic information as a subspace, and correspondingly formulate superpixel segmentation as a subspace clustering problem to preserve more detailed content boundaries. We show that a simple integration of superpixel segmentation with the conventional subspace clustering does not effectively work due to the spatial correlation of the pixels within a superpixel, which may lead to boundary confusion and segmentation error when the correlation is ignored. Consequently, we devise a spatial regularization and propose a novel convex locality-constrained subspace clustering model that is able to constrain the spatial adjacent pixels with similar attributes to be clustered into a superpixel and generate the content-aware superpixels with more detailed boundaries. Finally, the proposed model is solved by an efficient alternating direction method of multipliers (ADMM) solver. Experiments on different standard datasets demonstrate that the proposed method achieves superior performance both quantitatively and qualitatively compared with some state-of-the-art methods., Accepted by IEEE Transactions on Industrial Informatics, 2020

Cross-scene classification is one of the major challenges for hyperspectral image (HSI) classification, especially for target scenes without label samples. Most traditional domain adaptive methods learn a domain invariant subspace to reduce statistical shift while ignoring the fact that there may not exist a shared subspace when marginal distributions of source and target domains are very different. In addition, it is important for HSI classification to preserve discriminant information in the original space. To solve this issue, discriminative cooperative alignment (DCA) of subspace and distribution is proposed to cooperatively reduce the geometric and statistical shift. In the proposed framework, both geometrical and statistical alignments are considered to learn subspaces of the two domains with preserving discrimination information. Furthermore, a reconstruction constraint is imposed to enhance the robustness of subspace projection. Experimental results on three cross-scene HSI data sets demonstrate that the proposed DCA is significantly better than some state-of-the-art domain-adaptive approaches.