• Deep Unsupervised Convolutional Kernels: A deep hierarchical NMF architecture is proposed to learn multi-layer convolution kernels in an unsupervised manner. • Unsupervised Hybrid Spectral-Spatial Modules: Novel synergistic integration of PCA, Whitening, NMF, Convolution, ReLU, and texture-aware LBP features. • Progressive Feature Abstraction: Multi-layer NMF framework enables progressively abstract, discriminative feature learning from unlabeled HSI data. • Breaks Shallow NMF Barrier: First deep NMF extension overcoming traditional limitations, capturing complex HSI structures efficiently. • Maintains Efficiency & Interpretability: Combines CNN-like hierarchical feature learning with NMF’s computational efficiency and inherent interpretability. Hyperspectral image (HSI) classification is a key task in remote sensing but significantly limited by the scarcity of labeled training samples. Traditional Nonnegative Matrix Factorization (NMF) provides interpretable representation but lacks the depth to extract discriminative features for complex HSI data. Deep learning methods, while powerful, require abundant labels that are often unavailable. To address this, we propose DNMFNet that a deep NMF network for unsupervised feature extraction. Its core innovation lies in learning hierarchical convolutional kernels via NMF without supervision, enabling deep representation learning under extreme label scarcity. Specifically, we extend NMF into a multi-layer architecture that integrates PCA, whitening, NMF convolution, and ReLU operations, forming modules capable of extracting rich spectral-spatial features. A classification framework built on these features is then developed. Experiments on three benchmark HSI datasets demonstrate that DNMFNet consistently outperforms state-of-the-art methods designed for few-shot learning.

Convolutional neural networks (CNNs) have shown impressive performance in hyperspectral image (HSI) classification. However, these deep learning methods still face two major challenges. One is that they require a large number of training samples to train parameters, and the other is that high-dimensional nonlinear feature extraction and multi-source information fusion. This paper proposes a deep stochastic adaptive Fourier decomposition (SAFD) network integrated with back-propagation (BP) and multi-scale feature fusion to significantly improve classification accuracy. The main contributions are threefold: 1) A deep SAFD network with BP is designed, which introduces BP into the deep SAFD network for the first time, and achieves automatic dynamic optimization of network parameters through the back-propagation algorithm. 2) A Kalman filter-based multi-scale pyramid construction method is proposed, which extracts hierarchical spatial features through state recursion equations and enhances texture representation by fusing local binary patterns (LBP). 3) An efficient classification algorithm based on a deep stochastic adaptive Fourier decomposition network with a BP algorithm is developed to integrate deep SAFD features, multi-scale pyramid features, and LBP texture features, achieving higher classification accuracy. Experimental results show that the proposed method outperforms other selected HSI classification methods with similar principles. Moreover, compared with other state-of-the-art deep learning methods, the proposed method can achieve better classification performance.

Deep learning-based hyperspectral image (HSI) classification methods have recently shown excellent performance. However, the success of these deep learning methods mainly relies on the deep network architecture with a huge amount of parameters trained by a large number of training samples. In this article, a deep high-order tensor sparse representation (SR) network (DHTSRNet) is proposed, which can obtain better classification results in the case of small training samples. Specifically, we propose a high-order tensor SR (HTSR) model that can handle arbitrary-order tensor-type data, and extend it to a deep HTSR model that can be used to train deep high-order tensor filters and features. Then, a deep feature extraction network (DHTSRNet) based on the deep HTSR model is constructed, which is used for feature extraction of HSI. Finally, an HSI classification method is constructed by combining DHTSRNet and the classifier based on graph-based learning (GSL), which can obtain better classification results in the case of small training samples. Experimental results show that the DHTSRNet can obtain better classification performance compared with other state-of-the-art HSI classification methods.

Deep learning-based hyperspectral image (HSI) classification methods have recently shown excellent performance, however, there are two shortcomings that need to be addressed. One is that deep network training requires a large number of labeled images, and the other is that deep network needs to learn a large number of parameters. They are also general problems of deep networks, especially in applications that require professional techniques to acquire and label images, such as HSI and medical images. In this paper, we propose a deep network architecture (SAFDNet) based on the stochastic adaptive Fourier decomposition (SAFD) theory. SAFD has powerful unsupervised feature extraction capabilities, so the entire deep network only requires a small number of annotated images to train the classifier. In addition, we use fewer convolution kernels in the entire deep network, which greatly reduces the number of deep network parameters. SAFD is a newly developed signal processing tool with solid mathematical foundation, which is used to construct the unsupervised deep feature extraction mechanism of SAFDNet. Experimental results on three popular HSI classification datasets show that our proposed SAFDNet outperforms other compared state-of-the-art deep learning methods in HSI classification.

In deep learning, finding flat minima of loss function is a hot research topic in improving generalization. The existing methods usually find flat minima by sharpness minimization algorithms. However, these methods suffer from insufficient flexibility for optimization and generalization due to their ignorance of loss value. This article theoretically and experimentally explores the sharpness minimization algorithms for neural networks. First, a novel scale-invariant sharpness which is called scale-adaptive central moment sharpness (SA-CMS) is proposed. This sharpness is not only scale-invariant but can characterize the nature of loss surface clearly. Based on the proposed sharpness, this article further derives a new regularization term by integrating the different orders of the sharpness. Particularly, a host of sharpness minimization functions such as local entropy can be covered by this regularization term. Then the central moment sharpness generating function is introduced as a new objective function. Moreover, theoretical analyses indicate that the new objective function has a smoother landscape and prefer converging to flat local minima. Furthermore, a computationally efficient two-stage algorithm is developed to minimize the objective function. Compared with other algorithms, the two-stage loss-sharpness minimization (TSLSM) algorithm offers a more flexible optimization target for different training stages. On a variety of learning tasks with both small and large batch sizes, this algorithm is more universal and effective, and meanwhile achieves or surpasses the generalization performance of the state-of-the-art sharpness minimization algorithms.

Recently, hyperspectral image (HSI) classification methods based on deep learning have demonstrated excellent performance. However, these deep learning methods still face two major challenges. One is that they require a large number of labeled samples, and the other is that training parameters takes a lot of time. In this paper, we propose a dual-branch deep stochastic adaptive Fourier decomposition (SAFD) network (DSAFDNet) to alleviate the aforementioned two issues in HSI classification applications. SAFD is a newly developed signal processing tool with solid mathematical foundation. It can be used to find common filters (i.e. convolution kernels) of a set of random signals or multi-signals. Since the convolution kernels obtained by SAFD decomposition are complex numbers, few deep learning methods directly deal with such complex convolution kernels. To this end, we propose a dual-branch network to extract deep features from hyperspectral images using both real and imaginary parts of convolutional kernels. After deep feature extraction using DSAFDNet, we further investigate the classification performance of different classifiers on the extracted features. Experimental results show that the proposed method outperforms some HSI classification methods with similar principles. Moreover, compared with other state-of-the-art deep learning methods, the proposed method can achieve better classification performance.

Most hyperspectral image (HSI) data exist in the form of tensor; the tensor representation preserves the potential spatial–spectral structure information compared with the vector representation, which can help improve the classification performance of HSI. In this article, a deep high-order tensor convolutional sparse coding (CSC) model is proposed, which can be used to train deep high-order filters. Based on the deep high-order tensor CSC model, a deep feature extraction network (DHTCSCNet) is constructed, which is used for feature extraction of HSIs. By combining the spectral–spatial feature and the features extracted by the proposed DHTCSCNet at each layer, a combined feature that incorporates shallow, deep, spectral, and spatial features can be obtained. Then, the graph-based learning (GSL) methods are used to classify the combined feature. Experimental results show that the DHTCSCNet can obtain better classification performance compared with other HSI classification methods.

Hyperspectral unmixing (HU) has been one of the most significant tasks in hyperspectral image (HSI) processing. In recent years, nonnegative matrix factorization (NMF) has received great attention in the HU due to its simultaneous estimation, flexible modeling, and little requirement on prior information. However, several common NMF algorithms still suffer from high computational complexity, instability, and low convergence rate. Motivated by the matrix manifold theory, this article proposes a new sparse oblique-manifold ($\mathcal {OB}$) NMF method from the perspective of matrix manifold. The critical idea of the proposed method is to regard the abundance matrix as locating on the oblique manifold, which eliminates its constraint of nonnegativity and sum-to-one and incorporates its intrinsic Riemannian geometry. Meanwhile, the$L_{1/2}$-norm on the Euclidean space can be transformed equivalently into the$L_{1}$-norm on oblique manifold. Then, via solving this sparse$\mathcal {OB}$NMF by the Riemannian conjugated gradient (RCG) algorithm and the multiplicative iterative rule, the proposed method not only ensures improvement in the solution accuracy but also leads to a much faster convergence rate. Experimental results from the synthetic and real-world datasets illustrate the effectiveness and efficiency of the proposed method compared with the state-of-the-art NMF methods in HU.

Hyperspectral unmixing is a significant task in remote sensing image analysis. Existing learning-based methods for hyperspectral unmixing generally are in the form of an autoencoder and take geometric distances, such as spectral angle distance (SAD) as loss functions. These methods ignored the distribution similarity between the observation and the reconstruction, which might help improve the unmixing performance. Besides, the autoencoder is trained by directly comparing the difference between the observation and the reconstruction, and the difference between their features has been neglected. Based on the above considerations, we propose a joint metric neural network for hyperspectral unmixing, by introducing theWasserstein distanceandfeature matchingas regularization terms and SAD as the underlying loss. The proposed neural network consists of two parts: an autoencoder is used for endmember extraction and abundance estimation, while a discriminator is used to compute the Wasserstein distance. The Wasserstein distance can stably provide useful gradient information that promotes the autoencoder to reach a solution with better unmixing performance. The feature matching is adapted to an intermediate layer of the discriminator for enforcing the features of the observation and the reconstruction to be equal, which can lead to further improvement of the unmixing performance. The model analysis and the regularization parameter analysis are conducted to demonstrate the effectiveness of our method. Experimental results on four real-world hyperspectral data sets show that our method outperforms the state-of-the-art methods, especially in terms of abundance estimation.

In recent years, hyperspectral unmixing (HU) has been a crucial preprocess in hyperspectral imagery analysis. Current learning-based methods of HU are built on the autoencoder framework. Most of them hold a pointwise loss function only comparing the individual difference without the overall difference. As a remedy, we propose a probability metric-based autoencoder (PMAE) for HU. Specifically, we combine a distribution distance called maximum mean discrepancy (MMD) with underlying loss spectral angle distance (SAD) as the final loss function for training the unmixing autoencoder. The MMD can be seen as a regularization that is designed to match all orders of statistics between the input spectrums and the reconstructed spectrums. The SAD is to compare the individual difference, while the MMD compares the overall difference. Combing these two points, we can obtain more prior information to guide the autoencoder training toward boosting the unmixing performance. In order to validate this viewpoint, we conduct model analysis and a series of ablation studies, showing that adding the MMD into the autoencoder unmixing model, indeed, boosts the unmixing performance a lot compared to the single SAD objective. Experimental results on five real hyperspectral scenes demonstrate the effectiveness and competitiveness of the proposed PMAE compared with several classical and learning-based approaches.

The deep network has shown its superiority to extract discriminative features for hyperspectral image (HSI) classification. However, most existing methods only exploit label information of land classes to supervise the learning of deep features, and the learning process is totally automatic. Considering the complex spectral–spatial characteristic in real HSI, it is reasonable to utilize the manifold structure of input data to provide complementary information for precise classification. This article proposes a structure-preserving spectral–spatial network (SPSSN) to exploit the manifold structure information during the feature learning process, which can extract discriminative deep structure-preserving spectral–spatial features. Specifically, a basic spectral–spatial network (SSN), comprising a spectral module and a spatial module connected in series, is first built to learn spectral–spatial features from HSI cubes. Second, a novel structure-preserving constraint is introduced to transfer the intrinsic manifold structure of the input data into the learned deep spectral–spatial features, so as to enhance the discrimination. Furthermore, a feasible algorithm of imposing the constraint is designed to make it compatible with the deep learning framework, which results in a structure-preserving loss. Finally, the SSN is combined with the structure-preserving loss to obtain the SPSSN. Experiments on real HSI datasets verify the effectiveness and superiority of the SPSSN compared with several state-of-the-art methods in HSI classification.

Deconvolutional networks have attracted extensive attention and have been successfully applied in the field of computer vision. In this paper we propose a novel two-branch deconvolutional network (TBDN) that can improve the performance of conventional deconvolutional networks and reduce the computational complexity. A feasible iterative algorithm is designed to solve the optimization problem for the TBDN model, and a theoretical analysis of the convergence and computational complexity for the algorithm is also provided. The application of the TBDN in stereo matching is presented by constructing a disparity estimation network. Extensive experimental results on four commonly used datasets demonstrate the efficiency and effectiveness of the proposed TBDN.

Adaptive Fourier decomposition (AFD) is a newly developed signal processing tool that can adaptively decompose any single signal using a Szegö kernel dictionary. To process multiple signals, a novel stochastic-AFD (SAFD) theory was recently proposed. The innovation of this study is twofold. First, a SAFD-based general multi-signal sparse representation learning algorithm is designed and implemented for the first time in the literature, which can be used in many signal and image processing areas. Second, a novel SAFD based image compression framework is proposed. The algorithm design and implementation of the SAFD theory and image compression methods are presented in detail. The proposed compression methods are compared with 13 other state-of-the-art compression methods, including JPEG, JPEG2000, BPG, and other popular deep learning-based methods. The experimental results show that our methods achieve the best balanced performance. The proposed methods are based on single image adaptive sparse representation learning, and they require no pre-training. In addition, the decompression quality or compression efficiency can be easily adjusted by a single parameter, that is, the decomposition level. Our method is supported by a solid mathematical foundation, which has the potential to become a new core technology in image compression.

This article proposes a novel regularization deep cascade broad learning system (DCBLS) architecture, which includes one cascaded feature mapping nodes layer and one cascaded enhancement nodes layer. Then, the transformation feature representation is easily obtained by incorporating the enhancement nodes and the feature mapping nodes. Once such a representation is established, a final output layer is constructed by implementing a simple convex optimization model. Furthermore, a parallelization framework on the new method is designed to make it compatible with large-scale data. Simultaneously, an adaptive regularization parameter criterion is adopted under some conditions. Moreover, the stability and error estimate of this method are discussed and proved mathematically. The proposed method could extract sufficient available information from the raw data compared with the standard broad learning system and could achieve compellent successes in image denoising. The experiments results on benchmark datasets, including natural images as well as hyperspectral images, verify the effectiveness and superiority of the proposed method in comparison with the state-of-the-art approaches for image denoising.

A functional feature extraction method based on rational function approximation for hyperspectral image (HSI) classification is proposed. In digital imagery, the spectral information of a pixel can be regarded as a 1-D signal. An HSI is composed of these 1-D signals arranged in a certain spatial structure. According to the functional characteristic of hyperspectral data, 1-D signals can be approximated by a linear combination of basis functions. Thus, a joint rational basis function system (JRBFS) based on class adaptivity is here first built for an HSI by adaptive Fourier decomposition (AFD). Second, the functional representations (FRs) and corresponding reconstructed spectral curves are obtained by decomposing the original spectral information in a JRBFS. Furthermore, the functional spectral-spatial features are extracted on the basis of FRs by an edge-preserving filtering method, FR-EPFs. Finally, the functional spectral-spatial features are used for HSI classification by SVM. Experimental results for five commonly used HSI data sets demonstrate the effectiveness and advantages of the proposed method FR-EPFs.

This article proposes a functional data discriminant analysis (FDDA) method for hyperspectral image (HSI) classification. This method analyzes and processes the HSI data from a functional point of view, which is a novel perspective in HSI processing. The classical methods achieve dimensionality reduction by directly eliminating the redundancy of the HSI data. However, the proposed method extracts the functional features by utilizing the redundancy of the HSI data. Functional features can effectively reveal inherent characteristics of the HSI data with the change in the wavelengths. Based on this, a regularized weighted fitting model is first built for converting a spectral vector into a spectral curve. Second, an FDDA method defined in the function field is presented for extracting the functional features of the spectral curves. Finally, a novel spectral-spatial framework is designed for classification tasks of HSI data sets. Experimental results in three commonly used HSI data sets indicate that the proposed method is effective and leads to promising classification results compared with some benchmarking methods. More importantly, the work tries to diversify and develop the existing theory and methods of HSI classification from discrete (vector) data learning methods to continuous (functional) data learning methods.

Mixture noise removal is a fundamental problem in hyperspectral images' (HSIs) processing that holds significant practical importance for subsequent applications. This problem can be recast as an approximation issue of a low-rank matrix. In this paper, a novel smooth rank approximation (SRA) model is proposed to cope with these mixture noises for HSIs. The crux idea is to devise a general smooth function under some assumptions to directly approximate the rank function, which attempts to explore a closer approximation than conventional methods. This new optimization model can be easily solved by the convex analysis tool and can remove the mixture noises of HSIs quickly and effectively. Subsequently, we give a feasible iterative algorithm, and the corresponding convergence analysis is discussed mathematically. Experimental results from the simulated data set as well as real data sets illustrate that the proposed SRA method significantly outperforms the state-of-the-art methods on HSI denoising.

Matrix completion has been widely used in image processing, in which the popular approach is to formulate this issue as a general low-rank matrix approximation problem. This paper proposes a novel regularization method referred to as truncated Frobenius norm (TFN), and presents a hybrid truncated norm (HTN) model combining the truncated nuclear norm and truncated Frobenius norm for solving matrix completion problems. To address this model, a simple and effective two-step iteration algorithm is designed. Further, an adaptive way to change the penalty parameter is introduced to reduce the computational cost. Also, the convergence of the proposed method is discussed and proved mathematically. The proposed approach could not only effectively improve the recovery performance but also greatly promote the stability of the model. Meanwhile, the use of this new method could eliminate large variations that exist when estimating complex models, and achieve competitive successes in matrix completion. Experimental results on the synthetic data, real-world images as well as recommendation systems, particularly the use of the statistical analysis strategy, verify the effectiveness and superiority of the proposed method, i.e. the proposed method is more stable and effective than other state-of-the-art approaches.

This paper proposes a novel and simple multilayer feature learning method for image classification by employing the extreme learning machine (ELM). The proposed algorithm is composed of two stages: the multilayer ELM (ML-ELM) feature mapping stage and the ELM learning stage. The ML-ELM feature mapping stage is recursively built by alternating between feature map construction and maximum pooling operation. In particular, the input weights for constructing feature maps are randomly generated and hence need not be trained or tuned, which makes the algorithm highly efficient. Moreover, the maximum pooling operation enables the algorithm to be invariant to certain transformations. During the ELM learning stage, elastic-net regularization is proposed to learn the output weight. Elastic-net regularization helps to learn more compact and meaningful output weight. In addition, we preprocess the input data with the dense scale-invariant feature transform operation to improve both the robustness and invariance of the algorithm. To evaluate the effectiveness of the proposed method, several experiments are conducted on three challenging databases. Compared with the conventional deep learning methods and other related ones, the proposed method achieves the best classification results with high computational efficiency.

Spectral Clustering is one of pioneered clustering methods in machine learning and pattern recognition field. It relies on the spectral decomposition criterion to learn a low-dimensional embedding of data for a basic clustering algorithm such as the k-means. The recent sparse Spectral clustering (SSC) introduces the sparsity for the similarity in low-dimensional space by enforcing a sparsity-induced penalty, resulting a non-convex optimization, and the solution is calculated through a relaxed convex problem via the standard ADMM (Alternative Direction Method of Multipliers), rather than inferring latent representation from eigen-structure. This paper provides a direct solution as solving a new Grassmann optimization problem. By this way calculating latent embedding becomes part of optimization on manifolds and the recently developed manifold optimization methods can be applied. It turns out the learned new features are not only very informative for clustering, but also more intuitive and effective in visualization after dimensionality reduction. We conduct empirical studies on simulated datasets and several real-world benchmark datasets to validate the proposed methods. Experimental results exhibit the effectiveness of this new manifold-based clustering and dimensionality reduction method.

In hyperspectral image (HSI) classification, the combination of spectral information and spatial information can be applied to enhance the classification performance. In order to better characterize the variability of spatial features at different scales, we propose a new framework called multiscale spatial information fusion (MSIF). The MSIF consists of three parts: multiscale spatial information extraction, local 1-D embedding (L1-DE), and information fusion. First, spatial filter with different scales is used to extract multiscale spatial information. Then, L1-DE is utilized to map the spectral information and spatial information at different scales into 1-D space, respectively. Finally, the obtained 1-D coordinates are used to label the unlabeled spatial neighbors of the labeled samples. The proposed MSIF captures intrinsic spatial information contained in homogeneous regions of different sizes by multiscale strategy. Since the spatial information at different scales is processed separately in MSIF, the variance of spatial information at different scales can be reflected. The use of L1-DE reduces computational cost by mapping high-dimensional samples into 1-D space. In MSIF, the L1-DE and information fusion are used iteratively, and the iterative process terminates in a finite number of steps. The algorithm analysis demonstrates the effectiveness of the proposed method. The experimental results on four widely used HSI data sets show that the proposed method achieved higher classification accuracies compared with other state-of-the-art spectral-spatial classification methods.

This paper proposes a spectral-spatial classification algorithm based on principal components (PCs)-based smooth ordering and multiple 1-D interpolation, which can alleviate the general classification problems effectively. Because of the characteristics of hyperspectral image, there always exist easily separable samples (ESSs) and difficultly separable samples (DSSs) in view of the different sets of labeled samples. In this paper, the PC analysis is first used for reducing features and extracting the few first PCs of a hyperspectral image. Then, PC-based smooth ordering is designed for the separation of ESSs and DSSs, and multiple 1-D interpolation is used for the accurate classification of the ESSs. Next, the highly confident samples are selected from the ESSs by the spatial neighborhood information, which are added into the training set for the classification of DSSs. In the case of sufficient training samples, a supervised spectral-spatial method is used for classifying the DSSs by combining the spatial information built with popular extended multiattribute profiles. The proposed algorithm is compared with some state-of-the-art methods on three hyperspectral data sets. The results demonstrate that the presented algorithm achieves much better classification performance in terms of the accuracy and the computation time.

In the hyperspectral image classification area, a few number of labeled samples is a bottleneck for the improvement of classification accuracy. In order to tackle this problem, multiple one-dimensional embedding interpolation (M1DEI) has been used for hyperspectral image classification and achieved promising results. Despite the success, the complexity of M1DEI prevents its practical application. On the other hand, the percentage of newly added samples is set by experience when enlarging the labeled set. In this paper we develop a method by extending the M1DEI method with local strategy, called multiple local one-dimensional embedding interpolation (ML1DEI). We only map the labeled samples and their local spatial neighbors into the one-dimensional (1D) space. The local strategy can reduce the complexity of M1DEI, since only labeled samples and their neighbors need to be mapped. In addition, the local strategy ensures all these newly labeled samples come from the spatial neighborhood of labeled samples. Then, during the merging stage, we can incorporate all of them with the labeled samples. Moreover, the proposed ML1DEI can incorporate the spatial information and make full use of the unlabeled samples. Compared with other spatial-spectral classification methods, the proposed ML1DEI method obtains promising results. Experimental results on the commonly used hyperspectral data set validate the effectiveness of the proposed method.

Hyperspectral unmixing (HSU) plays an important role in hyperspectral image (HSI) analysis. Recently, the HSU method based on sparse regression has drawn much attention. This paper presents a new weighted sparse regression problem for HSU and proposes two iterative reweighted algorithms for solving this problem, where the weights used for the next iteration are computed from the value of the current solution, and all the mixed pixels of an HSI are unmixed simultaneously. The proposed algorithms can be seen as the combinations of alternating direction method of multipliers and iterative reweighting procedure. Experimental results on both synthetic and real data demonstrate some advantages of the proposed algorithms over some other state-of-the-art sparse unmixing approaches.

This note corrects an error in the proof of corollary 1 of Li et al. ( 2014 ). The original claim of the contraction principle in appendix D of Li et al. no longer holds.

The momentum wheel (MW) plays a significant role in ensuring the success of satellite missions, the reliability information of MW can be provided by collecting degradation data when there exists certain performance characteristics that degrade over time. In this paper, we develop a reliability modeling and life estimation approach for MW used in satellites based on the expectation maximization (EM) algorithm from a Wiener degradation model. The degradation model corresponding to a Wiener process with the random effect is first established using failure modes, mechanisms, and effects analysis. Afterwards, the first hitting time is employed to describe the failure time, and the explicit result of the reliability function is derived in terms of the Wiener degradation model. As the likelihood function for such a model contains unobserved latent variables, an EM algorithm is adopted to obtain the maximum likelihood estimators of model parameters efficiently. Finally, the effectiveness of the developed approach is validated using the degradation data from a specific type of MW.

Preference learning has caused great attention in machining learning. In this letter we propose a learning framework for pairwise loss based on empirical risk minimization of U-processes via Rademacher complexity. We first establish a uniform version of Bernstein inequality of U-processes of degree 2 via the entropy methods. Then we estimate the bound of the excess risk by using the Bernstein inequality and peeling skills. Finally, we apply the excess risk bound to the pairwise preference and derive the convergence rates of pairwise preference learning algorithms with squared loss and indicator loss by using the empirical risk minimization with respect to U-processes.

The large number of spectral bands acquired by hyperspectral imaging sensors allows us to better distinguish many subtle objects and materials. Unlike other classical hyperspectral image classification methods in the multivariate analysis framework, in this paper, a novel method using functional data analysis (FDA) for accurate classification of hyperspectral images has been proposed. The central idea of FDA is to treat multivariate data as continuous functions. From this perspective, the spectral curve of each pixel in the hyperspectral images is naturally viewed as a function. This can be beneficial for making full use of the abundant spectral information. The relevance between adjacent pixel elements in the hyperspectral images can also be utilized reasonably. Functional principal component analysis is applied to solve the classification problem of these functions. Experimental results on three hyperspectral images show that the proposed method can achieve higher classification accuracies in comparison to some state-of-the-art hyperspectral image classification methods.

Robust small target detection of low signal-to-noise ratio (SNR) is very important in infrared search and track applications for self-defense or attacks. Consequently, an effective small target detection algorithm inspired by the contrast mechanism of human vision system and derived kernel model is presented in this paper. At the first stage, the local contrast map of the input image is obtained using the proposed local contrast measure which measures the dissimilarity between the current location and its neighborhoods. In this way, target signal enhancement and background clutter suppression are achieved simultaneously. At the second stage, an adaptive threshold is adopted to segment the target. The experiments on two sequences have validated the detection capability of the proposed target detection method. Experimental evaluation results show that our method is simple and effective with respect to detection accuracy. In particular, the proposed method can improve the SNR of the image significantly.

Battery prognostics aims to predict the remaining life of a battery and to perform necessary maintenance service if necessary using the past and current information. A reliable prognostic model should be able to accurately predict the future state of the battery such that the maintenance service could be scheduled in advance. In this paper, a multistep-ahead prediction model based on the mean entropy and relevance vector machine (RVM) is developed, and applied to state of health (SOH) and remaining life prediction of the battery. A wavelet denoising approach is introduced into the RVM model to reduce the uncertainty and to determine trend information. The mean entropy based method is then used to select the optimal embedding dimension for correct time series reconstruction. Finally, RVM is employed as a novel nonlinear time-series prediction model to predict the future SOH and the remaining life of the battery. As more data become available, the accuracy and precision of the prediction improve. The presented approach is validated through experimental data collected from Li-ion batteries. The experimental results demonstrate the effectiveness of the proposed approach, which can be effectively applied to battery monitoring and prognostics.

In this paper, a hierarchical feature extraction method is proposed for image recognition. The key idea of the proposed method is to extract an effective feature, called local neural response (LNR), of the input image with nontrivial discrimination and invariance properties by alternating between local coding and maximum pooling operation. The local coding, which is carried out on the locally linear manifold, can extract the salient feature of image patches and leads to a sparse measure matrix on which maximum pooling is carried out. The maximum pooling operation builds the translation invariance into the model. We also show that other invariant properties, such as rotation and scaling, can be induced by the proposed model. In addition, a template selection algorithm is presented to reduce computational complexity and to improve the discrimination ability of the LNR. Experimental results show that our method is robust to local distortion and clutter compared with state-of-the-art algorithms.

Elastic-net regularization is a successful approach in statistical modeling. It can avoid large variations which occur in estimating complex models. In this paper, elastic-net regularization is extended to a more general setting, the matrix recovery (matrix completion) setting. Based on a combination of the nuclear-norm minimization and the Frobenius-norm minimization, we consider the matrix elastic-net (MEN) regularization algorithm, which is an analog to the elastic-net regularization scheme from compressive sensing. Some properties of the estimator are characterized by the singular value shrinkage operator. We estimate the error bounds of the MEN regularization algorithm in the framework of statistical learning theory. We compute the learning rate by estimates of the Hilbert-Schmidt operators. In addition, an adaptive scheme for selecting the regularization parameter is presented. Numerical experiments demonstrate the superiority of the MEN regularization algorithm.

The paper introduces two different types of frequencies of which one is the Arccosine Instantaneous Frequency (ArccosineIF) for the so called axial simple waves (ASWs); and the other is the α-Counting Instantaneous Frequency (α-CIF) for a more general class of signals called simple waves (SWs). The classes ASW and SW contain a wide range of signals for which the concept instantaneous frequency has a perfect physical sense. Then under wavelet decomposition the two types of frequencies are used to analyze the time-frequency distributions of the biomedical EEG signals with comparison. A set of experiments on publicly available database clearly indicate that the proposed approaches are very promising.

In this paper, we present an approach for writer identification using off-line Arabic handwriting. The proposed method introduced Arabic writing in a new form, by presenting Arabic writing in its basic components instead of alphabetic. We split the input document into two parts: one for the letters and the other for the diacritics, we extract all diacritics from the input image and calculate the LBP histogram for each diacritic then concatenate these histograms to use it as handwriting features. We use the IFN/ENIT database in the experiments reported here and our tests involve 287 writers. The results show that our method is very effective and makes the handling of the Arabic handwriting more easily than before.