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For any parameter vector (r , t , ω) in ℍ : = ℝ × ℝ n × ℝ n , the representation matrix S (r , t , ω) of the Heisenberg group (ℍ , ∗) is extended to a new form S B , W , A (r , t , ω) with nonsingular matrices B , W , A which are related to the directional translation B t : f → f (⋅ − B t) , directional modulation ℳ W ω : f (x) → e i x ′ W ω and dilation A : f → | det (A) | − 1 2 f (A − 1 ⋅) if B ′ W = I n , the identity matrix of order n. In the case B ′ W ≠ I n , an intrinsic group structure under the matrix S B , W , A (r , t , ω) is investigated and a unitary operator representation is offered. [ABSTRACT FROM AUTHOR]

Hypergraph neural networks (HGNNs), extending the techniques of graph neural networks, have been applied to various fields due to their ability to capture more complex high-order node relationships. However, for hyperspectral image (HSI) classification tasks, previous HGNN-based works usually constructed hypergraphs using pixels as nodes, resulting in massive computational costs. Meanwhile, pixel-level personalized features are required for HSI classification. To achieve high efficiency and accuracy simultaneously, this paper presents a fast hypergraph neural network with detail preservation (DPFHNet) for HSI classification. It constructs hypergraphs at the superpixel level to reduce time consumption and supplement pixel-level detail features through a classification refinement module. This framework contains multiple stages. Firstly, its main stage is designed with HGNNs from a superpixel viewpoint rather than pixels, providing a fast strategy to capture high-order complex relationships of multiple homogeneous irregular regions. After that, auxiliary stages based on convolutional neural networks are integrated into the main stage, which adopts a hierarchical design and attempts to acquire pixel-level spatial-spectral information before the hypergraph feature extraction of the main stage, assisting in learning more valuable features. Finally, a classification refinement module is constructed, which generates pixel-level detail features to refine the superpixel-level features obtained by HGNN. Experiments on three datasets illustrate that DPFHNet achieves competitive results and efficiency compared to advanced methodologies. [ABSTRACT FROM AUTHOR]

Graph neural networks (GNNs) have shown strong graph-structured data processing capabilities. However, most of them are generated based on the message-passing mechanism and lack of the systematic approach to guide their developments. Meanwhile, a unified point of view is hard to explain the design concepts of different GNN models. This paper presents a unified optimization framework from hybrid regularized graph signal reconstruction to establish the connection between the aggregation operations of different GNNs, showing that exploring the optimal solution is the process of GNN information aggregation. We use this new framework to mathematically explain several classic GNN models and summarizes their commonalities and differences from a macro perspective. The proposed framework not only provides convenience to understand GNNs, but also has a guiding significance for the proposal of new GNNs. Moreover, we design a model-driven fixed-point iteration method and a data-driven dictionary learning network according to the corresponding optimization objective and sparse representation. Then the new model, GNN based on model-driven and data-driven (GNN-MD), is established by using alternating iteration methods. We also theoretically analyze its convergence. Numerous node classification experiments on multiple datasets illustrate that the proposed GNN-MD has excellent performance and outperforms all baselines on high-feature-dimension datasets. [ABSTRACT FROM AUTHOR]

Scattered data are a class of common data in the real world. Naturally, how to efficiently process scattered data is important. This paper uses a class of feedforward neural networks with four layers as tool to fit scattered data and establishes the estimates of the approximation error. In particular, an inverse theorem of the approximation is established. Concretely, we first extend an existed result on [−1,1]2$$ {\left[-1,1\right]}^2 $$ to the case of arbitrary bounded convex set Ω$$ \boldsymbol{\Omega} $$ in ℝd$$ {\mathbb{R}}^d $$. Secondly, we introduce a modified feedforward neural network with four layers, which is a class of quasi‐interpolation operators and can keep the smoothness of the objective function. By establishing two Bernstein‐type inequalities for the operators, we establish both the direct and converse results of the approximation by the operator, which follows the equivalence characterization theorem of the approximation. [ABSTRACT FROM AUTHOR]

It is well known that feedforward neural networks (FNNs) are universal approximators. This fact constitutes the theoretical basis for FNN learning. Constructing FNNs and estimating their errors of approximation are important and interesting, which not only theoretically verify the generalization ability of the constructed FNNs without training, but also avoid the local minimum solution in the parameters optimization process. This paper aims to construct several classes of FNNs with generalized sigmoidal function, i.e., the sigmoidal function satisfying certain asymptotic behaviours. Another main purpose of this paper is to estimate approximation rates for the constructed FNNs. Using the modulus of continuity of function as a metric, the upper bounds of approximation are estimated. In particular, the results of this paper contain the corresponding results for FNNs consisting of some classical sigmoidal functions. [ABSTRACT FROM AUTHOR]

Although graph neural networks (GNNs) have been extensively employed in various research fields, they are susceptible to adversarial attacks, as revealed in previous studies. Targeted label attacks, in which the victim node is anticipated to fall into a desired category, are more consistent with practical circumstances than untargeted label attacks. However, there has been relatively little research on them, and existing attackers require access to the target model and do not consider the budget allocation; the budget refers to the maximum number of perturbations permitted. Furthermore, the performance of untargeted label attacks is weakened when they are converted into targeted label attacks. From the perspective of budget allocation, we devise an effective targeted label attack (ETLA). The prior knowledge includes training labels, node features, and the graph structure. The main concept is based on the strategical allocation of a given budget from the search space and optimisation objective. For the search space, a stratified node selection strategy and an adaptive edge choice strategy are developed to capture insertable and removable candidates. The former exploits unlabelled node information through massive pseudo-labels, whereas the latter capitalises on the similarity of node features. Regarding the optimisation objective, a temperature factor is introduced into the attack loss to better direct the flipping of the candidates. After a finite number of perturbations, the final disturbed graph is fed into various target models to evaluate attack performance. Generous trials indicate that our ETLA has excellent attack capability compared with other attack techniques with the same budget. [ABSTRACT FROM AUTHOR]

The universal approximation property of feedforward neural networks (FNNs) is the basis for all FNNs applications. In almost all existing FNN approximation studies, it is always assumed that the activation function of the network satisfies certain conditions, such as sigmoid or bounded continuity. This paper focuses on building simple architecture FNNs with approximation ability by constructing an activation function. First, for any continuous function defined on [0, 1] and an arbitrary accuracy ϵ > 0, an FNN is constructed, which has only one neuron and a fixed weight 1 and can approximate the function with an accuracy of ϵ. Thereafter, we study the representation of FNNs for polynomial functions by constructing a proper activation function. It is proved that any algebraic polynomial with the degree n can be represented by an FNN. Further, a piecewise function is constructed as an activation function of an FNN such that the FNN represents the famous Bernstein polynomials. [ABSTRACT FROM AUTHOR]

This study builds a fully deconvolutional neural network (FDNN) and addresses the problem of single image super-resolution (SISR) by using the FDNN. Although SISR using deep neural networks has been a major research focus, the problem of reconstructing a high resolution (HR) image with an FDNN has received little attention. A few recent approaches toward SISR are to embed deconvolution operations into multilayer feedforward neural networks. This paper constructs a deep FDNN for SISR that possesses two remarkable advantages compared to existing SISR approaches. The first improves the network performance without increasing the depth of the network or embedding complex structures. The second replaces all convolution operations with deconvolution operations to implement an effective reconstruction. That is, the proposed FDNN only contains deconvolution layers and learns an end-to-end mapping from low resolution (LR) to HR images. Furthermore, to avoid the oversmoothness of the mean squared error loss, the trained image is treated as a probability distribution, and the Kullback–Leibler divergence is introduced into the final loss function to achieve enhanced recovery. Although the proposed FDNN only has 10 layers, it is successfully evaluated through extensive experiments. Compared with other state-of-the-art methods and deep convolution neural networks with 20 or 30 layers, the proposed FDNN achieves better performance for SISR. [ABSTRACT FROM AUTHOR]

In recent years, convolutional neural networks have been successfully applied to single image super-resolution (SISR) tasks, making breakthrough progress both in accuracy and speed. In this work, an improved dual-scale residual network (IDSRN), achieving promising reconstruction performance without sacrificing too much calculations, is proposed for SISR. The proposed network extracts features through two independent parallel branches: dual-scale feature extraction branch and texture attention branch. The improved dual-scale residual block (IDSRB) combined with active weighted mapping strategy constitutes the dual-scale feature extraction branch, which aims to capture dual-scale features of the image. As regards the texture attention branch, an encoder–decoder network employing symmetric full convolutional-deconvolution structure acts as a feature selector to enhance the high-frequency details. The integration of two branches reaches the goal of capturing dual-scale features with high-frequency information. Comparative experiments and extensive studies indicate that the proposed IDSRN can catch up with the state-of-the-art approaches in terms of accuracy and efficiency. [ABSTRACT FROM AUTHOR]

This study presents a new architecture for deep convolution networks, end-to-end hybrid dilated residual networks wherein 3D cube images are input for hyperspectral image (HSI) classification, and this is termed as 3D-2D SSHDR. The proposed networks could greatly improve the performance of HSI classification as they select the spectral bands adaptively and avoid the limitations of handcrafted selection. Specifically, 3D spectral residual blocks are initially used to learn discriminant features from rich spectral features. Subsequently, extracted 3D images with spectral features are reshaped into 2D feature maps as the input for spatial feature learning, which does not affect the extraction of spatial-spectral features and could reduce the number of parameters. This is followed by using hybrid dilated convolution (HDC) residual blocks to continue learning discriminative spatial features, expanding the receptive field of the convolution kernel without increasing the computational complexity, and avoiding the gridding effect generated by the dilated convolution. Finally, the proposed networks are trained via supervised learning. Besides, this method could accelerate the convergence speed and alleviate the over-fitting problem due to the added batch normalization layers and the design of a multi-residual structure. Experimental results validate that the performance of the proposed network is superior on several HSI benchmark datasets when compared with that of existing methods. [ABSTRACT FROM AUTHOR]

For point cloud registration (PCR), a matching matrix is critical. Unfortunately, the existing approaches do not explicitly devise schemes to refine the matching matrix. Furthermore, previous studies focused on the design of feature interactions between two point clouds and lacked attention to the discriminative features required for point cloud registration. This study presents a novel PCR method called RecARONet. The method mainly includes two innovations: an adaptive relation-oriented convolution (ARO-Conv) with effectiveness and a recurrent refinement technique of the correspondence based on the adaptive neighbourhood consensus constraint, mainly for more accurate registration. Specifically, ARO-Conv reconstructs the node representation by weighting the relations in the local neighbourhood rather than generating point features from the embeddings of the neighbours. This simple but effective operation can reduce feature redundancy and alleviate structural smoothness to a certain extent. It can also assign appropriate weights to the relations and different channels of features to capture more distinct local topological information. In addition, a recurrent correspondence-walk with a semantic adornment algorithm based on the adaptive neighbourhood consensus constraint is depicted, which can adaptively capture the differences in the local structure among proxy point pairs and recurrently update correspondences. Registration evaluations were performed on several complete/partial point cloud datasets, which revealed that the constructed model achieved excellent performance. [ABSTRACT FROM AUTHOR]

White blood cell (WBC) image detection plays an important role in automatic morphological systems since it can simplify and facilitate WBC segmentation and classification procedures. However, existing WBC detection methods mainly rely on the location of the nucleus, which is found difficult to achieve accurate detection results. This paper proposes a novel WBC detection algorithm through sliding windows with varying sizes to traverse the image for candidates. Three cues are explored to measure the candidates, and a combined cue is used as a single output to distinguish positives from negatives. The ϵ -support vector regression is employed to determine the detection window from the candidates. In this paper, two applications of the proposed WBC detection approach are carried out, including an adaptive thresholding algorithm based on WBC detection for nucleus segmentation from images and target detection to lessen the users' interaction for automatic cytoplasm segmentation. [ABSTRACT FROM AUTHOR]

Recently, various convolutional neural networks (CNNs) based single image super-resolution (SR) methods have been vigorously explored, and a lot of impressive results have emerged. However, more or less unfortunately, most of the methods mainly focused on increasing the depth of network to improve reconstruction performance. As a matter of fact, deeper depth of network usually means an increase in parameters and computations, or worse still, the increase in parameters or computations often results in the difficulty to train the network. This paper develops a new SR approach called multi-scale residual channel attention network (MSRCAN), which is comparative shallow two-stage neural network structure, and can extract more details to effectively ameliorate the quality of SR. Specifically, a multi-scale residual channel attention block (MSRCAB) is designed to plenarily exploit the image features with convolutional kernels of different sizes. At the same time, a channel attention mechanism is introduced to recalibrate the channel significance of feature mappings adaptively. Furthermore, multiple short skip connections and a long skip connection are presented in each MSRCAB to complement information loss. Moreover, the two-stage design contributes to fully uncover low-level and high-level information. Evaluation on the benchmark data set indicates that the proposed method can rival the state-of-the-art convolutional methods. [ABSTRACT FROM AUTHOR]

More existing methods of single image super-resolution (SR) often direct super-resolving the details, but when the upsampling factor is larger, it is challenging to reconstruct high-frequency details. Lately, deep convolution neural networks have made significant progress with regard to SR. However, with an increase in networks width and depth, the information used for reconstruction is becoming increasingly weaker, and the training of neural networks is becoming more difficult. This paper proposes a novel architecture of a deep recursive convolution neural networks used to reconstruct a high-resolution image from an original low-resolution (LR) image in a step-by-step manner. The architecture consists of three parts: an embedding network, cascaded fine extraction blocks, and reconstruction networks. Concretely, a wide convolution is used to extract more features from the original LR images, cascaded fine extraction blocks are employed to extract more useful information through a step-by-step approach and remove redundant information, and a deconvolution operation is utilized to restore the features. The proposed networks adopt a residual-feature learning scheme, and the Caffe framework is chosen for training the networks. The experimental results show that the proposed method exhibits a superior performance compared with various other state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Abstract Learning-based super-resolution (SR) imaging has been extensively studied. In this study, a novel reconstruction method is proposed for SR that employs the geometrical structure of an image as well as the statistical priors based on clustering and local structure priors. In this approach, the training samples are divided into numerous overlapping sub-patches, and the sub-patches are then grouped into different clusters, where anchored centres for different subspaces are defined by training joint dictionaries. Variable low-resolution to high-resolution mappings are then learned according to the local similarities. Finally, the desired high resolution patch can be reconstructed by using the multiple learned local relationships corresponding to its sub-patches. Experimental results demonstrated the superior performance of the proposed method. Highlights • A measure is proposed for extracting local structural similarity. For each patch, the local structure prior can yield a robust representation. • An algorithm is developed for learning multiple local mappings. Different linear mappings are used simultaneously to reconstruct the desired image. • A model is proposed that combines hierarchical similarity and local structure priors. This model yields more reasonable and reliable results than the existing methods based on clustering or regression alone. [ABSTRACT FROM AUTHOR]

• A novel triplet teaching graph contrastive network is proposed. Its focus on the inherent link between augmented views broadens the idea of employing augmented views. • A self-evolving adaptive augmented view generating scheme is proposed. • A stochastic hybrid module for mining missing information in different contrastive concepts is proposed. The sample distribution in the contrastive space is further improved. Unsupervised graph contrastive learning has recently emerged as the solution to the crisis of label information scarcity for graph data in the real world. However, from the general paradigm of graph contrastive learning, most of the existing methods are still flawed in the design and use of augmented views and the design of contrastive targets. Therefore, the works on how to generate reasonable augmented views and utilize them canonically and how to construct efficient and comprehensive contrastive objectives are very meaningful. Based on the teaching concept, this paper proposes a new triplet teaching graph contrastive network with self-evolving adaptive augmentation. Firstly, after carefully analyzing the internal relationships between different augmented perspectives, we present a triple teaching graph neural network framework based on the improved triplet idea. It creates contrastive objectives depending on different contrastive angle levels, providing thorough guidance for graph encoders. Secondly, a self-evolving adaptive graph augmentation scheme based on topology and feature information is proposed. It is worth mentioning that with the continuous deepening of the training process, the scheme can utilize the learnable self-attention mechanism to constantly supply our network framework with an increasing number of reliable augmented views as input. Finally, when designing the contrastive objectives, we introduce a stochastic hybrid module to mine the unexploited information, which opportunely complements the contrastive sample space formed by our network framework. Furthermore, extensive experiments on multiple real-world node classification datasets demonstrate that our model can generate better-quality node embedding for downstream tasks. The implementation of this paper is available at https://github.com/PaperMiao/T-GCSA. [ABSTRACT FROM AUTHOR]

With the explosive growth in size of datasets, it becomes more significant to develop effective learning schemes for neural networks to deal with large scale data modelling. This paper proposes an iterative approximate Newton-type learning algorithm to build neural networks with random weights (NNRWs) for problem solving, where the whole training samples are divided into some small subsets under certain assumptions, and each subset is employed to construct a local learner model for integrating a unified classifier. The convergence of the output weights of the unified learner model is given. Experimental results on UCI datasets with comparisons demonstrate that the proposed algorithm is promising for large scale datasets. [ABSTRACT FROM AUTHOR]

It is well known that the support vector machine (SVM) is an effective learning algorithm. The alternating direction method of multipliers (ADMM) algorithm has emerged as a powerful technique for solving distributed optimisation models. This paper proposes a distributed SVM algorithm in a master–slave mode (MS-DSVM), which integrates a distributed SVM and ADMM acting in a master–slave configuration where the master node and slave nodes are connected, meaning the results can be broadcasted. The distributed SVM is regarded as a regularised optimisation problem and modelled as a series of convex optimisation sub-problems that are solved by ADMM. Additionally, the over-relaxation technique is utilised to accelerate the convergence rate of the proposed MS-DSVM. Our theoretical analysis demonstrates that the proposed MS-DSVM has linear convergence, meaning it possesses the fastest convergence rate among existing standard distributed ADMM algorithms. Numerical examples demonstrate that the convergence and accuracy of the proposed MS-DSVM are superior to those of existing methods under the ADMM framework. [ABSTRACT FROM AUTHOR]

Most recent learning-based image super-resolution (SR) methods have attracted much interest. This paper proposes a new SR method with multi-channel constraints, which integrates clustering, collaborative representation, and progressive multi-layer mapping relationships to reconstruct high-resolution (HR) color image. In order to collect chrominance information, the training patches from RGB channels are clustered into different subspaces, and a number of neighbor subsets are grouped. Then the optimization problem with color channel constraints is solved by using the classical gradient technique. Finally, a continuous reconstructive structure, which learns multi-layer mapping relationships between intermediate output and corresponding original HR image, is designed to obtain the desired HR image. Extensive experiments on several commonly used image SR testing datasets indicate that the proposed method achieves state-of-the-art image SR results. [ABSTRACT FROM AUTHOR]

White blood cells (WBCs) segmentation is a challenging problem in the study of automated morphological systems, due to both the complex nature of the cells and the uncertainty that is present in video microscopy. This paper investigates how to boost the effects of region-based nucleus segmentation in WBCs by means of optimal thresholding and low-rank representation. The main idea is firstly using optimal thresholding to obtain the possible uniform WBC regions in the input image. After that, a manifold-based low-rank representation technique is employed to infer a unified affinity matrix that implicitly encodes the segmentation of the pixels of possible WBC regions. This is achieved by separating the low-rank affinities from the feature matrix into a pair of sparse and low-rank matrices. The experiments show that the proposed method is possible to produce better segmentation results compared with existing approaches. [ABSTRACT FROM AUTHOR]

Sparse representation-based classification (SRC) method has gained great success in face recognition due to its encouraging and impressive performance. However, in SRC the data used to train or test are usually corrupted, and hence the performance is affected. This paper proposes a robust face recognition approach by means of learning a class-specific dictionary and a projection matrix. Firstly, the training data are decomposed into class-specific dictionary, non-class-specific dictionary, and sparse error matrix. Secondly, in order to correct the corrupted test data, the data are projected onto their corresponding underlying subspace, and a projection matrix between the original training data and the class-specific dictionary is learned. Then, the features of the class-specific dictionary and the corrected test data are extracted by using Eigenface method. Finally, the SRC is performed to classify. Extensive experiments conducted on publicly available data sets show that the proposed algorithm performs better than some state-of-the-art methods. [ABSTRACT FROM AUTHOR]

The error of a distributed algorithm for big data classification with a support vector machine (SVM) is analysed in this paper. First, the given big data sets are divided into small subsets, on which the classical SVM with Gaussian kernels is used. Then, the classification error of the SVM for each subset is analysed based on the Tsybakov exponent, geometric noise, and width of the Gaussian kernels. Finally, the whole error of the distributed algorithm is estimated in terms of the error of each subset. [ABSTRACT FROM AUTHOR]

We address the construction and approximation for feed-forward neural networks (FNNs) with zonal functions on the unit sphere. The filtered de la Vallée-Poussin operator and the spherical quadrature formula are used to construct the spherical FNNs. In particular, the upper and lower bounds of approximation errors by the FNNs are estimated, where the best polynomial approximation of a spherical function is used as a measure of approximation error. [ABSTRACT FROM AUTHOR]

Recovering the low-rank, sparse components of a given matrix is a challenging problem that arises in many real applications. Existing traditional approaches aimed at solving this problem are usually recast as a general approximation problem of a low-rank matrix. These approaches are based on the nuclear norm of the matrix, and thus in practice the rank may not be well approximated. This paper presents a new approach to solve this problem that is based on a new norm of a matrix, called the truncated nuclear norm (TNN). An efficient iterative scheme developed under the linearized alternating direction method multiple framework is proposed, where two novel iterative algorithms are designed to recover the sparse and low-rank components of matrix. More importantly, the convergence of the linearized alternating direction method multiple on our matrix recovering model is discussed and proved mathematically. To validate the effectiveness of the proposed methods, a series of comparative trials are performed on a variety of synthetic data sets. More specifically, the new methods are used to deal with problems associated with background subtraction (foreground object detection), and removing shadows and peculiarities from images of faces. Our experimental results illustrate that our new frameworks are more effective and accurate when compared with other methods. [ABSTRACT FROM AUTHOR]

Currently, most of the existing point cloud registration methods use stacked edge convolution as feature extractor, ignoring the importance of deep semantic information, meanwhile, the use of attention mechanism tends to increase the computational cost of the model and limits the matching effect. This paper proposes a dynamic graph aggregation framework for point cloud registration by building a dynamic deep network, which can capture richer semantic information and shape properties of point clouds. First, a hybrid feature extractor, which fully fuses local graph information and global graph information, is designed to obtain more discriminative feature descriptors. Second, a local graph neighborhood scoring module to update local graph features and achieve feature enhancement is built by learning the difference of similar point neighborhood features. Finally, a dual-constrained matching module is designed, which is used to measure the similarity of point pairs from the two aspects of Euclidean distance and affinity between features. The proposed framework achieves excellent registration performance, as demonstrated by experimental results on challenging 3D point cloud benchmarks. Especially in partial point cloud registration, MAE(R) achieved excellent results of 0.2614 and 0.2619 under unseen shapes and unseen categories. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of face recognition under pose and illumination variations, and proposes a novel algorithm inspired by the idea of sparse representation (SR). In order to make the SR early designed for the pose-invariant face recognition suitable for the case of pose variation, a multi-pose weighted sparse representation (MW-SR) algorithm is proposed to emphasize the contributions of the similar poses in the representation of the test image. Furthermore, when some illumination variations are added to the images, it is more reasonable to take advantage of the results of pose variable recognition and avoid the traditional SR method that adds all kinds of images with pose and illumination variations in the training dictionary. Here, a novel idea of the proposed algorithms is adding a general illumination dictionary to the training dictionary, and that once the illumination dictionary is designed, it is common for the other face databases. Extensive experiments illustrate that the proposed algorithms perform better than some existing methods for the face recognition under pose and illumination variations. [ABSTRACT FROM AUTHOR]

In this paper, some feed-forward neural networks (FNNs) interpolation operators based on scattered data are introduced. Further, these operators are used as approximators to approximate bivariate continuous target function. By means of the translations and dilates of logistic function, some FNNs quasi-interpolation and exact interpolation operators are constructed, respectively. Using the modulus of continuity of function and the mesh norm of scattered data as measures, the corresponding approximation errors of the constructed operators are estimated. In addition, the well-known central B-splines are used to construct FNNs interpolation operators with compact support, and the corresponding approximation errors are also estimated. [ABSTRACT FROM AUTHOR]

Approximation capabilities of the spherical neural networks (SNNs) are considered in this paper. Based on a known Taylor formula, we prove that, for non-polynomial target function, rates of simultaneously approximating the function itself and its (Laplace–Beltrami) derivatives by SNNs is not slower than those by the spherical polynomials (SPs). Then, the simultaneous approximation rates of SPs automatically derive the rates of SNNs. [ABSTRACT FROM AUTHOR]

In this article, a new human face recognition scheme is proposed. The proposed system is based on the sparsity and fuzziness, and utilizes independent component analysis (ICA). The scheme includes four parts: a fuzzy comprehensive judgment model for estimating whether the information carried by training samples is enough or not, a proper edge extraction operator to discover more hidden information for single image, ICA feature extractor, and a sparse representation model for correlation coefficient calculation to classify testing samples. In view of the intrinsic patterns of gray information distribution of face images, a weighted fuzzy distance for judgement model and cluster analysis is proposed. The new proposed method is tested on ORL, FERET and UMIST databases. The experiment results demonstrate and illustrate the feasibility of the proposed method and the effective performances on recognition rate. [ABSTRACT FROM AUTHOR]

Methods of achieving image super-resolution (SR) have been the object of research for some time. These approaches suggest that when a low-resolution (LR) image is directly downsampled from its corresponding high-resolution (HR) image without blurring, i.e., the blurring kernel is the Dirac delta function, the reconstruction becomes an image-interpolation problem. Hence, this is a pervasive way to explore the linear relationship among neighboring pixels to reconstruct a HR image from a LR input image. This paper seeks an efficient method to determine the local order of the linear model implicitly. According to the theory of low-rank matrix completion and recovery, a method for performing single-image SR is proposed by formulating the reconstruction as the recovery of a low-rank matrix, which can be solved by the augmented Lagrange multiplier method. In addition, the proposed method can be used to handle noisy data and random perturbations robustly. The experimental results show that the proposed method is effective and competitive compared with other methods. [ABSTRACT FROM PUBLISHER]

This paper studies the construction and approximation of quasi-interpolation for spherical scattered data. First of all, a kind of quasi-interpolation operator with Gaussian kernel is constructed to approximate the spherical function, and two Jackson type theorems are established. Second, the classical Shepard operator is extended from Euclidean space to the unit sphere, and the error of approximation by the spherical Shepard operator is estimated. Finally, the compact supported kernel is used to construct quasi-interpolation operator for fitting spherical scattered data, where the spherical modulus of continuity and separation distance of scattered sampling points are employed as the measurements of approximation error. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper we study the convergence rate and inverse theorem for spherical multiscale interpolation in L p and Sobolev norms. The multiscale interpolation is constructed using a sequence of scaled, compactly supported radial basis functions restricted to the unit sphere S n . For the interpolation scheme the problem called “native space barrier” is considered. In addition, a Bernstein type inequality is established to derive an inverse theorem for the multiscale interpolation, and some numerical experiments to illustrate the theoretical results are given. [ABSTRACT FROM AUTHOR]

This paper focuses on the multiscale moving least squares approximation scheme on the unit sphere, where the scale depends on the current evaluation points. The scheme is constructed by using a sequence of scaled weight functions, and is a little different from the classical moving least squares approximation on the sphere, which can be obtained by restricting compactly supported radial basis functions in R 3 to S 2 . More precisely, a multiscale moving least squares (MMLS) algorithm, in which the corresponding scale is changing with the associated given point set, is proposed. In addition, the convergence analysis for the multiscale scheme and some numerical experiments to illustrate the theoretical results are given. [ABSTRACT FROM AUTHOR]

Since the spherical Gaussian radial function is strictly positive definite, the authors use the linear combinations of translations of the Gaussian kernel to interpolate the scattered data on spheres in this article. Seeing that target functions are usually outside the native spaces, and that one has to solve a large scaled system of linear equations to obtain combinatorial coefficients of interpolant functions, the authors first probe into some problems about interpolation with Gaussian radial functions. Then they construct quasi-interpolation operators by Gaussian radial function, and get the degrees of approximation. Moreover, they show the error relations between quasi-interpolation and interpolation when they have the same basis functions. Finally, the authors discuss the construction and approximation of the quasi-interpolant with a local support function. [ABSTRACT FROM AUTHOR]

This paper aims to study the construction and multivariate approximation of a class of network operators with logistic sigmoidal functions. First, a class of even and bell-shaped function with support on R is constructed by using appropriate translation and combination of the logistic function. Then, the constructed function is employed as activation function to construct a kind of so-called Cardaliaguet–Euvrard type network operators. Finally, these network operators are used to approximate bivariate functions in C [ - 1 , 1 ] 2 , and a Jackson type theorem for the approximation errors is established. [ABSTRACT FROM AUTHOR]

In this paper, the multivariate Bernstein polynomials defined on a simplex are viewed as sampling operators, and a generalization by allowing the sampling operators to take place at scattered sites is studied. Both stochastic and deterministic aspects are applied in the study. On the stochastic aspect, a Chebyshev type estimate for the sampling operators is established. On the deterministic aspect, combining the theory of uniform distribution and the discrepancy method, the rate of approximating continuous function and L convergence for these operators are studied, respectively. [ABSTRACT FROM AUTHOR]

This paper discusses local uniform error estimates for spherical basis functions (SBFs) interpolation, where error bounds for target functions are restricted on spherical cap. The discussion is first carried out in the native space associated with the smooth SBFs, which is generated by a strictly positive definite zonal kernel. Then, the smooth SBFs are embedded in a larger space that is generated by a less smooth kernel, and for the target functions outside the original native space, the local uniform error estimates are established. Finally, some numerical experiments are given to illustrate the theoretical results. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper concerns about the approximation by a class of positive exponential type multiplier operators on the unit sphere $\mathbb{S}^n $ of the ( n + 1)-dimensional Euclidean space for n ⩾ 2. We prove that such operators form a strongly continuous contraction semigroup of class $(C_0 )$ and show the equivalence between the approximation errors of these operators and the K-functionals. We also give the saturation order and the saturation class of these operators. As examples, the rth Boolean of the generalized spherical Abel-Poisson operator ⊕ V and the rth Boolean of the generalized spherical Weierstrass operator ⊕ W for integer r ⩾ 1 and reals γ, κ ∈ (0, 1] have errors $\left\| { \oplus ^r V_t^\gamma f - f} \right\|_X \asymp \omega ^{r\gamma } (f,t^{1/\gamma } )_X $ and $\left\| { \oplus ^r W_t^\kappa f - f} \right\|_X \asymp \omega ^{r\kappa } (f,t^{1/(2\kappa )} )_X $ for all f ∈ $X$ and 0 ⩽ t ⩽ 2 π, where $X$ is the Banach space of all continuous functions or all ℒ integrable functions, 1 ⩽ p < +∞, on $\mathbb{S}^n $ with norm $\left\| \cdot \right\|_X $, and $\omega ^s (f,t)_X $ is the modulus of smoothness of degree s > 0 for f ∈ $X$. Moreover, ⊕ V and ⊕ W have the same saturation class if γ = 2 κ. [ABSTRACT FROM AUTHOR]

Highlights: [•] Gives sparse algorithms of random weights networks. [•] The algorithms have effective performance compared with some traditional algorithms. [•] The algorithms are used to diagnose the faults of switch reluctance motor. [•] The algorithms are employed effectively in the face recognition. [ABSTRACT FROM AUTHOR]

Abstract: In this article, we address the problem of compressed classification learning. A generalization bound of the support vector machines (SVMs) compressed classification algorithm with uniformly ergodic Markov chain samples is established. This bound indicates that the accuracy of the SVM classifier in the compressed domain is close to that of the best classifier in the data domain. In a sense, the fact that the compressed learning can avoid the curse of dimensionality in the learning process is shown. In addition, we show that compressed classification learning reduces the learning time at the price of decreasing the classification accuracy, but the decrement can be controlled. The numerical experiments further verify the results claimed in this article. [Copyright &y& Elsevier]

We establish a general oracle inequality for regularized risk minimizers with strongly mixing observations, and apply this inequality to support vector machine (SVM) type algorithms. The obtained main results extend the previous known results for independent and identically distributed samples to the case of exponentially strongly mixing observations. [ABSTRACT FROM AUTHOR]

Abstract: In this work, a new image classification method is proposed based on extreme k-means (EKM) and effective extreme learning machine (EELM). The proposed method has image decomposition with curvelet transform, reduces dimensionality with discriminative locality alignment (DLA), generates a set of distinctive features with EKM, and has a classification with EELM. Since EKM has a better clustering performance than k-means and EELM has a better accuracy than ELM, the proposed EKM-EELM algorithm has a significant improvement in classification rate. Extensive experiments are performed using challenging databases and results are compared against state of the art techniques. Experimental results show that the proposed method has superior performances on classification rate than some other traditional methods for image classification. [Copyright &y& Elsevier]

Some mathematical models in geophysics and graphic processing need to compute integrals with scattered data on the sphere. Thus cubature formula plays an important role in computing these spherical integrals. This paper is devoted to establishing an exact positive cubature formula for spherical basis function networks. The authors give an existence proof of the exact positive cubature formula for spherical basis function networks, and prove that the cubature points needed in the cubature formula are not larger than the number of the scattered data. [ABSTRACT FROM AUTHOR]