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Graph Neural Network (GNN) has attracted considerable research interest in various graph data modeling tasks. Most GNNs require efficient and sufficient label information during training phase. However, in open environments, the performance of existing GNNs sharply decrease according to the data (structure, attribute and label) missing and noising. Several recent attempts have been made to improve the performance and robustness of GNNs, most of which are contrastive learning-based and auto encoder-based strategies. In this paper, a semi-supervised learning framework is proposed for graph modeling tasks, i.e., robust graph neural network with Dirichlet regularization and Residual connection (DRGNN). Specifically, the structure and feature of the original graph are both masked to generate the masked graph, which is sent to the graph representation learning block (encoder) to learn the latent node representation. Additionally, an initial residual connect is introduced into the graph representation learning block to directly transmit the original node feature to the last layer to retain the inherent information of the node itself. Finally, the whole network is jointly optimized by the structure reconstructed loss, feature reconstructed loss and the classification loss. Note that a Dirichlet regularization constraint is introduced into the learning objective to dominate the latent node representation into a local smoothing scenario, which is more conforms with the manifold assumption of the graph representation learning. Extensive experiments demonstrate the state-of-the-art accuracy and the robustness of the proposed DRGNN on benchmark datasets. [ABSTRACT FROM AUTHOR]

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]

Point clouds in the real world are often sparse and incomplete. Point cloud completion aims to restore incomplete point clouds into meaningful shapes. In recent years, point cloud completion has attracted the interest of many researchers. In most existing methods, the efficiency of completion is generally ignored in favor of producing meaningful shapes with adequate details. This paper proposes a fast point completion network (FPCN). FPCN is mainly composed of a multi-scale attention encoder (MSAE) and a structural refinement (SR) module. MSAE first obtains multi-scale geometric information by extracting incomplete inputs at different resolutions. After that, MSAE fuses multi-scale geometric information through cross-attention mechanisms. Compared with existing mainstream encoders, MSAE can extract rich geometric information from input point clouds with low complexity. The SR module aims to extract local information from the coarse point clouds to guide the process of extending points. Furthermore, the process of extending points is achieved by a replication strategy. Compared to existing folding-based decoders, the SR module can produce fine point clouds with more local details. Compared to existing transformer-based decoders, the SR module has a lower calculation price by employing a replication strategy to generate high-resolution point clouds. In conclusion, FPCN can restore partial point clouds into meaningful shapes efficiently, and the outcomes of completion contain sufficient details. Extensive experiments on various datasets demonstrate the performance and efficiency of the FPCN in point cloud completion. Source code is available at https://github.com/doldolOuO/FPCN. [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]

Autism spectrum disorder (ASD) is a prevalent neurodevelopmental condition. Its early and accurate diagnosis is critical in enhancing the quality of life for affected individuals. Graph neural networks supply promising approaches for ASD diagnosis. However, existing works typically focus on brain-level or population-level classification methods, where the former usually disregards subjects' non-imaging information and inter-subject relationships, and the latter generally fails to adequately evaluate and detect disease-associated brain regions and biomarkers. Furthermore, relatively static graph structures and shallow network architectures hinder the abundant extraction of information, affecting the performance of ASD identification. Accordingly, this paper proposes a new spectral graph network with brain-population graph structure joint learning (BPGLNet) for ASD diagnosis. This new framework involves two main components. Firstly, a brain-level graph learning module is designed to acquire valuable features of brain regions and identify effective biomarkers for each subject. In particular, it constructs a brain-aware representation learning network by fusing an improved graph pooling strategy and spectral graph convolution to learn subgraph structures and features of brain regions. Subsequently, based on these generated features, a population-level graph learning module is developed to capture relationships between different subjects. It builds an adaptive edge generator network by integrating non-imaging and imaging data, forming a learnable population graph. Further, this module also devises a deep cascade spectral graph network to enrich high-level feature representation of data and complete ASD identification. Experiments on the benchmark dataset reveal the state-of-the-art performance of BPGLNet. [ABSTRACT FROM AUTHOR]

Point cloud classification and segmentation are challenging tasks due to the irregular structures, especially when there is translation variance in the point clouds. To overcome this barrier, this paper proposes a self-augment convolutional neural network (SACNN), which can not only extract more discriminative features from the points cloud but also alleviate the translation variance problem. Specifically, we first represent the point cloud through the dynamic graph, with the intention to keep the number of point clouds during the feature learning to avoid information loss. Benefiting from the dynamic graph, the global and local features of point clouds can be learned. Then, to reduce the translation variance in the dynamic graphs, a self-augment convolution (SAConv) module is designed to make points align their coordinates based on learned features. Finally, the local mixed aggregation module is proposed to combine the overview and the detailed descriptor of the neighbors. Experiments on several standard benchmarks verify the superiority of the SACNN over state-of-the-art methods in both 3D point cloud classification and segmentation tasks. [ABSTRACT FROM AUTHOR]

Rigid point cloud registration is a crucial upstream task in computer vision, whose goal is to align two misaligned point clouds using a rigid transformation. Existing methods, which directly utilize extracted point features for computing point relationships, are likely to result in a wrong-matching relationship since two or more similar feature points in the source point cloud easily correspond to the same point in the target point cloud. To this end, this paper proposes a two-view point cloud registration network that better alleviates the problem of similar feature points from both the feature and geometry levels. Specifically, at the feature level, a residual correction unit is proposed to learn feature-aware coefficients from raw 3D point clouds to adaptively increase or decrease the difference between features. An attention mechanism is established in two-point clouds to capture the implicit feature relationship between the two-point clouds, gathering the information of another point cloud to enrich the feature information of its own point cloud. Second, at the geometry level, a dual-view graph topology fusion module is described. All points in the graph structure are no longer independent but connected by their geometry structure. Therefore, each point can aggregate neighbor information in the same point cloud and in different point clouds through the constructed single graph and interactive graph, so that each point can enhance the difference between points through its geometry structure. In order to fuse the information of a single graph and an interactive graph, a cross-attention module is proposed to supplement contextual information to obtain point features that are more suitable for matching. Experimental results demonstrate that our method achieves excellent results on complete and partial noisy point clouds. [ABSTRACT FROM AUTHOR]

Cortical surface parcellation aims to segment the surface into anatomically and functionally significant regions, which are crucial for diagnosing and treating numerous neurological diseases. However, existing methods generally ignore the difficulty in learning labeling patterns of boundaries, hindering the performance of parcellation. To this end, this paper proposes a joint parcellation and boundary network (JPBNet) to promote the effectiveness of cortical surface parcellation. Its core is developing a multi-rate-shared dilated graph attention (MDGA) module and incorporating boundary learning into the parcellation process. The former, in particular, constructs a dilated graph attention strategy, extending the dilated convolution from regular data to irregular graph data. We fuse it with different dilated rates to extract context information in various scales by devising a shared graph attention layer. After that, a boundary enhancement module and a parcellation enhancement module based on graph attention mechanisms are built in each layer, forcing MDGA to capture informative and valuable features for boundary detection and parcellation tasks. Integrating MDGA, the boundary enhancement module, and the parcellation enhancement module at each layer to supervise boundary and parcellation information, an effective JPBNet is formed by stacking multiple layers. Experiments on the public dataset reveal that the proposed method outperforms comparison methods and performs well on boundaries for cortical surface parcellation. [ABSTRACT FROM AUTHOR]

As we know, feedforward neural networks (FNNs) with sigmoidal activation function are universal approximators. Theoretically, for any continuous function defined on a compact set, there exists an FNN such that the FNN can approximate the function with arbitrary accuracy, which constitutes a theoretical guarantee that FNN can be used as an efficient learning machine. This paper addresses the construction and approximation for FNNs. We construct an FNN with sigmoidal activation function and estimate its approximation error. In particular, an inverse theorem of the approximation is established, which implies the equivalence characterization theorem of the approximation and reveals the relationship between the topological structure of the FNN and its approximation ability. As keys in this study, the concepts of modulus of continuity of function, K-functional, and their relationship are utilized, and two Bernstein-type inequalities are established. [ABSTRACT FROM AUTHOR]

3D point cloud registration related to rigid transformation is a fundamental yet crucial task in computer vision and graphics. For rigid registration, the local alignment of two-point clouds is equivalent to a global alignment. Since sufficient information exchange is an effective way to enhance mutual understanding, it is necessary to design a reasonable and sufficient feature interaction across two-point clouds to to obtain discriminative features and explore overlapping points. Recently, although a series of learning-based registration methods have been explored, most of the existing methods lack attention to multi-level feature interactions. In addition, there seems to be no paper that explicitly proposes a method for two-stage registration. However, intermediate constraints can be set in the two-stage registration to supervise the coarse registration and better refine the fine registration. To this end, this paper proposes a multi-level interaction perception method for two-stage partial-to-partial point cloud registration that can hierarchically capture discriminative structural features by the interaction of local details and global features from different dimensions, as well as improve the perception of locality in the early information exchange. Also, a spatial overlap-aware transformer is constructed to highlight the common regions while perceiving the global information of the point cloud. Thus, overlap constraints with high confidence between source and target point clouds can be obtained. The registration evaluation is performed on numerous partial 3D point clouds with Gaussian noise, and the results reveal that our method can achieve superior performance. [ABSTRACT FROM AUTHOR]

Existing deep learning-based image super-resolution (SR) algorithms have made great achievements on synthetic LR–HR pairs in a fully supervised manner. However, the real image degradation process is complicated and unclear, leading to a domain gap between the synthetic LR images and real LR images. To address this issue, the most widely used alternatives are GAN-based methods trained with unpaired data. But most GAN-based methods tend to follow complex multi-stage pipelines and still suffer from the vast cost of hyperparameter tuning on the loss function. In this paper, in contrast to complicated two-stage or multi-stage GAN, a straightforward and simple one-stage GAN-based framework is proposed. Different from the current one-stage GAN, our approach exclusively fits the CycleGAN pattern without any other restrictions, fully leveraging images from unpaired datasets. Specifically, our framework consists of a DegradeNet and an SRNet, which implicitly models the degradation and SR process between the source LR domain and target HR domain. Such a simple one-stage GAN allows us to flexibly learn the data distribution without any assumptions, greatly reducing the model complexity and training difficulty. To further address the inherent practice of empirically setting hyperparameters in previous methods, we propose an adaptive weighting network to automatically learn the contribution weights of different losses in a meta-learning manner. This flexible strategy could shorten the gap between various losses and meanwhile help the model to adaptively optimize in an efficient way. Extensive experiments demonstrate the superiority of our proposed method in terms of indicators and perceptual quality. [ABSTRACT FROM AUTHOR]

The sparsity and incompleteness of point clouds generally result in challenges in point cloud analysis. Most existing point cloud completion methods use an individual Euclidean space feature to generate point clouds. Consequently, the generated point clouds are relatively rough. This paper proposes a multi-space and detail-supplemented attention point cloud completion network (MSDSA-Net). Here, the key is to utilize multi-space features to generate high-quality point clouds. First, we construct a dual-branch multi-space feature extractor (MSFE). A branch of the MSFE is a local-holistic geometric feature extractor based on Euclidean space and eigenvalue space. It can extract features with similar local geometric structures at points that are at a distance, to compensate for the missing part of the feature information of the point cloud. Another branch of the MSFE is a global feature extractor based on Euclidean space to extract the global features. Second, we continue to follow the coarse-to-fine decoding framework of general completion networks. However, in the fine generation stage, we propose a detail-supplemented (DS) module to supplement the features used to guide point cloud generation in detail. Extensive experiments demonstrate that our network has a good effect on the shape completion of point clouds. [ABSTRACT FROM AUTHOR]

Vision Transformer (ViT) has attracted tremendous attention and achieved remarkable success on high-level visual tasks. However, ViT relies on costly pre-training on large external datasets and is strict in data and calculations, making it an obstacle to running on common equipment. To address this challenge, we propose a simple and efficient Transformer namely SRT tailored for the image super-resolution (SR) reconstruction task. It is trained on a single GPU card without large-scale pre-training. At the beginning of the whole model, we introduce a convolutional stem module instead of straightforward tokenization of raw input images for low-level feature extraction and steady training. In the main Transformer learning phase, we exploit an additional head-convolution to make up for the lack of information interaction in multi-head self-attention (MHSA). Then further to strengthen the spatial correlation of neighboring tokens in MLP, a locally-enhanced feed-forward layer is thus employed to promote local dependencies. In terms of the inefficiency of Transformer, a channel reduction strategy is presented in MHSA, which dramatically reduces the complexity and space resources. Experimental results demonstrate the proposed Transformer model can rival the current state-of-the-art methods with a single GPU card. [ABSTRACT FROM AUTHOR]

Random forest, a popular ensemble approach in machine learning, has received much attention of researchers in different fields due to its excellent performance. Especially, in the study of classification, it is often used as an effective classifier. Considering that the accuracy and diversity of each base classifier are two main factors that affect the performance of random forest, this paper proposes a new rotation forest ensemble method to increase the diversity of each tree in the forest, which is based on feature extension and transformation. Also, a weighting vote for base classifiers is applied to integrate the final ensemble results instead of to average the accuracy of ensemble learners. In order to illustrate the effectiveness of the proposed algorithm, the experiments conduct with thirty benchmark classification datasets available from the UCI repository and two face recognition databases. Experimental results demonstrate that the proposed algorithm can achieve higher classification accuracy in most cases compared to the other ensemble classifiers. [ABSTRACT FROM AUTHOR]

Matrix completion is critical in a wide range of scientific and engineering applications, such as image restoration and recommendation systems. This topic is commonly expressed as a low-rank matrix optimization framework. In this paper, a universal and effective rank approximation method for matrix completion (RAMC) is provided. Fundamental to this strategy is developing a general function that meets specific conditions in order to directly approach the rank function and subsequently utilizing it to build a RAMC model. The major goal is to investigate a more accurate estimate of the rank function, allowing for more effective acquisition of the low-rank structure of incomplete data. Further, the RAMC model is easily implemented by a viable iterative method that may be successfully used to matrix completion tasks. Extensive experiments using the synthetic data and natural images reveal the excellent applicability of RAMC over the existing methods. [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]

Medical image segmentation often suffers from the challenges of class imbalance, blurred target boundaries, and small data. How to establish a framework to automatically segment medical images with these problems is an important task. Although there have been some studies on the issue, there is still a large room for improving the efficiency and quality of medical service. This paper utilizes the powerful ability of deep learning to extract features, and develops a two-stage decoding network with boundary attention (TSD-BA), which can locate the regions of interest in the target locating stage and obtain more spatial structure features in the detail refinement stage. Specifically, a deep fusion model (DFM) is used to aggregate high-level semantic features for accurately capturing the position of targets. Subsequently, a boundary attention module (BAM) is applied to further excavate the boundary features. Moreover, data augmentation and transfer learning are employed to avoid overfitting caused by small datasets. Finally, a pixel position aware (PPA) loss is introduced to focus on hard pixels and mitigate the class imbalance issues. Numerous experimental results indicate that the proposed TSD-BA achieves the best performance compared with state-of-the-art approaches. [ABSTRACT FROM AUTHOR]

Several studies have shown the excellent performance of deep learning in image segmentation. Usually, this benefits from a large amount of annotated data. Medical image segmentation is challenging, however, since there is always a scarcity of annotated data. This study constructs a novel deep network for medical image segmentation, referred to as asymmetric U-Net generative adversarial networks with multi-discriminators (AU-MultiGAN). Specifically, the asymmetric U-Net is designed to produce multiple segmentation maps simultaneously and use the dual-dilated blocks in the feature extraction stage only. Further, the multi-discriminator module is embedded into the asymmetric U-Net structure, which can capture the available information of samples sufficiently and thereby promote the information transmission of features. A hybrid loss by the combination of segmentation and discriminator losses is developed, and an adaptive method of selecting the scale factors is devised for this new loss. More importantly, the convergence of the proposed model is proved mathematically. The proposed AU-MultiGAN approach is implemented on some standard medical image benchmarks. Experimental results show that the proposed architecture can be successfully applied to medical image segmentation, and obtain superior performance in comparison with the state-of-the-art baselines. [ABSTRACT FROM AUTHOR]

3D shape classification is a basic but challenging task for point clouds analysis. How to learn the discriminative shape descriptors from point clouds is crucial and difficult for this task. This paper proposes a novel point-to-vector capsule (PVC) network, which can obtain effective 3D shape descriptors from point clouds directly. The entire network contains three main steps. Concretely, we firstly build a hierarchical local feature extraction module with geometric information to capture a series of detailed features on point clouds layer by layer. Subsequently, the high-level features are further extracted by a nonlinear feature mapping and then grouped to obtain different and rich feature vectors. These feature vectors are squeezed and packaged into primary capsules to preserve the integrity of the information. Finally, the features are sufficiently integrated and reorganized by the dynamic routing algorithm to form a 3D shape descriptor with high discriminative ability. Compared with the existing methods, the main difference is that the proposed method avoids the use of global pooling and directly constructs the 3D capsule network with geometric structure information into the point clouds shape descriptor learning process. This could effectively promote classification performance. Experimental results on several challenging point clouds datasets demonstrate the superiority and applicability of the proposed method in comparison with state-of-the-art methods in 3D shape classification. [ABSTRACT FROM AUTHOR]

The classification of 3D point clouds is a regular task, but remains a highly challenging problem because 3D point clouds usually contain a large amount of information on irregular shapes. Several recent studies have shown the excellent performance of deep learning in 3D point cloud classification. Convolutional neural network (CNN)-based 3D point cloud classification methods are also increasingly used owing to their efficient and convenient feature extraction capability. However, most of these methods do not take much prior information and local structural information into consideration, often resulting in their inability to extract sufficient information to improve the classification accuracy. In this study, we present a novel convolution operation named HyConv, which includes two key components. First, inspired by 2D convolution, we design a feature transformation module to capture more local structural information. Second, to extract the prior information, a hybrid weight module is introduced to estimate two types of weights on the basis of the distribution information of the spatial and feature domains. Additionally, we propose an adaptive method to learn hybrid weights to obtain hybrid distribution information. Finally, based on the proposed convolutional operator HyConv, we build a deep neural network Hybrid-CNN and conduct experiments on two commonly used datasets. The results show that our hybrid network outperforms most existing methods on ModelNet40. Furthermore, state-of-the-art performance is achieved with ScanObjectNN, which is a great improvement compared with existing methods. [ABSTRACT FROM AUTHOR]

Inspired by the perceived saturation of human visual system, this paper proposes a two-stream hybrid networks to simulate binocular vision for salient object detection (SOD). Each stream in our system consists of unsupervised and supervised methods to form a two-branch module, so as to model the interaction between human intuition and memory. The two-branch module parallel processes visual information with bottom-up and top-down SODs, and output two initial saliency maps. Then a polyharmonic neural network with random-weight (PNNRW) is utilized to fuse two-branch’s perception and refine the salient objects by learning online via multi-source cues. Depend on visual perceptual saturation, we can select optimal parameter of superpixel for unsupervised branch, locate sampling regions for PNNRW, and construct a positive feedback loop to facilitate perception saturated after the perception fusion. By comparing the binary outputs of the two-stream, the pixel annotation of predicted object with high saturation degree could be taken as new training samples. The presented method constitutes a semi-supervised learning framework actually. Supervised branches only need to be pre-trained initial, the system can collect the training samples with high confidence level and then train new models by itself. Extensive experiments show that the new framework can improve performance of the existing SOD methods, that exceeds the state-of-the-art methods in six popular benchmarks. [ABSTRACT FROM AUTHOR]

3D movies/videos have become increasingly popular in the market; however, they are usually produced by professionals. This paper presents a new technique for the automatic conversion of 2D to 3D video based on RGB-D sensors, which can be easily conducted by ordinary users. To generate a 3D image, one approach is to combine the original 2D color image and its corresponding depth map together to perform depth image-based rendering (DIBR). An RGB-D sensor is one of the inexpensive ways to capture an image and its corresponding depth map. The quality of the depth map and the DIBR algorithm are crucial to this process. Our approach is twofold. First, the depth maps captured directly by RGB-D sensors are generally of poor quality because there are many regions missing depth information, especially near the edges of objects. This paper proposes a new RGB-D sensor based depth map inpainting method that divides the regions with missing depths into interior holes and border holes. Different schemes are used to inpaint the different types of holes. Second, an improved hole filling approach for DIBR is proposed to synthesize the 3D images by using the corresponding color images and the inpainted depth maps. Extensive experiments were conducted on different evaluation datasets. The results show the effectiveness of our method. [ABSTRACT FROM AUTHOR]

In recent years, algorithms to recovery low-rank matrix have become one of the research hotspots, and more corresponding optimization models with nuclear norm have also been proposed. However, nuclear norm is not a good approximation to the rank function. This paper proposes a matrix completion model and a low-rank sparse decomposition model based on truncated Schatten p-norm, respectively, which combine Schatten p-norm with truncated nuclear norm, so that the models are more flexible. To solve these models, the function expansion method is first used to transform the non-convex optimization models into the convex optimization ones. Then, the two-step iterative algorithm based on alternating direction multiplier method (ADMM) is employed to solve the models. Further, the convergence of the proposed algorithm is proved mathematically. The superiority of the proposed method is further verified by comparing the existing methods in synthetic data and actual images. [ABSTRACT FROM AUTHOR]

Summary: This paper aims to solve the robust convex optimization (RCO) problem, where the constraints of RCO are parameterized with uncertainties, and the scenario approach is applied to transform RCO into standard convex optimization with a finite number of constraints through probabilistic approximation. The transformed problem is called a scenario problem (SP). Two consensus‐based distributed learning algorithms for SP are designed in consideration of a large number of sampled constraints. One is based on the distributed average consensus (DAC), and the other is based on the alternating direction method of multipliers (ADMM). It has regulated that data distributed to nodes are not allowed to communicate. Simulation results indicate that the proposed algorithms are suitable for handling large‐scale data and achieve excellent performance, with the ADMM‐based algorithm performing the best. Furthermore, the DAC‐based algorithm has certain advantages in terms of computational time and complexity. In addition, to improve the communicative efficiency based on a DAC, an efficient distributed average consensus (EDAC) is put forward. The average time for every node when using an EDAC is less than that of a DAC, despite the exact same performance. [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]

Sparse representation has been widely used in signal processing, pattern recognition and computer vision etc. Excellent achievements have been made in both theoretical researches and practical applications. However, there are two limitations on the application of classification. One is that sufficient training samples are required for each class, and the other is that samples should be uncorrupted. In order to alleviate above problems, a sparse and dense hybrid representation (SDR) framework has been proposed, where the training dictionary is decomposed into a class-specific dictionary and a non-class-specific dictionary. SDR puts ℓ1 constraint on the coefficients of class-specific dictionary. Nevertheless, it over-emphasizes the sparsity and overlooks the correlation information in class-specific dictionary, which may lead to poor classification results. To overcome this disadvantage, an adaptive sparse and dense hybrid representation with non-convex optimization (ASDR-NO) is proposed in this paper. The trace norm is adopted in class-specific dictionary, which is different from general approaches. By doing so, the dictionary structure becomes adaptive and the representation ability of the dictionary will be improved. Meanwhile, a non-convex surrogate is used to approximate the rank function in dictionary decomposition in order to avoid a suboptimal solution of the original rank minimization, which can be solved by iteratively reweighted nuclear norm (IRNN) algorithm. Extensive experiments conducted on benchmark data sets have verified the effectiveness and advancement of the proposed algorithm compared with the state-of-the-art sparse representation methods. [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]

This paper develops a classical visual tracker that is called a discriminative sparse similarity (DSS) tracker. Based on the classical Laplacian multi-task reverse sparse representation to get a DSS map in the DSS tracker, we introduce a sparse generative model (SGM) to handle the appearance variation in the DSS tracker. With the alliance of the DSS map and the SGM, our proposed method can track the object under the occlusion and appearance variations effectively. Numerous experiments on various challenging videos of a tracking benchmark illustrate that the proposed tracker performs favorably against several state-of-the-art trackers. [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]

Image super‐resolution (SR) reconstruction, which gains high‐pixel and multi‐detail image from single or several low‐pixel images, has attracted increasing interest in recent years. This study proposes a new SR method based on sparse representation, which made good use of the non‐local (NL) structure similarity and edge sharpness dictionary. Firstly, all the training patches are classified into different clusters according to diverse edge sharpness of patches. Secondly, different dictionaries are trained for different training patches in each cluster. Thirdly, the NL structure similarity is added into the constraint of NL structure similarity model, and the suitable dictionary is selected for current patch to achieve the coefficients according to the value of edge sharpness of patch. Finally, the high‐resolution (HR) image is obtained by integrating HR patches obtained by the product of HR dictionaries and coefficients. Moreover, by calculating edge sharpness, the different dictionaries which adapt to patches with different structure are obtained, and the NL similarity is well utilised and more details are added to HR patch. Compared to some classical and common methods, the proposed method possesses better reconstruction effects in numerical and visual aspects. [ABSTRACT FROM AUTHOR]

The detection and classification of white blood cells (WBCs, also known as Leukocytes) is a hot issue because of its important applications in disease diagnosis. Nowadays the morphological analysis of blood cells is operated manually by skilled operators, which results in some drawbacks such as slowness of the analysis, a non-standard accuracy, and the dependence on the operator's skills. Although there have been many papers studying the detection of WBCs or classification of WBCs independently, few papers consider them together. This paper proposes an automatic detection and classification system for WBCs from peripheral blood images. It firstly proposes an algorithm to detect WBCs from the microscope images based on the simple relation of colors R, B and morphological operation. Then a granularity feature (pairwise rotation invariant co-occurrence local binary pattern, PRICoLBP feature) and SVM are applied to classify eosinophil and basophil from other WBCs firstly. Lastly, convolution neural networks are used to extract features in high level from WBCs automatically, and a random forest is applied to these features to recognize the other three kinds of WBCs: neutrophil, monocyte and lymphocyte. Some detection experiments on Cellavison database and ALL-IDB database show that our proposed detection method has better effect almost than iterative threshold method with less cost time, and some classification experiments show that our proposed classification method has better accuracy almost than some other methods. [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]

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]

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]

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]

Extreme learning machine (ELM) is widely used in training single-hidden layer feedforward neural networks (SLFNs) because of its good generalization and fast speed. However, most improved ELMs usually discuss the approximation problem for sample data with output noises, not for sample data with noises both in input and output values, i.e., error-in-variable (EIV) model. In this paper, a novel algorithm, called (regularized) TLS-ELM, is proposed to approximate the EIV model based on ELM and total least squares (TLS) method. The proposed TLS-ELM uses the idea of ELM to choose the hidden weights, and applies TLS method to determine the output weights. Furthermore, the perturbation quantities of hidden output matrix and observed values are given simultaneously. Comparison experiments of our proposed TLS-ELM with least square method, TLS method and ELM show that our proposed TLS-ELM has better accuracy and less training time. [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]