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Point cloud registration is a critical research area in computer vision with extensive applications. Recent studies have unveiled the significant potential of graph neural networks (GNNs) for point cloud registration. One key approach is to leverage the smoothness of graph convolutions to extract similarity information between points. However, as the number of convolution layers increases, the features between points tend to become consistent, and distinctiveness is always neglected, which contradicts point cloud registration. To this end, this paper presents a new GNN framework with 3D graph smoothing-sharpening convolution (GNN-GSSC) for point cloud registration. It includes two new convolutional strategies: graph smoothing convolution (SmoothGConv) and graph sharpening convolution (SharpGConv). The former utilizes Laplacian smoothing to aggregate similar information from neighbouring nodes, whereas the latter encourages each node to move away from its neighbours to obtain more discriminative information. Specifically, we calculate the difference information between the central node and neighbouring nodes to supplement the node feature information while aggregating the similarity information of the nodes. In addition, we devise a Transformer-based overlapping point scoring module, enhancing the emphasis on overlapping areas while weakening the focus on non-overlapping areas by scoring each point. Experiments reveal that the proposed method is optimal compared to other existing methods. More importantly, SharpGConv is a plug-and-play graph convolution module that is particularly advantageous for extracting distinctive information in point cloud registration.

Deep learning-based methods have been widely used in medical image segmentation recently. However, existing works are usually difficult to simultaneously capture global long-range information from images and topological correlations among feature maps. Further, medical images often suffer from blurred target edges. Accordingly, this paper proposes a novel medical image segmentation framework named a label-decoupled network with spatial-channel graph convolution and dual attention enhancement mechanism (LADENet for short). It constructs learnable adjacency matrices and utilizes graph convolutions to effectively capture global long-range information on spatial locations and topological dependencies between different channels in an image. Then a label-decoupled strategy based on distance transformation is introduced to decouple an original segmentation label into a body label and an edge label for supervising the body branch and edge branch. Again, a dual attention enhancement mechanism, designing a body attention block in the body branch and an edge attention block in the edge branch, is built to promote the learning ability of spatial region and boundary features. Besides, a feature interactor is devised to fully consider the information interaction between the body and edge branches to improve segmentation performance. Experiments on benchmark datasets reveal the superiority of LADENet compared to state-of-the-art approaches.

Graph convolutional neural networks can effectively process geometric data and thus have been successfully used in point cloud data representation. However, existing graph-based methods usually adopt the K-nearest neighbor (KNN) algorithm to construct graphs, which may not be optimal for point cloud analysis tasks, owning to the solution of KNN is independent of network training. In this paper, we propose a novel graph structure learning convolutional neural network (GSLCN) for multiple point cloud analysis tasks. The fundamental concept is to propose a general graph structure learning architecture (GSL) that builds long-range and short-range dependency graphs. To learn optimal graphs that best serve to extract local features and investigate global contextual information, respectively, we integrated the GSL with the designed graph convolution operator under a unified framework. Furthermore, we design the graph structure losses with some prior knowledge to guide graph learning during network training. The main benefit is that given labels and prior knowledge are taken into account in GSLCN, providing useful supervised information to build graphs and thus facilitating the graph convolution operation for the point cloud. Experimental results on challenging benchmarks demonstrate that the proposed framework achieves excellent performance for point cloud classification, part segmentation, and semantic segmentation.

Graph neural networks (GNNs) have a powerful ability to capture long-range spatial correlations in hyperspectral images (HSIs). However, existing GNN-based HSI classification methods are vulnerable to hand-crafted graphs, as the manner in which these graphs are constructed are often inappropriate and are likely to violate intrinsic graph properties, such as sparsity and low-rank. More importantly, the goal of HSI classification is to categorize each individual pixel into a land-cover class, but existing methods usually overuse global dependencies and ignore the importance of individualized spectral characteristics. Therefore, this article proposes a Global-to-Local decoupling Graph network (GoLoG) to conduct HSI classification in a global-to-local framework, which jointly optimizes the graph structure and network parameters guided by both intrinsic graph properties and classification loss. Specifically, a novel global-to-local network framework with successive global and local graph convolutional stages is constructed. By decoupling global and local stages, global contextual information can be exploited, and the individualized information of each hyperspectral pixel can be emphasized for HSI classification. Second, a sparse and low-rank graph structure learning model is proposed to refine and renovate the initial-construct graph. Finally, to unify graph structure learning and network training, a joint alternating update algorithm is introduced to jointly optimize the sparse and low-rank graph structure learning model and the global-to-local network framework. Extensive experiments demonstrate that the proposed GoLoG has obvious advantages compared with other state-of-the-art HSI classification methods.

Graph Convolutional Networks (GCNs), as a prominent example of graph neural networks, are receiving extensive attention for their powerful capability in learning node representations on graphs. There are various extensions, either in sampling and/or node feature aggregation, to further improve GCNs’ performance, scalability and applicability in various domains. Still, there is room for further improvements on learning efficiency because performing batch gradient descent using the full dataset for every training iteration, as unavoidable for training (vanilla) GCNs, is not a viable option for large graphs. The good potential of random features in speeding up the training phase in large-scale problems motivates us to consider carefully whether GCNs with random weights are feasible. To investigate theoretically and empirically this issue, we propose a novel model termed Graph Convolutional Networks with Random Weights (GCN-RW) by revising the convolutional layer with random filters and simultaneously adjusting the learning objective with regularized least squares loss. Theoretical analyses on the model's approximation upper bound, structure complexity, stability and generalization, are provided with rigorous mathematical proofs. The effectiveness and efficiency of GCN-RW are verified on semi-supervised node classification task with several benchmark datasets. Experimental results demonstrate that, in comparison with some state-of-the-art approaches, GCN-RW can achieve better or matched accuracies with less training time cost.

In recent years, graph convolutional networks (GCNs) have made remarkable achievements in the hyperspectral image (HSI) classification task. However, existing GCN-based methods cannot adequately encode similarity edge relationship between superpixels, and few of them use hierarchical mechanism to extract complementary features. This paper addresses these issues and proposes a hierarchical structural graph neural network with local relation enhancement (HSLRE) for HSI classification. Specifically, the features of the pixel-level graph structures are extracted and then embedded into the superpixel-level graph structure to ensure that it does not lose the fine texture features of the original HSI. Secondly, a novel hierarchical framework, which consists of multiple coarsening and refining stages, is proposed to extract multi-level features. In the first coarsening stage, the relational graph convolution (RGC) is introduced to enhance local relations and obtain discriminative features from the superpixel-level graph. In the subsequent coarsening stages, graph convolution (GC) is used to extract features. The refining stages correspond to the coarsening stages, which are used to restore the graphs to their original structures. Finally, to enhance the fluidity of feature information, the fully connected layers and two different types of graph convolutional layers are utilized to extract the linear and nonlinear features of the nodes in parallel, which are fused in a weighted way to form effective features. Experimental results on several benchmark HSI datasets illustrate the effectiveness of the HSLRE. [ABSTRACT FROM AUTHOR]

Saliency detection is a fundamental problem in computer vision tasks. With the advent of convolutional neural networks (CNNs), computational models for salient object detection have evolved from relying on handcrafted features to high-level, deep contrast information. However, existing approaches to saliency detection rarely conduct an in-depth analysis of CNN features. This study discovers that a promising saliency map can be learned from low-, middle-, and high-layer feature maps. Moreover, only certain selected feature maps can facilitate improvement of the results. Those maps exhibiting significant similarities with ground truths contain increased contrast information and should be selected. These discoveries have motivated the design of our saliency detection system. For unknown ground truths, we construct a deep CNN to obtain the approximate salient area as the ground truth substitute for feature map selection. Thereafter, a CNN architecture with three convolutional layers is constructed on top of all selected feature maps to learn their deep contrast information, directly yielding improved saliency maps. The experimental results demonstrate that the proposed method significantly outperforms competing approaches on three widely used datasets. [ABSTRACT FROM AUTHOR]

This study proposes a novel super-resolution regularisation model based on adaptive sparse representation and self-learning frameworks. The fidelity term in the model ensures that the reconstructed image is consistent with the observation image. The adaptive sparsity regularisation term constrains the reconstructed image with an adaptive sparse representation, which successfully harmonises the sparse representation and the collaborative representation adaptively via producing suitable coefficients. To construct a more effective dictionary, the high-frequency features from the underlying image patches are extracted, and the dictionary learning and sparse representation are integrated. To this end, the alternating minimisation algorithm is used to divide this model into three subproblems, and the alternating direction method of multipliers and iterative back-projection method are used to solve the subproblems. To illustrate the effectiveness of the proposed method, additional experiments are conducted on some generic images. Compared with some state-of-the-art algorithms, the experimental results demonstrate that the proposed method achieves better results in terms of both visual quality and noise immunity.

Both the hybrid full memory Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm (termed as HFM) and its extension with regularisation learning framework (RHFM) have been widely used in training feed-forward neural networks, where the main feature lies in deploying an alternative optimisation (AO) technique for the hidden parameter learning (based on gradient-based optimisation) and the output weights evaluation (according to linear least square problem). However, either HFM or RHFM can perform effectively and favourably in data modelling with training samples contaminated by noises or outliers. This paper develops a robust learning algorithm by weighting the residual error resulted from RHFM, named by WRHFM, aiming to control the contribution of each training sample for the regularised cost function. For algorithm implementation, the AO technique is employed in updating iteratively the weighting factors with well-defined statistical estimates, the hidden parameters with gradient descending, and the output weights with a closed form solution. Performance evaluation is carried out on a function approximation example and several real-world data sets, where comparisons against error back-propagation, support vector machine (SVM), HFM and RHFM has demonstrated the advantages of the proposed WRHFM algorithm in data regression with outliers.

Previous studies have shown that image patches can be well represented as a sparse linear combination of elements from an appropriately selected over-complete dictionary. Recently, single-image super-resolution (SISR) via sparse representation using blurred and downsampled low-resolution images has attracted increasing interest, where the aim is to obtain the coefficients for sparse representation by solving an \ell 0 or \ell 1 norm optimization problem. The \ell 0 optimization is a nonconvex and NP-hard problem, while the \ell 1 optimization usually requires many more measurements and presents new challenges even when the image is the usual size, so we propose a new approach for SISR recovery based on \ell p (0

Feedforward neural networks with random weights (FNNRWs), as random basis function approximators, have received considerable attention due to their potential applications in dealing with large scale datasets. Special characteristics of such a learner model come from weights specification, that is, the input weights and biases are randomly assigned and the output weights can be analytically evaluated by a Moore–Penrose generalized inverse of the hidden output matrix. When the size of data samples becomes very large, such a learning scheme is infeasible for problem solving. This paper aims to develop an iterative solution for training FNNRWs with large scale datasets, where a regularization model is employed to potentially produce a learner model with improved generalization capability. Theoretical results on the convergence and stability of the proposed learning algorithm are established. Experiments on some UCI benchmark datasets and a face recognition dataset are carried out, and the results and comparisons indicate the applicability and effectiveness of our proposed learning algorithm for dealing with large scale datasets. [ABSTRACT FROM AUTHOR]

Previous studies have shown that image patches can be well represented as a sparse linear combination of elements from an appropriately selected over-complete dictionary. Recently, single-image super-resolution (SISR) via sparse representation using blurred and downsampled low-resolution images has attracted increasing interest, where the aim is to obtain the coefficients for sparse representation by solving an $\ell _{0}$ or $\ell _{1}$ norm optimization problem. The $\ell _{0}$ optimization is a nonconvex and NP-hard problem, while the $\ell _{1}$ optimization usually requires many more measurements and presents new challenges even when the image is the usual size, so we propose a new approach for SISR recovery based on $\ell _{p} (0<p<1)$ regularization nonconvex optimization. The proposed approach is potentially a powerful method for recovering SISR via sparse representations, and it can yield a sparser solution than the $\ell _{1}$ regularization method. We also consider the best choice for $\ell _{p}$ regularization with all $p$ in (0, 1), where we propose a scheme that adaptively selects the norm value for each image patch. In addition, we provide a method for estimating the best value of the regularization parameter $\lambda $ adaptively, and we discuss an alternate iteration method for selecting $p$ and $\lambda $ . We perform experiments, which demonstrates that the proposed $\ell _{p} (0<p<1)$ regularization nonconvex optimization method can outperform the convex optimization method and generate higher quality images.

Robust modeling approaches have received considerable attention due to its practical value to deal with the presence of outliers in data. This paper proposes a probabilistic robust learning algorithm for neural networks with random weights (NNRWs) to improve the modeling performance. The robust NNRW model is trained by optimizing a hybrid regularization loss function according to the sparsity of outliers and compressive sensing theory. The well-known expectation maximization (EM) algorithm is employed to implement our proposed algorithm under some assumptions on noise distribution. Experimental results on function approximation as well as UCI data sets for regression and classification demonstrate that the proposed algorithm is promising with good potential for real world applications. [ABSTRACT FROM AUTHOR]

Since simulations of classical artificial neural networks (CANNs) run on classical computers, the massive parallel processing speed advantage of a neural network is lost. A quantum computer is a computation device that makes direct use of quantum–mechanical phenomena while large-scale quantum computers will be able to solve certain problems much quicker than any classical computer using the best currently known algorithms. Combining the advantages of quantum computers and the idea of CANNs, we propose in this paper a new type of neural networks, named a quantum artificial neural network (QANN), which is presented as a system of interconnected “quantum neurons” which can compute quantum states from input-quantum states by feeding information through the network and can be simulated on quantum computers. To show the ability of approximation of a QANN, we prove a universal approximation theorem (UAT) which reads every continuous mapping that transforms n quantum states as a non-normalized quantum state can be uniformly approximated by a QANN. The UAT implies that QANNs would suggest a potential computing tool for dealing with quantum information. For instance, we prove that the state of a quantum system driven by a time-dependent Hamiltonian can be approximated uniformly by a QANN. This provides a possible way for finding approximate solution to a Schrödinger equation with a time-dependent Hamiltonian. [ABSTRACT FROM AUTHOR]

This paper addresses the learning algorithm on the unit sphere. The main purpose is to present an error analysis for regression generated by regularized least square algorithms with spherical harmonics kernel. The excess error can be estimated by the sum of sample errors and regularization errors. Our study shows that by introducing a suitable spherical harmonics kernel, the regularization parameter can decrease arbitrarily fast with the sample size.This paper addresses the learning algorithm on the unit sphere. The main purpose is to present an error analysis for regression generated by regularized least square algorithms with spherical harmonics kernel. The excess error can be estimated by the sum of sample errors and regularization errors. Our study shows that by introducing a suitable spherical harmonics kernel, the regularization parameter can decrease arbitrarily fast with the sample size.

Abstract: In many applications, the pre-information on regression function is always unknown. Therefore, it is necessary to learn regression function by means of some valid tools. In this paper we investigate the regression problem in learning theory, i.e., convergence rate of regression learning algorithm with least square schemes in multi-dimensional polynomial space. Our main aim is to analyze the generalization error for multi-regression problems in learning theory. By using the famous Jackson operators in approximation theory, covering number, entropy number and relative probability inequalities, we obtain the estimates of upper and lower bounds for the convergence rate of learning algorithm. In particular, it is shown that for multi-variable smooth regression functions, the estimates are able to achieve almost optimal rate of convergence except for a logarithmic factor. Our results are significant for the research of convergence, stability and complexity of regression learning algorithm.

Based on the simplicity and calculability of polyline function, we consider, in this paper, the regularized regression learning algorithm associated with the least square loss and the set of polyline function Fd. The target is the error analysis for the regression problem. The approach presented in the paper yields satisfactory learning rates. The rates depend on the approximation property of Fdand on the capacity of Fdmeasured by covering numbers. Under some certain conditions, the rates achieve m−4/5log m. Copyright © 2012 John Wiley & Sons, Ltd.

Compared with planar hyperplane, fitting data on the sphere has been an important and an active issue in geoscience, metrology, brain imaging, and so on. In this paper, with the help of the Jackson‐type theorem of polynomial approximation on the sphere, we construct spherical feed‐forward neural networks to approximate the continuous function defined on the sphere. As a metric, the modulus of smoothness of spherical function is used to measure the error of the approximation, and a Jackson‐type theorem on the approximation is established. Copyright © 2011 John Wiley & Sons, Ltd.

Abstract: In this paper, we investigate the radial function manifolds generated by a linear combination of radial functions. Let W p r ($\mathbb{B}^d $) be the usual Sobolev class of functions on the unit ball $\mathbb{B}^d $. We study the deviation from the radial function manifolds to W p r ($\mathbb{B}^d $). Our results show that the upper and lower bounds of approximation by a linear combination of radial functions are asymptotically identical. We also find that the radial function manifolds and ridge function manifolds generated by a linear combination of ridge functions possess the same rate of approximation.

Compared with planar hyperplane, fitting data on the sphere has been an important and active issue in geoscience, metrology, brain imaging, and so on. In this paper, using a functional approach, we rigorously prove that for given distinct samples on the unit sphere there exists a feed‐forward neural network with single hidden layer which can interpolate the samples, and simultaneously near best approximate the target function in continuous function space. Also, by using the relation between spherical positive definite radial basis functions and the basis function on the Euclidean space ℝd+ 1, a similar result in a spherical Sobolev space is established. Copyright © 2010 John Wiley & Sons, Ltd.

This paper proposes some distributed algorithms to solve the sparse factorization of a large-scale nonnegative matrix (SFNM). These distributed algorithms combine some merits of classical nonnegative matrix factorization (NMF) algorithms and distributed learning network. Our proposed algorithms utilize the whole nodes of network to solve a factorization problem of a nonnegative matrix; the fact is that per node copes with a part of the matrix, then uses the distributed average consensus (DAC) algorithm or regional nodes to communicate the parameters gained by each node to ensure them to be convergent or easy to calculation. Different from other existing distributed learning algorithms of NMF, which always need high-qualified hardware or complicated computing methods, our algorithms make a full use of the simplicity of traditional NMF algorithms and distributed thoughts. Some artificial datasets are used for testing these algorithms, and the experimental results with comparisons show that the proposed algorithms perform favorably in terms of accuracy and efficiency.

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 ℓ1constraint 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.

This paper presents an approach for modeling a stochastic age-structured capital system (SASCS) with Poisson jumps, in which the transfer rate of capital, noise intensity and jump intensity are approximated by a type of feedforward neural networks (FNNs). The approximate stock of capital for the system is calculated using Euler's scheme in time discretization. Based on Barkholder-Davis-Gundys inequality and Gronwalls lemma, the error between the approximate stock of capital and the actual stock of capital is estimated by using mean squares. Theoretical analysis of the convergence of the approximate stock of capital is conducted, and some numerical results are presented to justify our findings. [ABSTRACT FROM AUTHOR]

Site-specific DNA–protein interactions can be studied by using experimental and computational methods. Understanding the relationship between these two perspectives and finding ways to improve both is a major challenge of modern molecular biology. Computational approaches for finding DNA motifs are well recognized as useful tools to biologists, which greatly help in saving experimental time and cost in wet laboratories. Over these years, many motif search algorithms and Web-based tools have been developed based on computational intelligence systems and data mining techniques in light of classical electronic computers. In order to use quantum computers in DNA motif model discovering, a related quantum algorithm is necessary. In this paper, based on the quantum adiabatic theorem, an adiabatic quantum algorithm and its application to DNA motif model discovery are obtained in terms of the MISCORE-based motif score. The proposed method can be used to deal with discovering of DNA motif models with big data by a quantum computer, e.g. D-Wave. [ABSTRACT FROM AUTHOR]

This paper proposes a novel approach for the fault diagnosis of induction motors. The invariant character vectors of fault signals are first extracted from the training samples. A single-class support vector machine (SC-SVM) is then used to detect the occurrence of faults, and the obtained invariant character vectors are employed as the desired references to classify the faults associated with the nearest neighbor classifier. The new diagnosis algorithm is validated for an induction motor (Y132S-4), which has shown excellent performance. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the expressions of epidemiological parameters using a class of feedforward neural networks (FNNs) based on the data collected from Chinese Center for Disease Control and Prevention (CCDCP), and establish a stochastic age-structured HIV/AIDS model with parameter perturbation. In order to ensure the mathematical and epidemiological rationality of the model, we discuss the existence, uniqueness, and boundedness of its positive solution. Due to the difficulty of solving the true solution for the stochastic age-structured HIV/AIDS model, we propose a full-discrete scheme using the Galerkin finite element method in age discretization and the Euler's scheme in time discretization. The error estimation between the numerical solution and the true solution is established. The results are justified by computer simulations. [ABSTRACT FROM AUTHOR]