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• The different variants of firefly algorithm are classified and analyzed to summarize the latest research and developments related to nature-inspired computing in the most general sense. • This review has proved that firefly algorithms can be practically applied within every problem domain. Moreover, this review has presented to researchers new technological trends and design challenges they have to cope with, while designing systems using this algorithm. Firefly algorithm (FA) is one of the popular algorithms of Swarm Intelligence domain. The literature has expanded significantly in the past few years. This paper provides a timely review of the FA and its new variants. The different variants of FA are classified and analyzed. The applications and case studies in the rapidly evolving domain are also reviewed and summarized in detail here. The problems to be further solved and future research directions of firefly algorithms will be given at the end of this paper. [ABSTRACT FROM AUTHOR]

The distributed online convex optimization problem with time-varying constraints for multi-agent networks is addressed in this article. The purpose is to optimize a sequence of time-varying global cost functions defined as the accumulated values of local cost functions, also attempt to meet the requirement of a sequence of time-varying coupled constraint functions which denote the sum of local constraint functions. Cost functions and constraint functions are unknown to agents beforehand. It is supposed that each agent in the network communicates with its neighbours through a uniformly strongly connected sequence of time-varying directed communication topologies. This paper proposes the bandit distributed primal-dual mirror descent push-sum (BDPDMDPS) algorithm constructed by bandit primal-dual, mirror descent and push-sum methods. Operational performance of the presented algorithm is measured by expected regret and expected constraint violation, both of which are proved to be sublinear with respect to the total iteration span T in this paper. Finally, a numerical simulation example is shown, which confirms the results for expected regret and expected constraint violation of BDPDMDPS algorithm. [ABSTRACT FROM AUTHOR]

This paper investigates fully distributed scaled non-negative edge-consensus problems of networked systems with actuator saturation and unmeasurable internal states. By using the adaptive control method, output-feedback-based low-gain technique, and graph theory, a new adaptive algorithm is designed to obtain scaled edge-consensus conditions, under which the difficulties caused by the constraints on edge states and controllers are overcome. There are three interesting characteristics that any global information of networks is not used in this paper's algorithm and result, including the number of vertexes and edges; the feasible solutions of the scaled edge-consensus conditions exist and can be easily obtained; the convergence rate of the controller is adjustable. Furthermore, the designed algorithm is expanded in the cases without actuator saturation. Finally, three examples are given to verify the theoretical results. [ABSTRACT FROM AUTHOR]

Since most of the rainy scene datasets used for training single image rain removal (SIRR) algorithms are constructed by blending artificial rain streaks with source images, it is difficult for a machine trained with such datasets to understand the patterns of real or realistic rain streaks. So, several studies have been attempted to build a real rainy scene dataset. However, since collecting real rainy scenes itself requires significant costs, the real rainy scene datasets provided by some studies cover only very limited rainy environment(s). This paper presents a new approach to synthesize realistic rainy scenes using GAN, which is a world-first attempt as far as we know. The proposed method builds a representation space to which rain streaks of multiple styles are smoothly mapped by learning the distributions of various rain datasets. The representation space allows control over the generated rain streaks. Also, the proposed method can synthesize multiple rainy scenes per clean (source) scene simultaneously, thereby a synthesized rain image dataset (SyRa) (Dataset can be found here: https://github.com/jaewoong1/SyRa-Synthesized%5fRain%5fdataset) consisting of 11 K clean images and 55 K rainy images was constructed. Finally, this paper provides benchmarking results of several SIRR methods trained with SyRa. This result will be very useful for developing SIRR algorithms that can cope well with the actual rain environment. [ABSTRACT FROM AUTHOR]

Time-variant Yang-Baxter-like matrix equation (YBLME) with the disturbances of noises is the hotspot in various scientific disciplines. The existing research, either can not handle the noise, or rely on the build-in numerical algorithm provided by MATLAB. Therefore, it is necessary to further study the digital-computer discrete solution of this problem. In this paper, the authors propose a noise-handling ten-instant discrete solution for the time-variant YBLME. By defining the matrix-form error function, Zhang neural network (ZNN) is exploited to design the continuous-time noise-handling ZNN model. For potential digital hardware (i.e., digital computer) realization, a discrete-time ZNN-based noise-handling ten-instant (DTZNH10i) algorithm, which is capable of handling three types of noises, is proposed on the basis of a Zhang time discretization (ZTD) formula. The convergence and precision of the proposed DTZNH10i algorithm are investigated and discussed. Theoretical analyses show the correctness and effectiveness of the proposed algorithm. The paper offers three examples of time-variant YBLME with disturbances of constant, linear, and bounded random noises to illustrate the efficacy and convergence of the proposed algorithm. [ABSTRACT FROM AUTHOR]

The process of aligning one image, in the coordinate system of another is called registration. Image registration is vital in the medical domain and is used for diagnosis, therapy planning, and treatment of diseases. Due to its huge applicability and importance, medical image registration has emerged to be a separate domain of research. Beginning from the invasive landmark based registration, innumerable algorithms have been proposed to register two images of the human physiology. However, a breakthrough in the literature occurred when an information theory based measure, mutual information was used to register two images. Since then a large number of new algorithms have developed, which use mutual information for fully automatic registration of medical images. This paper is a survey of these algorithms. Beginning from its development, it discusses about some of the major works done on mutual information based image registration. Some comparative studies with other algorithms have also been discussed. The paper ends with a discussion of the developments in medical image registration algorithms post mutual information, which primarily include deep neural network (DNN) based algorithms. [ABSTRACT FROM AUTHOR]

In numerous domains, there is ample evidence indicating that a significant portion of real-world data exhibits temporal variations, such as medical research and meteorological studies. Particularly in the era of big data, not only does the size of data change dynamically but also its dimensions at an unprecedented pace. Consequently, employing traditional methods to handle such dynamic data becomes highly impractical. To address this limitation, this paper proposes an incremental feature selection algorithm tailored for dynamic feature variations. For scenarios involving an increase in features, the novel algorithm efficiently identifies a target subset with effective features. In order to showcase the efficacy of the proposed algorithm, this paper conduct experiments using four commonly used classifiers and five UCI data sets. The experimental results further validate both the feasibility and efficiency of the new approach. [ABSTRACT FROM AUTHOR]

In this paper, we propose a control framework for intelligent surgical robots under the Remote Center of Motion (RCM). The goal of a surgical robot is to assist surgeons in performing complex surgeries. RCM constraint implies that the surgical tip attached to the end-effector of the surgical robot does not slide away from the point of the incision while performing surgery. Implementation of a control algorithm to comply with RCM constraints is a complicated task because of the nonlinear model of the surgical robots and stringent conditions of accuracy imposed by the patient's safety. This paper proposes an optimization-driven approach to perform the surgical maneuver under RCM constraints. We then applied a bio-inspired optimization algorithm to solve the problem efficiently. For testing the performance of ZNNBAS, we used MATLAB to simulate a surgical procedure. A 7-DOF surgical robot (KUKA LBR IIWA 7) was used as a test bench for running the simulations. The simulation results show that the ZNNBAS is comparable with BAS, PSO, and GA and efficiently and robustly performed the task commanded maneuvers while enforcing the RCM constraints. [ABSTRACT FROM AUTHOR]

Dynamic networks are popularly used to describe networks that change with time. Although there have been a large number of research works on understanding dynamic networks using link prediction, node classification and community detection, there is rare work that is specially designed to address the challenge of big network size of dynamic networks. To this end, we study in this paper an emerging and challenging problem of network coarsening in dynamic networks. Network coarsening refers to a class of network "zoom-out" operations where node pairs and edges are grouped together for efficient analysis on big networks. However, existing network coarsening approaches can only handle static networks where network structure weights have been predefined before the coarsening calculation. Under the observation that big networks are highly dynamic and naturally change over time, we consider in this paper to embed information diffusion data which reflect the dynamics of networks for network coarsening. Specifically, we present a new Semi-NetCoarsen approach that jointly maximizes the likelihood of observing the information diffusion data and minimizes the network regularization with respect to the predefined network structural data. The learning function is convex and we use the accelerated proximal gradient algorithm to obtain the global optimal solution. We conduct experiments on two synthetic and five real-world data sets to validate the performance of the proposed method. [ABSTRACT FROM AUTHOR]

• The paper provides a robust regression method for interval-valued variables. • The objective function of the method considers the full interval information. • The computation of the sum of squares errors uses exponential-type kernel functions. • Outliers have a small weight for both center and radius parameter estimates. • Applications on synthetic and real data sets corroborate the proposed method. Interval-valued data are needed to manage either the uncertainty related to measurements, or the variability inherent to the description of complex objects representing group of individuals. A number of regression methods suitable to interval variables describing variability of complex objects are already available. However, less attention has been given to methods that, simultaneously, take into account the full interval information and are resistant to interval outlier observations, even with the frequent presence of atypical observations on interval-valued data sets. This paper proposes a new robust linear regression method for interval variables, where the presence of outliers either in the center or in the radius penalize both the center and the radius regression models. Moreover, the interval observations with outliers on both center and radius are more penalized than those observations with outliers only in the center (or in the radius). Besides, this paper provides a suitable iterative algorithm to estimate the parameters of the proposed method. The algorithm estimates the parameters of the center (or of the radius) model taking into account both information of the center and the radius. The convergence and time complexity of the iterative algorithm are also presented. Finally, the performance of the new method is compared with some previous robust regression approaches and evaluated on synthetic and real interval-valued data sets. [ABSTRACT FROM AUTHOR]

This paper investigates the development of an adaptive cooperative control scheme for the consensus of uncertain nonlinear multi-agent systems subjected to uncertain time-varying control direction, disturbances, and dead-zone nonlinearity. The dead-zone nonlinearity is described by an uncertain nonlinear function of the control input which can represent a wide class of practical input nonlinearities. It is assumed that no prior knowledge about the uncertain nonlinearities of agents, disturbances, dead-zone parameters, magnitude and sign of the control gain is available. In this paper, a Nussbaum function is used to deal with the unknown time-varying control directions problem and a disturbance-like term in the dead-zone description is approximated by an adaptive TSK-type fuzzy system. Then, by using the dynamic surface control approach and radial-basis function neural network, an adaptive distributed controller is designed for each follower agent. Stability analysis shows that all signals of the closed-loop multi-agent system are semi-globally uniformly ultimately bounded and the consensus error can be made arbitrary small by the proper selection of design parameters. Simulation and comparison results demonstrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

• An analysis of lexicographic optimization for feature selection and data classification. • Cooperative co-evolution for feature selection while the classifier hyperparameters are also being optimized. • Optimization of multiple objectives using a simple evolutionary algorithm. • A new lexicographic ranking methodology to compare the results of different feature selection methods. • Quite good results for real high-dimensional datasets. This paper starts with two hypotheses. The first one is that the simultaneous optimization of the hyperparameters regulating the classifier within a wrapper method, while the best subset of features is being determined, should improve the results with respect to those obtained with a pre-parameterized classifier. The second one is that solving these two problems can be formulated as a lexicographic optimization problem, allowing the use of a simple single-objective evolutionary algorithm to solve this multi-objective problem. The fitness function is of key importance for such wrapper methods. It is responsible for guiding the search towards potentially good solutions and it also consumes most of the runtime. Having these issues in mind, this paper also proposes a new lexicographic fitness function, designed to minimize the runtime of the algorithm and also to avoid over-fitting. Furthermore, the execution time and the quality of the results obtained by the wrapper procedure also depend on some algorithmic hyperparameters: the similarity thresholds used when comparing two different solutions lexicographically and the percentage of data samples used for validation during the training process. Thus, an experimental analysis has been carried out to find adequate values for these hyperparameters. Finally, the lexicographic cooperative co-evolutionary wrapper approach, using the new fitness function proposed in this paper, has been tested with several datasets belonging to the University of California, Irvine (UCI) repository and also with some real high-dimensional datasets, obtaining quite good results, compared to other state-of-the-art wrapper methods. The comparison has also been made lexicographically, with a new methodology proposed in this paper. [ABSTRACT FROM AUTHOR]

Object detection is one of the most important tasks involved in intelligent agriculture systems, especially in pest detection. This paper focuses on a most devastated agricultural disaster: grasshopper plagues. Grasshopper detection and monitoring is of paramount importance in preventing grasshopper plagues. This paper proposes a probabilistic faster R-CNN algorithm with stochastic region proposing, where a probabilistic region proposal network, an image classification network, and an object detection network are integrated to detect and locate grasshoppers. More specifically, in the proposed framework, the probabilistic region proposal network considers attributes (e.g. size, shape) of region proposals and the image classification network identifies the existence of grasshoppers while the object detection network scores recognition confidence for a region proposal. By integrating these three networks, the uncertainty can be passed from end to end, and the final confidence is obtained for each region proposal can be explicitly quantified. To enhance algorithm robustness, a stochastic region proposing algorithm is developed to screen region proposals rather than using a predetermined threshold. The proposed algorithm is validated by recently collected grasshopper datasets. The experimental results demonstrate that the proposed algorithm not only outperforms competing algorithms in terms of average precision (0.91), average missed rate (0.36), and maximum F 1 -score (0.9263), but also reduces the false positive rate of recognising the existence of grasshoppers in an open field. [ABSTRACT FROM AUTHOR]

Person re-identification is to recognize a pedestrian who has been observed at different places in monitoring system, which is done by computer automatically. Important practical significance can be found in this paper on improving the intelligence of monitoring system. There are two challenging problems needed to be solved for person re-identification, which is feature representation and matching. Designing a suitable feature representation method is both challenging and crucial. Ideally, the extracted features should be robust enough to cope with the various situations of the monitoring environment, such as posture difference, illumination changing, and shooting angle difference, etc. There are a lot of challenges for feature matching too, such as small sample size, inter-class confusion, and intra-class variation, etc. In order to meet these challenges, a new person re-identification scheme was put forward in this paper. The following three aspects would be used to describe it. First, an improved BOF feature extraction algorithm based on SURF was put forwarded, SURF algorithm extracts the preliminary feature descriptor and generates visual dictionary, so the influence factors such as illumination and scale invariants can be deal with. And then, covariance descriptor was adopted by the algorithm. It has high robustness, and matching accuracy can be improved too for the case of small sample. Finally, an effective classifier was designed by LIBSVM based on improved BOF algorithm, so the efficiency of the person re-identification algorithm can be improved. The proposed method was compared with the current mainstream algorithm through experiment, and it can be found through the experimental results that it is effective to solve the difficult problems for person re-identification. [ABSTRACT FROM AUTHOR]

Single-object tracking is regarded as a challenging task in computer vision, especially in complex spatio-temporal contexts. The changes in the environment and object deformation make it difficult to track. In the last 10 years, the application of correlation filters and deep learning enhances the performance of trackers to a large extent. This paper summarizes single-object tracking algorithms based on correlation filters and deep learning. Firstly, we explain the definition of single-object tracking and analyze the components of general object tracking algorithms. Secondly, the single-object tracking algorithms proposed in the past decade are summarized according to different categories. Finally, this paper summarizes the achievements and problems of existing algorithms by analyzing experimental results and discusses the development trends. [ABSTRACT FROM AUTHOR]

This paper considers the leader-following consensus problem for delayed neural networks with multi-layer signed digraph topologies. Both structurally balanced and unbalanced topologies are considered. By using the structural balance theory and the pinning control strategy, some sufficient conditions are given to guarantee that the bipartite leader-following consensus can be reached in structurally balanced multi-layer signed neural networks, which depend on the node dynamics and the topology of the multi-layer signed network. In addition, a scheme is designed for selecting the pinning nodes and gains of each layer to achieve bipartite leader-following consensus. When the multi-layer signed network is structurally unbalanced, the asymptotic stability of the neural network is investigated by decomposing the structurally unbalanced network into a structurally balanced subgraph and some special edges. The conditions proposed in this paper are also suitable for addressing the consensus problem of traditional single layer signed neural networks. Numerical examples are given to illustrate the correctness and effectiveness of the proposed theorems and algorithms. [ABSTRACT FROM AUTHOR]

Low rank tensor recovery (LRTR) problem has attracted wide attentions and researches, and has been applied to various fields. In this paper, we mainly consider the nonconvex relaxtion methods for LRTR. Firstly, we newly propose the tensor schatten capped p ( SC p ) norm as a nonconvex surrogate of the tensor tubal rank, which can provide a closer approximation of the tubal rank compared with some existing nonconvex approximations. Secondly, we introduce an implicit Plug-and-Play (PnP)-based regularization into the nonconvex model to further improve the recovered performance. The proposed model is abbreviated as SC p -PnP. Based on the alternating direction method of multipliers, we propose an efficient algorithm to solve SC p -PnP. The convergence of this algorithm is also provided. Finally, extensive experiments on different kinds of datasets show that our method significantly outperforms several state-of-the-art LRTR methods in terms of both quality metrics and visual effects. [ABSTRACT FROM AUTHOR]

Multi-view clustering has gained soar attention in the field of data mining in recent years. Most multi-view clustering methods are considered to be complete for each view. However, in many applications, some views may contain missing instances, resulting in the incomplete multi-view learning problem. Incomplete views cannot be directly dealt with traditional multi-view clustering methods. In this paper, we propose a One-step multi-view subspace clustering with incomplete views (OMVSC-IV) method based on low-rank matrix factorization to overcome this problem. Specifically, the proposed algorithm uses low-rank matrix factorization to learn a consensus representation matrix, and then combined with the objective function of non-negative embedding and spectral embedding subspace clustering proposed in this paper. The whole process is established into the same objective function for joint optimization and requires no post-processing (e.g., K -means), thus avoiding the defect of being sensitive to initial values. Furthermore, the accuracy, parameter, sensitivity and convergence of the algorithm are studied by experiments. Experimental results on nine data sets show that the proposed algorithm performs superior to some of the latest algorithms. [ABSTRACT FROM AUTHOR]

Graph Neural Networks(GNNs) are powerful methods to analyze the non-Euclidean data. As a dominant type of GNN, Graph Convolutional Networks(GCNs) have wide applications. However, the analysis of the generalization error for GCNs with multilayer is limited. Based on the review of single-layer GCNs, this paper analyzes the generalization error of two-layers GCNs and extends the conclusion to the general GCNs models. Firstly, this paper examines two-layers GCNs and obtains the stability of the GCNs algorithm. And then, based on this algorithmic stability, the generalization stability of multilayer GCNs is obtained. This paper shows that the algorithmic stability of GCNs depends upon the graph filters and its product with node features as well as the training procedure. Furthermore, the generalization error gap of GCNs tends to be enlarged with more layers, which can interpret why GCNs with deeper layers have relatively poorer performance in test datasets. [ABSTRACT FROM AUTHOR]

With the enhancement of people's security awareness, transmitting secret information securely has gradually become a demand for the public. Steganography is a technology of representing secret information within another carrier, aiming at transmitting secret information without causing suspicion. Most of the traditional steganographic algorithms hide secret information by modifying the statistical characteristics, which will leave traces to the carriers. Although these modifications are too tiny to be distinguished by human eyes, they can be detected by steganalysis algorithms. Differently, coverless steganography, also written as steganography without embedding, accomplish the process of information hiding by constructing the relationship between secret information and carriers. Due to no modification to the carriers, all of the steganalysis algorithms are expired. In this paper, more than 90 papers are included to provide a review in coverless steganographic algorithms, covering the major development process of coverless image and video steganographic algorithms. The main contribution of the existing methods is summarized. Besides, the current general issues of capacity, robustness, and security are discussed adequately for both image and video algorithms. Especially, the security of coverless steganography is discussed for the first time from theoretical analysis to actual investigation in this review. [ABSTRACT FROM AUTHOR]

• Teaching-learning-based optimization (TLBO) is one of population-based heuristic stochastic swarm intelligent algorithm. • In this paper, a comprehensive survey on the recent advances in TLBO is presented. • Literature survey reveals some interesting challenges and future research directions. Teaching-learning-based optimization (TLBO) algorithm which imitates the teaching–learning process in a classroom, is one of population-based heuristic stochastic swarm intelligent algorithms. TLBO executes through similar iterative evolution processes as utilized by a standard evolutionary algorithm. Unlike traditional evolutionary algorithms and swarm intelligent algorithms, the iterative computation process of teaching–learning-based optimization is divided into two phases and each phase executes iterative learning operation. In this paper, we present a comprehensive survey on the recent advances in TLBO. A review of the current literature reveals intriguing challenges and suggests potential future research directions. [ABSTRACT FROM AUTHOR]

This paper investigates the security state estimation issue facing replay attacks in confidential cyber–physical systems. Smart sensor equipped with a power harvester transmits critical measurements to the remote estimator over wireless networks, in which the transmission modes include encrypted and normal. In order to complete the persistent threats, the adversary launches multi-stage discontinuous replay attacks to compromise the estimation process. In virtue of the designed label detection scheme, we transform attack detection into encryption scheduling optimization under the constraint of sensor energy harvesting and acquire a rigorous relationship between detection probability, attack duration, and encryption ratio. Different from most existing studies only focusing on attack detection, the localization of replay interval measured by detection immediacy is also analyzed. Subsequently, the optimal periodic encryption scheduling strategy is given to maximally determine the attack interval by adopting an optimization-based approach. Further, a complete algorithm of replay attack detection, isolation, and recovery (RADIR) is designed to minimize deterioration from multi-stage attacks, which can guarantee the estimated performance of the system as much as possible. Finally, the unmanned ground vehicle system is applied to validate the theoretical results, where the dataset of replay attacks is obtained by capturing the normal operation data of a moving vehicle. Also, we compare the optimal encryption strategy designed in this paper with general centralized and random scheduling strategies. [ABSTRACT FROM AUTHOR]

As a classical machine learning model, support vector machine (SVM) has attracted much attention due to its rigorous theoretical foundation and powerful discriminative performance. The doubly regularized SVM (DRSVM) is an important variant of SVM based on elastic-net regularization, which considers both the sparsity and stability of the model. To tackle the problems of explosive increases in data dimensions and data volume, the alternating direction method of multipliers (ADMM) algorithm can be used to train the DRSVM model. ADMM is an effective iterative algorithm for solving convex optimization problems by decomposing a large issue into a series of solvable subproblems, which is also well suited for distributed computing. However, lack of guaranteed convergence and slow convergence rate are two critical limitations of ADMM. In this paper, a 3-block ADMM algorithm based on the over-relaxation technique is proposed to accelerate DRSVM training, namely, the over-relaxed DRSVM (O-RDRSVM). The main strategy of the over-relaxation technique is to further append the information from the previous iteration to the next iteration to improve the convergence of ADMM. We also propose a distributed version of O-RDRSVM to handle parallel and distributed computing faster, termed DO-RDRSVM. Moreover, we develop a fast O-RDRSVM algorithm (FO-RDRSVM) and a fast DO-RDRSVM algorithm (FDO-RDRSVM), which further reduce the computational cost of O-RDRSVM and DO-RDRSVM by employing the matrix inversion lemma. The convergence analyses ensure the effectiveness of our algorithms for DRSVM training. Finally, extensive experiments on public datasets demonstrate the advantages of our algorithms in terms of convergence rate and training time while maintaining accuracy and sparsity comparable to those of previous works. [ABSTRACT FROM AUTHOR]

Recently, few studies have been made on the stereophonic acoustic echo cancellation (SAEC) with nonlinear systems. To identify such nonlinear model, the functional link artificial neural network (FLANN) and the widely linear model can provide an approach to explore the SAEC with complex random variable. In this paper, a class of augmented complex-value functional link network (ACFLN) adaptive algorithms is developed. Based on the augmented complex-value functional least-mean-square (ACFLMS) algorithm, we have proposed the recursive augmented complex-value functional least-mean-square (RACFLMS) algorithm designed by a recursive structure. To further reduce its computational complexity and enhance its performance, a novel inverse square root function is employed in its structure of the RACFLMS algorithm. The results of several experiments demonstrate that our approach can effectively model the nonlinear systems and verify the improvement of the proposed algorithms. [ABSTRACT FROM AUTHOR]

Analyzing the runtime behaviors of Android apps is crucial for malware detection. In this paper, we attempt to learn the behavior level features of an app from function calls. The challenges of this task are twofold. First, the absence of function attributes hinders the understanding of app behaviors. Second, the graphical representation of function calls cannot be directly processed by classical machine learning algorithms. In this paper, we develop two methods to overcome these challenges. Based on function embedding, we first propose the concept of enhanced function call graphs (E-FCGs) to characterize app runtime behaviors. We then develop a Graph Convolutional Network (GCN) based algorithm to obtain vector representations of E-FCGs. Extensive experiments show that the features learned by our method can achieve surprisingly high detection performance on a variety of classifiers (e.g., LR, DT, SVM, KNN, RF, MLP and CNN), significantly outperforming the traditional static features. [ABSTRACT FROM AUTHOR]

The prediction of short term power load owns a great influence on performance of the whole electric system. Raising the result of power load forecasting is always a research spot. This paper proposes a method combined Elman neural network (ENN) and the particle swarm optimization (PSO) for the short-term power load forecasting. Firstly, this paper introduces the principle of ENN and PSO algorithm respectively and analyzes performance of network influenced by parameters of ENN. Then the particle swarm optimization algorithm is applied to searching the optimal learning rate of ENN. To study the capability of the method proposed in this paper, the method is utilized for the short-term power load forecasting, which is suitable to be solved by ENN. Besides, a comparison experiment on this method (PSO–ENN) with general regression neural network (GRNN), the original ENN and the traditional back-propagation neural network (BPNN) is given out to illustrate effectiveness of PSO–ENN. [ABSTRACT FROM AUTHOR]

In this paper, a novel control scheme is developed to solve an optimal containment control problem of unknown continuous-time multi-agent systems. Different from traditional adaptive dynamic programming (ADP) algorithms, this paper proposes an internal reinforcement ADP algorithm (IR-ADP), in which the internal reinforcement signals are added in order to facilitate the learning process. Then a distributed containment control law is designed for each agent with the internal reinforcement signal. The convergence of this IR-ADP algorithm and the stability of the closed-loop multi-agent system are analyzed theoretically. For the implementation of the optimal controllers, three neural networks (NNs), namely internal reinforcement NNs, critic NNs and actor NNs, are utilized to approximate the internal reinforcement signals, the performance indices and optimal control laws, respectively. Finally, some simulation results are provided to demonstrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Deep learning technologies have been rapidly developing recently. They have shown excellent performances in many fields. However, deep learning networks have weak adaptability to small sample sizes.Usually, deep learning networks require tens of thousands of samples to avoid overfitting. In contrast, the kernel method can deal with small sample sizes. In this paper, we use only dozens of samples to train a successful classifier. Deep multiple kernel learning (DMKL) has emerged in recent years. It combines the ideas of deep learning and multiple kernel learning. Unfortunately, the DMKL network with a fixed structure cannot adapt to data of different dimensions and sizes. Therefore, in this paper, we propose a novel depth-width-scaling multiple kernel learning (DWS-MKL) algorithm. It has the ability to adjust the architecture according to the input data. We optimize the estimation of leave-one-out error by using the span bound instead of the dual objective function. Finally, we choose a large number of data sets from the UCI benchmark data sets for classification tasks. We also evaluate DWS-MKL on the MNIST data set. The experimental results show that different frameworks have different performances on the same dataset. Our DWS-MKL algorithm obtains better classification results than the state-of-the-art kernel learning algorithms, as determined by a thorough comparison. The encouraging results demonstrate that our method has the potential to improve generalization performance of the model. [ABSTRACT FROM AUTHOR]

This paper investigates the fully complex mini-batch gradient algorithm for training complex-valued neural networks. Mini-batch gradient method has been widely used in neural network training, however, its convergence analysis is usually restricted to real-valued neural networks and of probability nature. By introducing a new Taylor mean value theorem for analytic functions, in this paper we establish deterministic convergence results for the fully complex mini-batch gradient algorithm under mild conditions. The deterministic convergence here means that the algorithm will deterministically converge, and both the weak convergence and strong convergence will be proved. Benefited from the newly introduced mean value theorem, our results are of global nature in that they are valid for arbitrarily given initial values of the weights. The theoretical findings are validated with a simulation example. [ABSTRACT FROM AUTHOR]

Spectral clustering is one of the most important clustering approaches, often yielding performance superior to other clustering approaches. However, it is not scalable to large data sets in its original form due to the computational burden of the required large-matrix eigen-decomposition. In this paper, a two-step spectral clustering algorithm is introduced by extending recent advances of scalable spectral clustering based on low-rank affinity matrix using landmarks. In the first step, a scalable spectral clustering algorithm using raw landmark-based affinity matrix is adopted. In the second step, a novel low-rank affinity matrix is learnt via the probability density estimators, constructed from the estimated clusters as derived from the first step. Since the prior information on cluster labels can be utilised in the second step, this learnt affinity matrix reflects intrinsic pairwise data relationships much better. While the proposed more complicated algorithm results in a higher computational cost than the previous landmark-based spectral research, it can be shown that the associated computational cost still scales well with data size. It is demonstrated that the proposed algorithm is capable of achieving far superior performance than other state-of-the-art algorithms for several benchmark multi-class image data sets. [ABSTRACT FROM AUTHOR]

Almost all systems are inevitably subject to various uncertainties or disturbances from the external environment in practical applications. Taking these factors into consideration, in this paper a distributed algorithm with state noise and gradient disturbance is proposed for solving distributed optimization problem with closed convex set constraint based on multi-agent system under weight-balanced graph. Moreover, based on the gradient tracking and projection methods, the proposed distributed algorithm with gradient tracking can improve the convergence rate by introducing a projection error term and an auxiliary parameter. In contrast to some existing constrained distributed gradient algorithms, the proposed one can make the convergence faster and enhance the performance of convergence. The proposed algorithm is illustrated with two simulation examples to show its effectiveness and robustness. [ABSTRACT FROM AUTHOR]

Matrix completion is extensively studied due to its wide applications in science and technology. In this paper, we concentrate our study on the matrix completion problem for image analysis tasks due to their immense importance and pervasive use in many fields. A rich collection of models has been proposed to capture both linear and nonlinear relationships latent in a matrix. Even though nonlinear models possess more powerful matrix completion capabilities than their linear counterparts, these models generally carry higher model complexity and tuning difficulties. To take advantage of the superior discriminative power offered by nonlinear models while curbing its deployment overheads, this paper proposes a novel nonlinear matrix completion model utilizing a deep learning-based approach. In contrast to existing nonlinear models, the new model carefully explores and exploits spatial locality among adjacent matrix elements exhibited in patches of various sizes and locations in a target matrix. Building upon this idea, a new patch-based nonlinear matrix completion algorithm is designed. The algorithm leverages a convolutional neural network to learn the predictive relationship between a matrix element and its surrounding elements through an end-to-end trainable fashion, leading to a capable and easy-to-deploy nonlinear matrix completion solution. To identify an optimal patch size suited for tackling a given matrix completion task without exhaustively enumerating all candidate patch sizes, the new algorithm is coupled with a fast stochastic search procedure, yielding a good trade-off between computational efficiency and accuracy. Extensive experiments are conducted to validate the effectiveness and advantages of the proposed algorithm for nonlinear matrix completion problem in comparison with a series of state-of-the-art algorithms. Experimental results consistently demonstrate the superiority of the new algorithm in completing images with a variety of random and textual noises. [ABSTRACT FROM AUTHOR]

In this paper, we study an important recommendation problem of exploiting users' one-class positive feedback such as "likes", which is usually termed as one-class collaborative filtering (OCCF). For modeling users' preferences beneath the observed one-class positive feedback, the similarity between two users is a key concept of constructing a neighborhood structure with like-minded users. With a well-constructed neighborhood, we can make a prediction of a user's preference to an un-interacted item by aggregating his or her neighboring users' tastes. However, the neighborhood constructed by a typical traditional method is usually asymmetric, meaning that a certain user may belong to the neighborhood of another user but the inverse is not necessarily true. Such an asymmetric structure may result in a less strong neighborhood, which is our major finding in this paper. As a response, we exploit the reciprocal neighborhood among users in order to construct a better neighborhood structure with more high-value users, which is expected to be less influenced by the active users. We then design a corresponding recommendation algorithm called k -reciprocal nearest neighbors algorithm (k -RNN). Extensive empirical studies on two large and public datasets show that our k -RNN performs significantly better than a closely related algorithm with the traditional asymmetric neighborhood and some competitive model-based recommendation methods. [ABSTRACT FROM AUTHOR]

In this paper, we investigate quantized synchronization control problem of memristive neural networks (MNNs) with time-varying delays via super-twisting algorithm. A feedback controller is introduced with quantized method. To enormously reduce the computational complexity of the controller under super-twisting algorithm, two quantized control schemes are proposed with uniform quantizer and logarithmic quantization. We obtain some sufficient conditions of specific control plans to guarantee that the driving MNNs can synchronize with the response MNNs. A neoteric Lyapunov functional is designed to analyze the synchronization problem. Finally, in this paper ending, some illustrative examples are given in support of our results. [ABSTRACT FROM AUTHOR]

• We propose a novel matrix inversion free algorithm for solving the Bayesian linear regression problem with Gaussian priors. • Compared with the conventional gradient based and EM algorithms, our proposed one runs significantly faster while achieving the similar precision performance. • An iterative method from a perspective of latent matrices is proposed for optimal search without breaking the symmetric positive definite manifold constraint. The Bayesian linear regression is a useful tool for many scientific communities. This paper presents a novel algorithm for solving the Bayesian linear regression problem with Gaussian priors, which shares the same spirit as the gradient based methods. In addition, the standard scheme for this task, the Expectation Maximization (EM) algorithm, involves matrix inversions but our proposed algorithm is free of. Numerical experiments demonstrate that the proposed algorithm performs as well as the gradient based and EM algorithms in term of precision, but runs significantly faster than the gradient based and EM algorithms. Due to its matrix-inversion-free nature, the algorithm of this paper is a viable alternative to the competing methods available in the literature. [ABSTRACT FROM AUTHOR]

• Proposed the infimal convolution smoothing technique to approximate the non-differentiable loss function. • Introduced a relaxation factor to transform the non-differentiable loss function into a smooth counterpart. • Provided convergence analysis for the algorithm under the APG and mAPG framework. • Evaluated the effectiveness of the proposed algorithm via numerical experiments. This paper addresses the robust sparse recovery problem in the presence of impulsive measurement noise. In order to overcome the poor performance of ℓ 2 -norm loss function with the outliers under the impulsive noise, we employ the ℓ 1 -norm as the loss function for the residual error, which is less sensitive to outliers in the measurements than the popular ℓ 2 -loss. To rise to the challenges introduced by the non-smooth problem, we first employ two smoothing strategies to approximate the ℓ 1 -norm loss function: one introduces a relaxation factor in the ℓ 1 -norm and the other uses the infimal convolution smoothing technique to transform it into a smooth counterpart. Both of them can approximate the ℓ 1 -norm with arbitrary degree of accuracy and provide a Lipschitz continuous gradient loss function. Then, we employ the accelerated proximal gradient (APG) and monotone APG (mAPG) frameworks for the convex and non-convex regularization functions, respectively. The convergence performance is discussed for generalized regularization penalty. The simulation result demonstrates our conclusions and indicates that the algorithm proposed in this paper can improve the reconstruction quality. [ABSTRACT FROM AUTHOR]

• The 0-1 knapsack problem (KP01) is one of the classic variants of knapsack problems in which the aim is to select the items with the total profit to be in the knapsack. • In this paper, a comprehensive survey on the recent advances in 0-1 knapsack problem is presented. • Literature survey reveals some interesting challenges and future research directions. 0-1 knapsack problem (KP01) is one of the classic variants of knapsack problems in which the aim is to select the items with the total profit to be in the knapsack. In contrast, the constraint of the maximum capacity of the knapsack is satisfied. KP01 has many applications in real-world complex problems such as resource distribution, portfolio optimization, etc. This study reviews the basic theory and main algorithms of 0-1 knapsack, proposes many different types of nature-inspired metaheuristic algorithms, and divides existing 0-1 knapsack problems into 6 types according to the different coding methods of the algorithms, for a comprehensive overview of it. In this paper, a comprehensive survey on the recent advances in 0-1 knapsack problem is presented. Literature survey reveals some interesting challenges and future research directions. [ABSTRACT FROM AUTHOR]

To improve the classification performance of existing adaptive boosting (AdaBoost) based algorithms effectively, an improved AdaBoost algorithm based on misclassified samples oriented feature selection and weighted non-negative matrix factorization (WNMF) is proposed in this paper. Firstly, in order to consider the effects of sample weights, a misclassified samples oriented feature selection (called MOFS) is proposed to select the most discriminative features which occur in the samples with high weights. Secondly, the explicit features and the part-based features of the training samples are both considered, and the WNMF algorithm is introduced and combined with MOFS to reduce the dimension of the training sample set. Finally, the concept of misclassification degree is introduced and a fine grained sample weight updating method is proposed to distinguish the samples with different misclassification degrees. Numerical experiments show that the proposed MOFS method achieves higher accuracy compared to traditional feature selection methods, and the proposed MOFS and WNMF based AdaBoost method obtains significant improvement on classification accuracy when comparing with typical existing AdaBoost based algorithms using different classifiers. [ABSTRACT FROM AUTHOR]

In this paper, the measured input–output data sequences with pinning gain are proposed via the topology of multi-agent systems (MAS), where the requirement of reinforcement learning algorithm on internal state is avoided by pinning gain and the measured data of leader and neighbors. Besides, a data-based tracking state is given, which can be applied to MAS with different control matrices. According to the sequences and tracking state, a distributed control policy and corresponding reinforcement learning algorithm are proposed for the output synchronization. The proposed algorithm overcomes the shortcoming that previous algorithms can not be applied to MAS with different control matrices in the absence of model information and full-state vector. Finally, the effectiveness of proposed algorithm is verified by simulation examples. [ABSTRACT FROM AUTHOR]

In this paper, a distributed nonsmooth nonconvex optimization (DNNO) problem with affine inequality and nonsmooth convex inequality constraints is studied. A continuous-time distributed neurodynamic algorithm is proposed to solve this problem. Under the assumed conditions, for any initial state, the solution of distributed neurodynamic algorithm is bounded and globally exists, and will converge to the critical point set of distributed problems in a finite time. Compared with other DNNO algorithms, distributed neurodynamic algorithm has a lower dimension and does not need to satisfy the assumption that the feasible region is bounded. Finally, a series of numerical examples are given to verify the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

• An advanced shuffled frog leaping algorithm (DSSRLFLA) is developed for model evaluation and feature selection. • A dynamic step size adjustment strategy based on historical information is designed to balance exploration and exploitation. • Specular reflection learning mechanism increases the possibility of searching for valid solutions and enhances the search ability. • An improved simulated annealing strategy is executed for each memetic to improve the efficiency of local exploitation. • DSSRLFLA can obtain higher quality optimal solutions compared to some competitive algorithms. The shuffled frog leaping algorithm is a new optimization algorithm proposed to solve the combinatorial optimization problem, which effectively combines the memetic algorithm based on a memetic algorithm and the particle swarm algorithm based on population behavior. The algorithm is widely used because it is easy to implement and requires few parameters to be adjusted. However, there are still some characteristics of this method that need to be improved because it is easy to fall into local optimization or poor search ability. To alleviate this limitation, a new version of the improved SFLA is proposed in this paper, which incorporates a dynamic step size adjustment strategy based on historical information, a specular reflection learning mechanism, and a simulated annealing mechanism based on chaotic mapping and levy flight. Firstly, the dynamic step size adjustment strategy based on historical information effectively helps to balance local exploration and global exploitation and alleviates the problem of falling into local optimum. Second, the specular reflection learning mechanism increases the possibility of searching for valid solutions in feasible domains and enhances the search ability of individuals in the population. Finally, an improved simulated annealing strategy is executed for each memetic, which improves the efficiency of local exploitation. In order to test the performance of the proposed algorithm, 31 test functions were selected from IEEE CEC2014 and 23 essential benchmark functions, and comparative experiments were carried out from the two dimensions of 30 and 100. Furthermore, a series of competing algorithms are selected, which involve nine classical standard algorithms, including PSO, BA, SSA, FA, SCA, WOA, GWO, MFO, and SFLA, as well as, six well-known improved algorithms, including LSFLA, DDSFLA, GOTLBO, ALCPSO, BLPSO, CLPSO. Furthermore, Wilcoxon signed-rank test and Friedman test are used as testing tools to illustrate the scalability of the proposed algorithm. From the analysis of the results, it can be seen that this proposed method has been effectively improved concerning stability and the quality of the optimal solution obtained from the search, both in low and high dimensions, and the ability to jump out of the local optimum has also been enhanced. In addition, to prove that this method has a reliable performance in discrete problems and continuous problems, DSSRLFLA is mapped into a discrete space, and 24 UCI data sets are also selected to evaluate the performance of the new feature selection method. The experimental results illustrate that this improved method can obtain fewer features and higher classification accuracy than some well-known feature selection methods. [ABSTRACT FROM AUTHOR]

In multi-view multi-label learning, instances can be described by a variety of view features, and they are also associated with a set of labels. Most of the existing multi-view multi-label learning methods extract common and private features from views. However, these methods ignore the fact that the extracted features have different importance for multi-label prediction. To address this issue, this paper proposes a multi-view multi-label learning framework with view feature attention allocation. First, the common and private features between different views are obtained. Then, the original features are compared with the common features to obtain the similarity. Next, the attention weight matrix can be obtained by multiplying the similarity with the synergistic feature matrix. Finally, the acquired attention is used to reconstruct the synergistic feature matrix that indicates the semantic information of the view for multi-label prediction. To verify the effectiveness of the proposed algorithm, experiments are conducted on seven multi-view multi-label datasets, and five advanced algorithms are taken for performance comparison. The extensive experimental results demonstrate the superiority of our algorithm. [ABSTRACT FROM AUTHOR]

Spectral clustering is one of the most popular clustering methods. However, how to balance the efficiency and effectiveness of the large-scale spectral clustering with limited computing resources has not been properly solved for a long time. In this paper, we propose a divide-and-conquer based large-scale spectral clustering method to strike a good balance between efficiency and effectiveness. In the proposed method, a divide-and-conquer based landmark selection algorithm and a novel approximate similarity matrix approach are designed to construct a sparse similarity matrix within low computational complexities. Then clustering results can be computed quickly through a bipartite graph partition process. The proposed method achieves the lower computational complexity than most existing large-scale spectral clustering methods. Experimental results on ten large-scale datasets have demonstrated the efficiency and effectiveness of the proposed method. The MATLAB code of the proposed method and experimental datasets are available at https://github.com/Li-Hongmin/MyPaperWithCode. [ABSTRACT FROM AUTHOR]

A critical prerequisite for controlling complex networks is to find a driver node set with a structural controllability guarantee. This paper introduces the control capacity for a driver node set and solves the problem of finding a complete minimum driver node set that not only guarantees network structural controllability but achieves the desired level of control capacity. A novel algorithmic framework is proposed which is based on the concept of equivalent set and approximate matching replacement technique. The proposed algorithmic framework is shown to outperform the state-of-the-art approaches in the literature. The validity of the proposed algorithm is analyzed and the performance is evaluated by experiments on artificial and real-world complex networks. [ABSTRACT FROM AUTHOR]

Symmetric nonnegative tensor factorization (SNTF) is an important tool for clustering analysis. To date, most of algorithms for SNTF are based on multiplicative update rules, which have many attractive properties, e.g., they are often simple to implement and can enforce nonnegativity without extra projection steps. However, the existing multiplicative algorithms often converge slowly due to the conservative multiplicative learning steps or the use of low-level BLAS (basic linear algebra subprograms) in their implementation. In this paper, three new multiplicative algorithms are proposed for SNTF to overcome the drawback of slow convergence. First, a parallel multiplicative algorithm, which can be implemented with high-level BLAS, is derived by auxiliary optimization. To further accelerate the convergence, two new parallel multiplicative algorithms, which enable larger learning steps for improving efficiency, are developed based on weighted geometric mean and weighted arithmetic mean, respectively. Finally, we apply the proposed algorithms to multiway probabilistic clustering, where a new hyper-stochastic normalization scheme based on Euclidean distance is developed for better data preprocessing. The experiment results on both synthetic and real-world data show that the proposed SNTF algorithms converge faster than the state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

The target net method has been the foundation of deep reinforcement learning since Deepmind first proposed it in 2015. Almost all the current popular reinforcement learning algorithms include target net. However, while the slowly updated target network improves the stability of the algorithm, it also reduces the performance of the algorithm. In this paper, the authors design a novel triple-network algorithm(TPN). TPN combines the temporal-difference(TD) algorithm and policy gradient(PG) theorem. Using three networks to estimate the state value(v), action value (q) , and policy(π). These networks have no primary or secondary distinction but are trained synchronously and influence each other. The author found that through this TPN architecture, the convergence and stability of the algorithm can be greatly improved without increasing the amount of calculation. Although it is only a basic framework at present. The calculation process of TPN is simple and easy to implement. Experiments prove that the convergence speed and stability of TPN in discrete cases are better than PPO. • Proposed a new deep reinforcement learning algorithm that does not rely on target networks. • Presented the complete derivation process of the TPN algorithm. • Verified the effectiveness of proposed algorithm through experiments. [ABSTRACT FROM AUTHOR]

Most traditional multi-view spectral clustering algorithms involve two separate steps: solving the spectral embedding matrix and clustering, which may introduce errors during the clustering process. Moreover, in practical applications, the number of available views may increase over time, and the approach of re-fusing all views in each computation would result in elevated computational costs. In this paper, we propose a novel model: One-step Incremental Multi-view Spectral Clustering based on Graph Linkage learning (OIMvSC). OIMvSC only needs to store the consensus spectral embedding matrix and the consensus label matrix of all previous views and combines them with the spectral embedding matrix of the newly available view to solve the fused consensus spectral embedding matrix and consensus label matrix. To further enhance clustering performance, OIMvSC introduces graph linkage learning, which reduces erroneous connections between clusters while preserving correct connections within clusters. A convergent iterative algorithm for solving OIMvSC is proposed. Experimental results demonstrate that OIMvSC exhibits excellent clustering performance. [ABSTRACT FROM AUTHOR]

In the research of complex networks, how to find a set of nodes in the network with the most extensive range in the propagation process, i.e., the Influence Maximization (IM) problem, is one of the focal topics. Existing studies mainly consider the information dissemination process on networks and how to select diffusive nodes efficiently, but little attention has been paid to changes related to the network structure. In reality, networked systems are exposed to uncertain interferences and even destructive sabotages, and cascading failures are one common destruction that can cause networks to collapse even if only a small number of nodes fail. In the case of various complex environmental factors, how to select robust and influential nodes, i.e., the robust influence maximization (RIM) problem, is of great importance in promoting the realistic application of the influence maximization problem. This paper investigates the RIM problem under cascading failures to address the shortcomings in previous studies. Based on existing research, a new performance evaluation metric, R S-cf , is designed to assess the level of robust influence in a numerical form. For solving the seed determination problem, a Memetic algorithm towards the RIM problem under cascading failures, MA-RIM CF , is designed to find nodes with stable information propagation capability guided by R S-cf. Experiments have been conducted on both synthetic and realistic networks to validate the performance of the algorithm. Results indicate that MA-RIM CF can obtain competitive candidates over existing approaches, and seeds with robust and influential abilities are generated to solve diffusion dilemmas. [ABSTRACT FROM AUTHOR]

Combinatorial optimization problems (COPs) play an important role in both industrial production and theoretical research. As a classical class of optimization algorithms, evolutionary algorithms have shown good performance in COPs. However, as the size of the problem increases, it becomes difficult for evolutionary algorithms to produce satisfactory solutions within the specified time. In recent years, neural network algorithms have been applied to solve COPs and have shown superior effects. Inspired by this, this paper proposes a new algorithm based on graph structure for solving COPs. Through relaxation, COPs are transformed into their corresponding continuous optimization problems. The output state of our algorithm is converted to a discrete solution by approximation method. Compared with previous algorithms, our algorithm can not only solve COPs with general form such as binary quadratic programming (BQP), but also solve COPs with special form, which greatly expands the application scope of neural network algorithms. In addition, our algorithm can be embedded into other problem frameworks such as solving multi-objective combinatorial optimization problem (MOCOP) through scalarization method. A new penalty function is added to the objective function, which enables our algorithm to overcome the inconsistency between the optimal solution of the original problem and the corresponding continuous problem, so that our algorithm can perform well on various problems. Several numerical simulations are used to illustrate the effectiveness of our algorithm in solving COPs. Experimental results show that our algorithm can effectively solve COPs with general form and has a shorter solving time compared to traditional evolutionary algorithms. [ABSTRACT FROM AUTHOR]

The Wasserstein distance in the optimal transport (OT) model is being widely used in machine learning applications due to its mathematical and geometric properties. Since the entropy regularized OT is a convex problem, and for its large-scale problems, many algorithms have been proposed. Existing methods mainly adopt iterative random projection techniques to approximate the Wasserstein distance in the OT model. In this paper, we employ the entropic domain decomposition algorithm with mini-batch learning to calculate the entropy regularized OT problem and investigate the stability of this algorithm. The algorithm performs on different cells of the domain instead of using the projection technique and it is based on a mini-batch loss function. The corresponding solution in each iteration is derived from the dual problem of entropy regularized OT on each decomposed cell. Once the solutions to the dual problem on all decomposed cells are obtained, the corresponding transport plan in each iteration can be obtained. We show that the transport plan computed by its dual variables is admissible, and we also give the sub-gradient approximation result. In addition, we exploit the statistical concentration result of the subsampled mini-batch Wasserstein distance on decomposed cells. Finally, the numerical experiments validate that the proposed algorithm can save computational time further. [ABSTRACT FROM AUTHOR]