Search

We propose a novel semi-supervised learning (SSL) assumption—the high separation probability (HSP) assumption—that is complementary to the common low density separation (LDS) assumption, and a highly accurate and efficient SSL algorithm, the transductive minimax probability machine (TMPM). Under the HSP assumption, a preferred classifier should ensure that with high probability the samples are far away from the decision boundary. Similarly, the LDS assumption states that the decision boundary should lie in a low-density region. A remarkable property of HSP is that it provides an elegant theoretical framework for analyzing the generalization performance of SSL, while it remains difficult for the LDS assumption to have a quantitative criterion on how it fits the data. Moreover, it has the same paradigm as the minimax probability machine (MPM) and yields an intractable mixed-integer optimization for solving the transductive label assignment problem. Consequently, we propose TMPM with a label-switching strategy and iterative manner to formalize our approximate solution. Theoretically, we analyze the computational complexity, convergence property, and generalization error bound of TMPM. Empirically, we show that TMPM achieves competitive performance on a wide range of datasets, while being almost one order of magnitude faster than existing SSL approaches. [ABSTRACT FROM AUTHOR]

Many inverse problems in machine learning, system identification, and image processing include nuisance parameters, which are important for the recovering of other parameters. Separable nonlinear optimization problems fall into this category. The special separable structure in these problems has inspired several efficient optimization strategies. A well-known method is the variable projection (VP) that projects out a subset of the estimated parameters, resulting in a reduced problem that includes fewer parameters. The expectation maximization (EM) is another separated method that provides a powerful framework for the estimation of nuisance parameters. The relationships between EM and VP were ignored in previous studies, though they deal with a part of parameters in a similar way. In this article, we explore the internal relationships and differences between VP and EM. Unlike the algorithms that separate the parameters directly, the hierarchical identification algorithm decomposes a complex model into several linked submodels and identifies the corresponding parameters. Therefore, this article also studies the difference and connection between the hierarchical algorithm and the parameter-separated algorithms like VP and EM. In the numerical simulation part, Monte Carlo experiments are performed to further compare the performance of different algorithms. The results show that the VP algorithm usually converges faster than the other two algorithms and is more robust to the initial point of the parameters. [ABSTRACT FROM AUTHOR]

Online streaming feature selection (OSFS) has attracted extensive attention during the past decades. Current approaches commonly assume that the feature space of fixed data instances dynamically increases without any missing data. However, this assumption does not always hold in many real applications. Motivated by this observation, this study aims to implement online feature selection from sparse streaming features, i.e., features flow in one by one with missing data as instance count remains fixed. To do so, this study proposes a latent-factor-analysis-based online sparse-streaming-feature selection algorithm (LOSSA). Its main idea is to apply latent factor analysis to pre-estimate missing data in sparse streaming features before conducting feature selection, thereby addressing the missing data issue effectively and efficiently. Theoretical and empirical studies indicate that LOSSA can significantly improve the quality of OSFS when missing data are encountered in target instances. [ABSTRACT FROM AUTHOR]

This article investigates the finite-time distributed approximate optimization problem of higher order multiagent systems, where the local cost functions are considered to be quadratic functions. This problem is solved via penalty-function-based method. First, by the penalty-function method, a global approximate cost function is constructed. Second, nonlinear distributed optimization algorithms are proposed for higher order multiagent systems by the tool of adding a power integrator technique. In the optimization algorithms design, the gradients of the approximate cost function are utilized. Under the proposed optimization algorithms, the agents approach the approximate optimal solution in finite time. Although there exist errors (they may be called approximation errors) between the approximate minimizers and the global accurate minimizer, the approximation errors can be regulated by penalty parameter and the relationship between the bound of the approximation errors and the penalty parameter is given explicitly. Furthermore, the proposed distributed approximate optimization algorithms are applied to the optimal rendezvous problem of wheeled multimobile robots, making the mobile robots achieve approximate optimization rendezvous in finite time. The effectiveness of the proposed distributed optimization algorithms and their applications to optimal rendezvous problem are validated by simulations. [ABSTRACT FROM AUTHOR]

Revenue maximization (RM) is one of the most important problems in social networks, which attempts to find a small subset of users that make the expected revenue maximized. It has been studied in depth before. However, most of the existing literature was based on nonadaptive seeding strategies and simple information diffusion models. It considered the number of influenced users as a measurement unit to quantify the revenue. Until the emergence of the collaborate game model, it considered the activity as a basic object to compute the revenue. An activity initiated by a user can only influence those users whose distances are within ${k}$ -hop from the initiator. Based on that, we adopt an adaptive seed strategy and formulate an RM under the size budget (RMSB) problem. If taking into account the product’s promotion, we extend it to an RM under the community budget problem, where the influence can be distributed over the whole network uniformly. We can prove that our objective function is adaptive monotone and not adaptive submodular, but it is adaptive submodular in some special cases. We study these two problems under both the special submodular cases and general nonsubmodular cases, and propose RMSBSolver and RMCBSolver to solve them with strong theoretical guarantees, respectively. In particular, we give a data-dependent approximation ratio by adaptive primal curvature for the RMSB in general nonsubmodular cases. Finally, we evaluate our proposed algorithms by conducting experiments on real datasets, and show the effectiveness and accuracy of our solutions. [ABSTRACT FROM AUTHOR]

Toward better approximation for the minimum-weighted vertex cover (MWVC) problem in multiagent systems, we present a distributed algorithm from the perspective of learning in games. For self-organized coordination and optimization, we see each vertex as a potential game player who makes decisions using local information of its own and the immediate neighbors. The resulting Nash equilibrium is classified into two categories, i.e., the inferior Nash equilibrium (INE) and the dominant Nash equilibrium (DNE). We show that the optimal solution must be a DNE. To achieve better approximation ratios, local rules of perturbation and weighted memory are designed, with the former destroying the stability of an INE and the latter facilitating the refinement of a DNE. By showing the existence of an improvement path from any INE to a DNE, we prove that when the memory length is larger than 1, our algorithm converges in finite time to DNEs, which could not be improved by exchanging the action of a selected node with all its unselected neighbors. Moreover, additional freedom for solution efficiency refinement is provided by increasing the memory length. Finally, intensive comparison experiments demonstrate the superiority of the presented methodology to the state of the art, both in solution efficiency and computation speed. [ABSTRACT FROM AUTHOR]

This article investigates optimal control problem for a class of discrete-time (DT) nonlinear systems with unknown dynamics. With the help of a broad learning system (BLS), a novel online adaptive dynamic programming (ADP) controller is presented. First, to approximate the unknown system dynamics, an approximator based on BLS is presented. The connection weights are calculated by the data of the system by using the ridge regression algorithm. Then, two BLSs are adopted to approximate the optimal cost function and optimal control law, respectively. The connection weights of these two BLSs are updated using the given weights tuning law at each sampling instant. The proposed optimal controller is proved to ensure that all the system states and estimation errors are uniform ultimate bounded. Finally, simulation examples are carried out to further demonstrate the effectiveness of the proposed BLS-based approximator and optimal controller. [ABSTRACT FROM AUTHOR]

We consider decentralized large-scale continuous submodular constrained optimization problems over networks, where the goal is to maximize a sum of nonconvex functions with diminishing returns property. However, the computations of the projection step and the whole gradient can become prohibitive in high-dimensional constrained optimization problems. For this reason, a decentralized randomized block-coordinate Frank-Wolfe algorithm is proposed for submoduar maximization over networks by local communication and computation, which adopts the randomized block-coordinate descent and the Frank-Wolfe technique. We also show that the proposed algorithm converges to an approximation fact $(1-e^{-p_{\max }/p_{\min }})$ of the global maximal points at a rate of $\mathcal {O}(1/T)$ by choosing a suitable stepsize, where $T$ is the number of iterations. In addition, we confirm the theoretical results by experiments. [ABSTRACT FROM AUTHOR]

Spectral clustering is becoming more and more popular because it has good performance in discovering clusters with varying characteristics. However, it suffers from high computational cost, unstable clustering results and noises. This work presents a novel approximate spectral clustering based on dense cores and density peaks, called DCDP-ASC. It first finds a reduced data set by introducing the concept of dense cores; then defines a new distance based on the common neighborhood of dense cores and calculates geodesic distances between dense cores according to the new defined distance; after that constructs a decision graph with a parameter-free local density and geodesic distance for obtaining initial centers; finally calculates the similarity between dense cores with their new defined geodesic distance, employs normalized spectral clustering method to divide dense cores, and expands the result on dense cores to the whole data set by assigning each point to its representative. The results on some challenging data sets and the comparison of our algorithm with some other excellent methods demonstrate that the proposed method DCDP-ASC is more advantageous in identifying complex structured clusters containing a lot of noises. [ABSTRACT FROM AUTHOR]

Area coverage and network lifetime are two contradictory issues to the architecture development of a wireless sensor network (WSN). A satisfactory balance could be achieved by deploying abundant sensor nodes randomly and dividing them into $k$ exclusive cover sets. Toward self-organized partition with higher efficiency, we address the problem from the perspective of networked potential games and propose a memorial mixed-response algorithm (MMRA), which is implemented in a distributed and synchronous manner. Being viewed as a game player, each sensor node first updates its memory using a temporary action, which is generated by following a mixed response rule. After this, the coordination evolves into the next iteration by each player randomly drawing an action from its memory with equal probabilities. We prove that our algorithm converges with probability 1 to a convention of Nash equilibria, with the worst approximation ratio strictly larger than 0.5. Moreover, it is also found that a tradeoff between solution efficiency and computation time could be achieved via the adjustment of the amount of randomness introduced via the memory length $m$ as well as the probability $p_{m}$ , where better partition results are more likely to be generated using a larger $m$ and smaller $p_{m}$. Comparisons with existing distributed methods demonstrate the superiority of our method in terms of solution refinement as well as convergence speed. [ABSTRACT FROM AUTHOR]

The minimum dominating set (MDS) of the network is a node subset of smallest size that every node in the network is either in this subset or is adjacent to one or more nodes of this subset. MDS has found wide applications, ranging from network monitoring, routing, to epidemic control, and text processing. However, the majority of existing studies on MDS problem are confined to single networks. In real world, more and more complex systems consist of a set of elements linked up by different types of connections, which are best modeled as multiplex networks with interacting network layers. Though vastly important, the MDS of the multiplex networks has not yet been formally defined and its application and identification remain open issues. In this article, we present the definition of the MDS of the multiplex network and show some of its possible applications. For solving the MDS problem of the multiplex network, we built a spin-glass model and solve it through the belief-propagation (BP) equations under the replica symmetry mean-field theory. As a consequence, we can predict the relative size of the MDS of the multiplex network theoretically and we can propose a BP-guided decimation algorithm to construct an approximate optimal dominating set in practice. Then the algorithm is improved in both accuracy and efficiency by embedding a novel multiplex network-oriented leaf-removal strategy. The effectiveness of the proposed algorithms is finally verified by comparing with other methods on a number of the multiplex network examples. [ABSTRACT FROM AUTHOR]

Path tracking control of intelligent vehicles has to deal with the difficulties of model uncertainties and nonlinearities. As a class of adaptive optimal control methods, reinforcement learning (RL) has received increasing attention in solving difficult control problems. However, feature representation and online learning ability are two major problems to be solved for learning control of uncertain dynamic systems. In this article, we propose a multi-kernel online RL approach for path tracking control of intelligent vehicles. In the proposed approach, a multiple kernel feature learning framework is designed for online learning control based on dual heuristic programming (DHP) and the new online learning control algorithm is called multi-kernel DHP (MKDHP). In MKDHP, instead of the expert knowledge for selecting and fine-tuning of a suitable kernel function, only a set of basic kernel functions is required to be predefined and the multi-kernel features can be learned for value function approximation in the critic. The simulation studies on path tracking control for intelligent vehicles have been conducted under $S$ -curve and urban road conditions. The results demonstrated that compared with other typical path tracking controllers for intelligent vehicles, such as the linear quadratic regulator (LQR), the pure pursuit controller and the ribbon-based controller, the proposed multi-kernel learning controller can achieve better performance in terms of tracking precision and smoothness. [ABSTRACT FROM AUTHOR]

This article proposes a robust particle filtering (PF) approach for a generic class of nonlinear systems with both additive time-varying uncertainty (ATVU) in the state transition equation and inaccurate process noise covariance matrices. To avoid sampling efficiency degradation of the PF approach caused by ATVU, we employ the disturbance observer-based PF (DOBPF) approach where the effect of ATVU is compensated in the particle generation stage. Different from the existing DOBPF method where disturbance estimation is achieved via the Kalman filter, the disturbance observer adopted in this article is in the form of variational Bayesian adaptive Kalman filter (VBAKF) which deals with the inaccurate process noise covariance matrices in both the dynamic models of the state and the ATVU. Compared with conventional PF approaches, the proposed method, named VBAKF-PF, exhibits enhanced robustness against both the ATVU in the state transition equation and the uncertainties of process noise covariance matrices. The simulation results demonstrate the superiority of VBAKF-PF over both the VBAKF and DOBPF methods. [ABSTRACT FROM AUTHOR]

This article addresses the design and implementation of observer-based sliding mode controller with $H_{\infty }$ performance for underactuated rendezvous system under the constraints of fault signals, maximum input, and disturbances. The nonlinear constrained model considered in this article is an underactuated system since the number of control input variables is less than that of state variables, besides, owing to the full state information is unavailable or not so accurate for the controller design, an observer is first constructed to estimate the full state of system, and then the state of observer is adopted to synthesize the integral-type sliding surface function. Considering three fault signals, input constraint, and disturbances, the stability criteria with $H_{\infty }$ performance are derived based on Lyapunov method and the ellipsoidal approximation algorithm. Furthermore, the sliding mode control law is formulated to guarantee the sliding mode dynamic could be driven onto the sliding surface and remain there for subsequent time. Finally, the simulation experiments are implemented to verify the effectiveness of the proposed scheme for the underactuated rendezvous system. [ABSTRACT FROM AUTHOR]

This article investigates the optimal control problem for nonlinear nonzero-sum differential game in the environment of no initial admissible policies while considering the control constraint. An adaptive learning algorithm is thus developed based on policy iteration technique to approximately obtain the Nash equilibrium using real-time data. A two-player continuous-time system is used to present this approximate mechanism, which is implemented as a critic–actor architecture for every player. The constraint is incorporated into this optimization by introducing the nonquadratic value function, and the associated constrained Hamilton–Jacobi equation is derived. The critic neural network (NN) and actor NN are utilized to learn the value function and the optimal control policy, respectively, in the light of novel weight tuning laws. In order to tackle the stability during the learning phase, two stable operators are designed for two actors. The proposed algorithm is proved to be convergent as a Newton’s iteration, and the stability of this closed-loop system is also ensured by Lyapunov analysis. Finally, two simulation examples demonstrate the effectiveness of the proposed learning scheme by considering different constraint scenes. [ABSTRACT FROM AUTHOR]

A distributed optimization problem (DOP) with affine equality and convex inequality constraints is studied in this article. First, the consensus constraint of the considered DOP is relaxed and a related approximate DOP (ADOP) is presented. It is proved that the optimal solutions of the ADOP (i.e., the near-optimal solutions of the original DOP) are able to approach the optimal solutions of the original DOP. A continuous-time algorithm is proposed for the ADOP and it is demonstrated that the state solution of the presented algorithm converges to the critical point set of the ADOP with general locally Lipschitz continuous objective functions. This means the presented algorithm is efficient for distributed nonconvex optimization problems. Particularly, when the objective functions are convex ones, the state solution of the presented algorithm is further proved to converge to a near-optimal solution of the original DOP. One illustrative example and an application on load sharing problems are shown to validate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Large-scale data clustering is an essential key for big data problem. However, no current existing approach is “optimal” for big data due to high complexity, which remains it a great challenge. In this article, a simple but fast approximate DBSCAN, namely, KNN-BLOCK DBSCAN, is proposed based on two findings: 1) the problem of identifying whether a point is a core point or not is, in fact, a kNN problem and 2) a point has a similar density distribution to its neighbors, and neighbor points are highly possible to be the same type (core point, border point, or noise). KNN-BLOCK DBSCAN uses a fast approximate kNN algorithm, namely, FLANN, to detect core-blocks (CBs), noncore-blocks, and noise-blocks within which all points have the same type, then a fast algorithm for merging CBs and assigning noncore points to proper clusters is also invented to speedup the clustering process. The experimental results show that KNN-BLOCK DBSCAN is an effective approximate DBSCAN algorithm with high accuracy, and outperforms other current variants of DBSCAN, including ρ-approximate DBSCAN and AnyDBC. [ABSTRACT FROM AUTHOR]

Consistency, multiplicative and ordinal, of fuzzy preference relations (FPRs) is investigated. The geometric consistency index (GCI) approximated thresholds are extended to measure the degree of consistency for an FPR. For inconsistent FPRs, two algorithms are devised: 1) to find the multiplicative inconsistent elements and 2) to detect the ordinally inconsistent elements. An integrated algorithm is proposed to improve simultaneously the ordinal and multiplicative consistencies. Finally, some examples, comparative analysis, and simulation experiments are provided to demonstrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

As a class of batch-mode reinforcement learning (RL) methods for Markov decision problems with large or continuous state spaces, approximate policy iteration (API) has received increasing attention in the past decades. One open problem in the design of API algorithms is how to construct the basis functions or features for value function approximation (VFA). In this paper, we propose a novel batch-mode RL approach with randomly projected features for VFA. The proposed approach can be viewed as an extension of extreme learning machines (ELMs) to RL problems so it can be called ELM-API. The ELMs have been popularly studied in supervised learning problems, but there is not much work on the extension of ELMs to learning control problems. The proposed approach has advantages over the previous API algorithms in that the features for VFA can be quickly generated without complex parameter selection and the performance will be adaptive to different sample sets in batch-mode RL. In particular, the ELM-API approach can realize fast and efficient feature reconstruction when training sample sets are relatively small. Comprehensive simulation studies on two benchmark learning control problems were carried out to test the performance of API algorithms with different feature construction methods. It is shown that the ELM-API algorithm can obtain comparable or better performance than the previous API approaches. To further show the effectiveness of ELM-API in real-world applications, the simulation results on a more challenging high-dimensional lane-changing decision problem in dynamic traffic environment are also reported, which show the capability of the ELM-API algorithm in learning satisfactory lane-changing policies with high data efficiency. [ABSTRACT FROM AUTHOR]

This paper proposes fast convergent distributed algorithms for weighted average consensus of input data. For acyclic graphs, we give an algorithm that converges to the exact weighted average consensus in a finite number of iterations, equal to the graph diameter. For loopy (cyclic) graphs, we offer two remedies. In the first one, we give another distributed algorithm to enable our average consensus algorithm applicable to a loopy graph by converting it into a spanning tree. In the second one, we consider a slightly modified average consensus problem whose optimal solution approximates the consensus solution with arbitrary precision, and give a modified average consensus algorithm with guaranteed exponential convergence to the optimal solution. The proposed average consensus algorithms enjoy low complexities, robustness to transmission adversaries, and asynchronous implementation. Our algorithms are conceptually different from the popular graph Laplacian approach, and converge much faster than the latter approach. [ABSTRACT FROM AUTHOR]

This paper considers the identification problem of finite impulse response (FIR) systems with binary-valued observations under the assumption of fixed threshold and bounded persistently excitations. A recursive projection algorithm is constructed to estimate the unknown parameter. For first-order FIR systems, the convergence properties of the algorithm are analyzed theoretically. With mild conditions on the weight coefficients in the parameter update, the algorithm is proved to be convergent in mean square and the convergence rate can be the reciprocal of the number of observations, which has the same order as the optimal estimation when the system output is exactly known. Furthermore, it is also shown that the Cramér–Rao (CR) lower bound is achieved asymptotically with proper weight coefficients, which indicates that the algorithm is optimal in the sense of asymptotic efficiency. Some numerical examples are simulated to demonstrate the effectiveness of the proposed algorithm in both first-order and high-order FIR systems. [ABSTRACT FROM AUTHOR]

Nonlinear optimization problems with dynamical parameters are widely arising in many practical scientific and engineering applications, and various computational models are presented for solving them under the hypothesis of short-time invariance. To eliminate the large lagging error in the solution of the inherently dynamic nonlinear optimization problem, the only way is to estimate the future unknown information by using the present and previous data during the solving process, which is termed the future dynamic nonlinear optimization (FDNO) problem. In this paper, to suppress noises and improve the accuracy in solving FDNO problems, a novel noise-tolerant neural (NTN) algorithm based on zeroing neural dynamics is proposed and investigated. In addition, for reducing algorithm complexity, the quasi-Newton Broyden–Fletcher–Goldfarb–Shanno (BFGS) method is employed to eliminate the intensively computational burden for matrix inversion, termed NTN-BFGS algorithm. Moreover, theoretical analyses are conducted, which show that the proposed algorithms are able to globally converge to a tiny error bound with or without the pollution of noises. Finally, numerical experiments are conducted to validate the superiority of the proposed NTN and NTN-BFGS algorithms for the online solution of FDNO problems. [ABSTRACT FROM AUTHOR]

In this paper, a 2-point algorithm is proposed to estimate the relative pose as well as the absolute scale between two vehicle-mounted cameras efficiently. The system model is deduced by combining a two-view geometric model and the planar motion constraint to reduce the degrees of freedom. 2-point correspondences are utilized to calculate the rotation information independently from the translation information, which indicates that the proposed algorithm can deal with pure rotation scenes. Besides, provided that the camera’s configuration satisfies a certain condition, the absolute scale can be recovered. An approximation algorithm is developed and combined with the random sample and consensus scheme to deal with the uneven ground surfaces in practice. As only 2-point correspondences are required, less iterations are demanded in the estimating procedure compared with many other existing related algorithms. Both simulation and experiments are implemented to evaluate the proposed algorithm, in which the synthetic data, virtual robot experimentation platform, KITTI Vision Benchmark, and SUMMIT-XL platform are acquired. According to the results, the proposed algorithm performs better than many related algorithms including the well-known 5-point algorithm in many cases, especially when the camera’s trajectory contains sharp corners. [ABSTRACT FROM AUTHOR]

In surgical simulation, the Navier–Stokes (N–S) equation is commonly employed to imitate the physical characteristics of bleeding and the smooth particle hydrodynamics (SPHs) algorithm is applied to solve the numerical solution of the N–S equation. However, blood is viscous, incompressible and non-Newtonian fluid whose physical properties cannot be fully incorporated by the simple N–S equation, and the kernel approximation of the SPH algorithm may lead to both edge and volume distortions plus high computational cost. In this paper, both the tension force and the effect of platelets on the viscous force of bleeding particles are incorporated into the N–S equation in order to render more realistic visual effect and biological features of bleeding in surgical simulation. Constant core radius of the kernel function of the SPH algorithm is substituted with a function of particle density, avoiding potential edge distortions in simulating bleeding area. A repulsive force between particles is introduced, which effectively prevents volume distortions. Besides, accelerated search for particles based on the cube mesh improves the computational efficiency. The simulation results show that the presented simulation method leads to smooth bleeding surface and improves the visual effects of edge and volume in comparison with existing methods, and relatively high computational efficiency can be achieved as well. [ABSTRACT FROM AUTHOR]

This article reviews the recent development of adaptive dynamic programming (ADP) with applications in control. First, its applications in optimal regulation are introduced, and some skilled and efficient algorithms are presented. Next, the use of ADP to solve game problems, mainly nonzero-sum game problems, is elaborated. It is followed by applications in large-scale systems. Note that although the functions presented in this article are based on continuous-time systems, various applications of ADP in discrete-time systems are also analyzed. Moreover, in each section, not only some existing techniques are discussed, but also possible directions for future work are pointed out. Finally, some overall prospects for the future are given, followed by conclusions of this article. Through a comprehensive and complete investigation of its applications in many existing fields, this article fully demonstrates that the ADP intelligent control method is promising in today’s artificial intelligence era. Furthermore, it also plays a significant role in promoting economic and social development. [ABSTRACT FROM AUTHOR]

When dealing with complex nonlinear signals in intelligent system, by defining the inner product of two data vectors in the feature space, the kernel function can reflect the nonlinear mapping relationship between reproducing kernel Hilbert space (RKHS) and original data space. Therefore, by implementing classical linear adaptive filtering in RKHS space, the filtering operation can be expressed as a special relation of inner product with kernel function, which is referred to as “kernel trick.” As long as these algorithms can be expressed in the form of inner product, not only the convex least squares problem can be solved iteratively, but also the nonlinear adaptive filtering algorithms can be obtained, which have both general approximation characteristics and convexity. Therefore, the combination of kernel method and adaptive filtering algorithm is realized. On the other hand, since the Gram matrix is used, the dimension of kernel adaptive algorithm is determined by the number of data samples. When the number of observation sample point is increasing, the size of the state space increases exponentially with the growth of the dimension. Thereby, the kernel adaptive algorithm should solve the problem of online sparsification to avoid “curse of dimensionality.” As part II, based on online sparse kernel learning and the classical adaptive filtering algorithm, the kernel adaptive algorithms and online sparse algorithms are investigated in this paper. The main works of this paper have two aspects. First, combined with classical adaptive algorithm and kernel feature mapping, this paper investigates the basic concept of kernel adaptive algorithm and the realization mechanism of four kernel adaptive algorithm intensively: 1) kernel least mean squares; 2) kernel recursive least squares; 3) kernel affine projection algorithm; and 4) kernel principal component analysis. Second, in order to reduce the computational complexity, this paper studies some online sparse algorithms which include novel criterion, approximate linear dependency, sliding window, coherence criterion, surprise criterion, and so on. Finally, this paper summarizes the essence of existing conclusions of above algorithms and perspectives the future research direction. [ABSTRACT FROM AUTHOR]

This paper considers the networked system optimization problem by cooperatively finding an approximately optimal solution to the overall network convex cost function, which is the sum of the individual cost functions of nodes (agents) in a networked system. A new distributed gradient descent algorithm is proposed based on the distributed estimation of the sum of gradients of individual cost functions using a consensus-type coordination algorithm. The proposed algorithm can address unknown directed communication topologies and only requires limited communications and information exchanges among nodes in the networked system. Under the assumption that the communication graph is strongly connected, the convergence of the proposed algorithm is rigorously analyzed. Simulation examples are presented to demonstrate the applicability and effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

The acquired industrial data often contain missing outputs because of the irregularities of complicated industrial environment, which make the outputs of the training dataset incomplete. In this paper, a semi-supervised sparse Bayesian regression model is proposed for dealing with the incomplete outputs problem by employing a variational inference technique. Within the settings of specific hierarchical priors over the missing outputs, in this paper, we derive the posterior probability distribution over the uncertain variables including the missing outputs. Given that the posterior distribution is not analytically tractable, a hybrid learning procedure is designed for combining the variational inference with a gradient-based method to obtain optimal approximate posteriors. To verify the performance of the proposed method, a number of comparative experiments are conducted and analyzed by using the datasets (including artificial and real world ones) coming with different proportions of missing outputs. Compared to the existing semi-supervised regression approaches, we demonstrated the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

We consider the tasks of feature selection and policy evaluation based on linear value function approximation in reinforcement learning problems. High-dimension feature vectors and limited number of samples can easily cause over-fitting and computation expensive. To prevent this problem, ${\ell _{1}}$ -regularized method obtains sparse solutions and thus improves generalization performance. We propose an efficient ${\ell _{1}}$ -regularized recursive least squares-based online algorithm with ${O}$ (${n} ^{{2}}$) complexity per time-step, termed ${\ell _{1}}$ -RC. With the help of nested optimization decomposition, ${\ell _{1}}$ -RC solves a series of standard optimization problems and avoids minimizing mean squares projected Bellman error with ${\ell _{1}}$ -regularization directly. In ${\ell _{1}}$ -RC, we propose RC with iterative refinement to minimize the operator error, and we propose an alternating direction method of multipliers with proximal operator to minimize the fixed-point error. The convergence of ${\ell _{1}}$ -RC is established based on ordinary differential equation method and some extensions are also given. In empirical computations, some state-of-the-art ${\ell _{1}}$ -regularized methods are chosen as the baselines, and ${\ell _{1}}$ -RC are tested in both policy evaluation and learning control benchmarks. The empirical results show the effectiveness and advantages of ${\ell _{1}}$ -RC. [ABSTRACT FROM AUTHOR]

This article presents a novel event-driven guaranteed cost control method for nonlinear systems subject to actuator faults. For the purpose of handling the problem of actuator faults and obtaining the event-driven approximate optimal guaranteed cost control approach for general nonlinear dynamics, the reinforcement learning (RL) algorithm is utilized to develop a sliding-mode control (SMC) strategy. To begin with, the unknown faults can be estimated by designing a fault observer. Meanwhile, an SMC technique is presented aiming at countering the effect of abrupt faults. In addition, the optimal performance of the equivalent sliding mode dynamics is considered, then an event-driven guaranteed cost control mechanism is implemented by using RL principle. In the control process, a general cost function, which has a simpler structure, is given to reduce the computation complexity. At the same time, a modified cost function is approximated to obtain optimal guaranteed cost control by using a single critic neural network (NN). In addition, a modified weight update law for critic NN is presented to relax the persistence of excitation (PE) condition. Moreover, a newly triggering condition, which is easy to be implemented, is designed, and the critic NN update law makes sure that the system states are stable. Furthermore, in light of the Lyapunov analysis, it is demonstrated that the developed event-driven control method guarantees the uniformly ultimately bounded (UUB) property of all the signals. Finally, three simulation results are given to validate the designed control method. [ABSTRACT FROM AUTHOR]

In this paper, a novel adaptive dynamic programming (ADP) algorithm is developed for the infinite-horizon ($H_{\infty}$) optimal control problems with unknown continuous-time (CT) nonlinear systems subject to external disturbances. To facilitate the implementation of the algorithm, generalized fuzzy hyperbolic models (GFHMs) are utilized to establish an identifier–critic architecture, where the identifier is designed to reconstruct the unknown system dynamics, and the GFHM-based critic network is employed to approximate the value functions. The CT $H_{\infty}$ optimal control issue is converted into a two-player zero-sum game and the corresponding Hamilton–Jacobi–Isaacs equation is derived. The learning procedure of the critic design is adaptively implemented with the help of the reconstructed model, thus the requirement of the complete system dynamics is relaxed. Furthermore, by the means of Lyapunov direct method, the uniform ultimate boundedness stability analysis of the closed-loop control system is explicitly provided. Finally, to compare the control performances and disturbance attenuation properties of the proposed method and the existing ADP algorithms, two numerical examples are given. [ABSTRACT FROM AUTHOR]

Periodic vehicle routing problem with time windows (PVRPTWs) is an important combinatorial optimization problem that can be applied in different fields. It is essentially a multiobjective optimization problem due to the problem nature. In this paper, a typical multiobjective PVRPTW with five objectives is first defined and new nonsymmetric real-world multiobjective PVRPTW instances are generated. Then, a hybrid multiobjective memetic algorithm is proposed for solving multiobjective PVRPTW. In the proposed algorithm, a two-phase strategy is devised to improve the comprehensive performance in terms of the convergence and diversity. In this strategy, several extreme solutions near an approximate Pareto front (PF) are identified at Phase I, and then the approximate PF is extended at Phase II. The proposed algorithm is extensively tested on both real-world instances and traditional instances. Experiment results show that the proposed algorithm outperforms two representative competitor algorithms on most of the instances. The effectiveness of the two-phase strategy is also confirmed. [ABSTRACT FROM AUTHOR]

A method to find the minimized state machine cover of live and safe Petri nets (PNs) is proposed in this paper. It is required that a cover be obtained in some implementation methods of PN-based control algorithms and other applications such as data mining. Most of the known methods of its computation have at least exponential time and space complexity; this is true not only for the methods which guarantee a minimal cover is obtained but also for some methods of finding approximate solutions. The proposed algorithm is an approximation algorithm and has polynomial computational complexity. The experimental verification shows a very high efficiency of the presented technique. The proposed method is especially valuable in the case of large systems where a solution is obtained hundreds of times quicker than by other methods. [ABSTRACT FROM AUTHOR]

Autonomous decision making is a critical and difficult task for intelligent vehicles in dynamic transportation environments. In this paper, a reinforcement learning approach with value function approximation and feature learning is proposed for autonomous decision making of intelligent vehicles on highways. In the proposed approach, the sequential decision making problem for lane changing and overtaking is modeled as a Markov decision process with multiple goals, including safety, speediness, smoothness, etc. In order to learn optimized policies for autonomous decision-making, a multiobjective approximate policy iteration (MO-API) algorithm is presented. The features for value function approximation are learned in a data-driven way, where sparse kernel-based features or manifold-based features can be constructed based on data samples. Compared with previous RL algorithms such as multiobjective Q-learning, the MO-API approach uses data-driven feature representation for value and policy approximation so that better learning efficiency can be achieved. A highway simulation environment using a 14 degree-of-freedom vehicle dynamics model was established to generate training data and test the performance of different decision-making methods for intelligent vehicles on highways. The results illustrate the advantages of the proposed MO-API method under different traffic conditions. Furthermore, we also tested the learned decision policy on a real autonomous vehicle to implement overtaking decision and control under normal traffic on highways. The experimental results also demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, a novel event-sampled robust optimal controller is proposed for a class of continuous-time constrained-input nonlinear systems with unknown dynamics. In order to solve the robust optimal control problem, an online data-driven identifier is established to construct the system dynamics, and an event-sampled critic-only adaptive dynamic programming method is developed to replace the conventional time-driven actor–critic structure. The designed online identification method runs during the solving process and is not applied as a priori part for the solutions, which simplifies the architecture and reduces computational load. The proposed robust optimal control algorithm tunes the parameters of critic-only neural network (NN) by event-triggering condition and runs in a plug-n-play framework without system functions, where fewer transmissions and less computation are required as all the measurements received simultaneously. Based on the novel design, the stability of system and the convergence of critic NN are demonstrated by Lyapunov theory, where the state is asymptotically stable and weight error is guaranteed to be uniformly ultimately bounded. Finally, the applications in a basic nonlinear system and the complex rotational–translational actuator problem demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper presents a novel decentralized control strategy for a class of uncertain nonlinear large-scale systems with mismatched interconnections. First, it is shown that the decentralized controller for the overall system can be represented by an array of optimal control policies of auxiliary subsystems. Then, within the framework of adaptive dynamic programming, a simultaneous policy iteration (SPI) algorithm is developed to solve the Hamilton–Jacobi–Bellman equations associated with auxiliary subsystem optimal control policies. The convergence of the SPI algorithm is guaranteed by an equivalence relationship. To implement the present SPI algorithm, actor and critic neural networks are applied to approximate the optimal control policies and the optimal value functions, respectively. Meanwhile, both the least squares method and the Monte Carlo integration technique are employed to derive the unknown weight parameters. Furthermore, by using Lyapunov’s direct method, the overall system with the obtained decentralized controller is proved to be asymptotically stable. Finally, the effectiveness of the proposed decentralized control scheme is illustrated via simulations for nonlinear plants and unstable power systems. [ABSTRACT FROM AUTHOR]

In this paper, a dynamic model of a wheeled mobile robotic (WMR) system with coupled control input is developed, which will increase the complexity of its tracking control with time-varying advance angle. To deal with this problem, a partial reinforcement learning neural network (PRLNN)-based tracking algorithm is proposed for the WMR systems. The main contributions of the PRLNN adaptive tracking control method is that it is the first control method to introduce the PRLNN adaptive control to the WMR system, which determines to solve the WMR tracking control with the time-varying advance angle. The critic neural network (NN) and action NN adaptive laws for the decoupled controllers are designed using the standard gradient-based adaptation method. According to the Lyapunov stability analysis theorem, the uniform ultimate boundedness of all signals in the WMR system can be guaranteed with the design parameters chose properly, and the tracking error converge to a small compact set nearby zero. A numerical simulation is presented to verify the effectiveness of the proposed control algorithm. [ABSTRACT FROM AUTHOR]

The classic approach for estimating parameters of a model using historical data is to solve a nonlinear least squares optimization problem using numerical methods. We develop an I-frame methodology to solve the nonlinear least squares problem quickly which can be applied to both offline and online (where data is streamed in real time) parameter estimation. Using the concept of I-frames from imaging and animation, we approximate a solution to the nonlinear least squares problem via a two-step process, an I-frame optimization, and an incremental optimization. The I-frame optimization solves for the parameters using a subset of data points and the incremental optimization adjusts the parameters in between the I-frames. We show that the criterion of generating I-frames can affect the average squared error of the final solution. Our methodology benefits from being scalable as the number of parameters and amount of data increases with an appropriate I-frame generation criterion. [ABSTRACT FROM AUTHOR]

Graph matching is a fundamental problem in theoretical computer science and artificial intelligence, and lays the foundation for many computer vision and machine learning tasks. Approximate algorithms are necessary for graph matching due to its NP-complete nature. Inspired by the usage in network-related tasks, random walk is generalized to graph matching as a type of approximate algorithm. However, it may be inappropriate for the previous random walk-based graph matching algorithms to utilize continuous techniques without considering the discrete property. In this paper, we propose a novel random walk-based graph matching algorithm by incorporating both continuous and discrete constraints in the optimization process. Specifically, after interpreting graph matching by random walk, the continuous constraints are directly embedded in the random walk constraint in each iteration. Further, both the assignment matrix (vector) and the pairwise similarity measure between graphs are iteratively updated according the discrete constraints, which automatically leads the continuous solution to the discrete domain. Comparisons on both synthetic and real-world data demonstrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper investigates the expected rate of convergence to consensus in an asymmetric network represented by a weighted directed graph. The initial state of the network is represented by a random vector and the expectation is taken with respect to the random initial condition of the network. The proposed convergence rate is described in terms of the eigenvalues of the Laplacian matrix of the network graph. The generalized power iteration algorithm is then introduced based on the Krylov subspace method to compute the proposed expected convergence rate in a centralized fashion. To this end, the Laplacian matrix of the network is transformed to a new matrix such that existing techniques can be used to find the eigenvalue representing the expected convergence rate of the network. The convergence analysis of the centralized algorithm is performed with a prescribed upper bound on the approximation error of the algorithm. A distributed version of the centralized algorithm is then developed using the notion of consensus observer. The efficiency of the algorithms is subsequently demonstrated by simulations. [ABSTRACT FROM AUTHOR]

Inspired by Nash game theory, a multiplayer mixed-zero-sum (MZS) nonlinear game considering both two situations [zero-sum and nonzero-sum (NZS) Nash games] is proposed in this paper. A synchronous reinforcement learning (RL) scheme based on the identifier-critic structure is developed to learn the Nash equilibrium solution of the proposed MZS game. First, the MZS game formulation is presented, where the performance indexes for players 1 to ${N}$ − 1 and ${N}$ NZS Nash game are presented, and another performance index for players ${N}$ and ${N}$ + 1 zero-sum game is presented, such that player ${N}$ cooperates with players 1 to ${N}$ − 1, while competes with player ${N}$ + 1, which leads to a Nash equilibrium of all players. A single-layer neural network (NN) is then used to approximate the unknown dynamics of the nonlinear game system. Finally, an RL scheme based on NNs is developed to learn the optimal performance indexes, which can be used to produce the optimal control policy of every player such that Nash equilibrium can be obtained. Thus, the widely used actor NN in RL literature is not needed. To this end, a recently proposed adaptive law is used to estimate the unknown identifier coefficient vectors, and an improved adaptive law with the error performance index is further developed to update the critic coefficient vectors. Both linear and nonlinear simulations are presented to demonstrate the existence of Nash equilibrium for MZS game and performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Time-series prediction is important in diverse fields. Traditionally, methods for time-series prediction were based on fixed linear models because of mathematical tractability. Researchers turned their attention to artificial neural networks due to their better approximation capability. In this paper, we use feedforward neural networks with a single hidden layer, and present a rather simple online sequential learning algorithm (OSLA) together with its proof. The convergence properties of this algorithm are those of the well-known recursive least squares algorithm. We demonstrate that the prediction performance is better than other OSLAs, and show that it is statistically different from them. In addition, we also present the multiple models, switching, and tuning methodology that enhances the prediction performance of the learning algorithm. [ABSTRACT FROM AUTHOR]

This paper presents a parameterized batch reinforcement learning algorithm for near-optimal longitudinal control of autonomous land vehicles (ALVs). The proposed approach uses an actor-critic architecture, where parameterized feature vectors based on kernels are learned from collected samples for approximating the value functions and policies. One difference between the parameterized batch actor-critic (PBAC) algorithm and previous actor-critic learning approaches is that the critic and actor in PBAC share the same linear features, which has been theoretically proved to be a beneficial property for the convergence of actor-critic learning approaches. In order to obtain better learning efficiency, least-squares-based batch updating rules are designed for the critic and actor, respectively. Based on the PBAC learning algorithm, a data-driven longitudinal control method is presented for ALVs to obtain near-optimal control policies which adaptively tune the fuel/brake control signals to track different speeds. A multiobjective reward function is designed so that both tracking precision and driving smoothness are considered. Extensive experiments were conducted on a real ALV platform while driving on flat, slippery, sloping, and bumpy roads. The experimental results illustrate the superiority of the PBAC-based self-learning controller over conventional longitudinal control methods such as proportional-integral (PI) control and learning-based PI control. [ABSTRACT FROM AUTHOR]

We consider a model of competition on complex networks, in which two competitors are fixed to opposite states while other agents, called normal agents, adjust their states according to a distributed consensus protocol. Suppose that one of the competitors could enhance its influence by creating new links. A natural question is, when the number of new links is limited due to the limited resource, how to add these links so as to maximize the influence of the given competitor over the other one (called competitiveness). We consider two competitiveness maximization problems: Problem 1 tries to maximize the number of supporters of the competitor, while Problem 2 tries to maximize the total supporting degree of normal agents toward the competitor. We prove that Problem 1 is NP-hard. We also show that the objective function of Problem 2 is monotonous and submodular, and hence there exists a polynomial-time greedy algorithm (GA) approximately solving Problem 2. Several centrality-based heuristic algorithms of less computational burden are also designed to provide approximate solutions to these two problems. We carry out extensive simulations to check the performances of these algorithms in six real networks. We find that GA always provides the best approximate solution to Problem 2, while for Problem 1, GA only has the best performance in directed networks. Furthermore, among those heuristic algorithms, an algorithm based on centrality in descending order is better than its counterpart in ascending order in solving Problem 2 in statistical sense. But for Problem 1, the performance of the centrality-based heuristic algorithms is more sensitive to the network structure and the locations of competitors. [ABSTRACT FROM AUTHOR]

The inventory routing problem (IRP) arises in vendor-managed inventory systems, which is a combination of vehicle routing and inventory management. Differing from the traditional IRPs in which the time consumption in transportation is often ignored, in this paper, we take the time consumption into consideration, which brings the lead-time to replenishment. In this situation, the lead-time for replenishment depends on the routing decisions made by the vendor. Consequently, IRPs become more interesting because decisions on the replenishment quantity and routing depend more tightly on each other. The general case of the IRP with replenishment lead-time (i.e., one vendor and N retailers) is modeled mathematically. To solve the problem, first a simple case (i.e., one vendor and two retailers) is analyzed to obtain the theoretical optimal policy. By proving the K -convexity of the objective function, we confirm that the structure of the optimal replenishment and routing policy is of switching curve type. In this policy, the state space, which is composed of the inventory positions of the two retailers, is divided into several domains; and for inventory positions in each domain, there exists an optimal order-up-to level. This structure reveals, for managerial insight, that when lead-time is considered, the current routing decision is not independent of the previous one. Second, since the optimal policy is difficult to realize in practice, a myopic policy that is easier to implement is proposed and numerical experiments are conducted to examine the near-optimal performance of the myopic policy. Finally, the myopic policy is extended to a realistic-size IRP with replenishment lead-time (i.e., the IRP for the case of one vendor and multiple retailers) and a numerical example is provided to indicate the feasibility of the policy. [ABSTRACT FROM AUTHOR]

The extreme learning machine (ELM) has become one of the most important and popular algorithms of machine learning, because of its extremely fast training speed, good generalization, and universal approximation/classification capability. The proposal of hierarchical ELM (H-ELM) extends ELM from single hidden layer feedforward networks to multilayer perceptron, greatly strengthening the applicability of ELM. Generally speaking, during training H-ELM, large-scale datasets (DSTs) are needed. Therefore, how to make use of H-ELM framework in processing big data is worth further exploration. This paper proposes a parallel H-ELM algorithm based on Flink, which is one of the in-memory cluster computing platforms, and graphics processing units (GPUs). Several optimizations are adopted to improve the performance, such as cache-based scheme, reasonable partitioning strategy, memory mapping scheme for mapping specific Java virtual machine objects to buffers. Most importantly, our proposed framework for utilizing GPUs to accelerate Flink for big data is general. This framework can be utilized to accelerate many other variants of ELM and other machine learning algorithms. To the best of our knowledge, it is the first kind of library, which combines in-memory cluster computing with GPUs to parallelize H-ELM. The experimental results have demonstrated that our proposed GPU-accelerated parallel H-ELM named as GPH-ELM can efficiently process large-scale DSTs with good performance of speedup and scalability, leveraging the computing power of both CPUs and GPUs in the cluster. [ABSTRACT FROM AUTHOR]

Decomposed fuzzy system (DFS) is a fuzzy system with a novel structure. Due to its excellent learning performance, DFS is originally proposed for an online learning control scheme and is shown to have effective learning performance. This paper is about the use of DFS for modeling dynamic systems. Since the learning mechanism used in online learning control is not suitable for modeling tasks, a commonly used back propagation learning algorithm is adapted for the use of DFS in modeling dynamic systems. The structure of DFS is to decompose each fuzzy variable into fuzzy subsystems that are called component fuzzy systems. Owing to the independency among component fuzzy systems, the learning for those parameters is also independent among different component fuzzy systems and thus, the learning can become more efficient. From the simulation results, it is evident that the proposed DFS can have much faster convergent speed. In addition, the DFS has a smaller testing error than those of other fuzzy systems. [ABSTRACT FROM PUBLISHER]

In this paper, we present error bound analysis of the Q -function for the action-dependent adaptive dynamic programming for solving discounted optimal control problems of unknown discrete-time nonlinear systems. The convergence of Q -functions derived by a policy iteration algorithm under ideal conditions is given. Considering the approximated errors of the Q -function and control policy in the policy evaluation step and policy improvement step, we establish error bounds of approximate Q -functions in each iteration. With the given boundedness conditions, the approximate Q -function will converge to a finite neighborhood of the optimal Q -function. To implement the presented algorithm, two three-layer neural networks are employed to approximate the Q -function and the control policy, respectively. Finally, a simulation example is utilized to verify the validity of the presented algorithm. [ABSTRACT FROM AUTHOR]

Recently, Shabtay considered a scheduling problem on a single serial-batching machine with rejection to minimize the dual criteria of total completion time and total rejection cost, where the number of jobs to be included in each batch is not restricted. He studied four variants of the problem: the first is to minimize the sum of the two criteria; the second and third are to minimize one criterion, subject to the other criterion not exceeding a given value; and the last is to find the Pareto-optimal solutions for the bicriterion problem. Shabtay provided an O ( \textitn^\mathbf 5 ) algorithm for the first variant and an O ( n ^\mathbf 6/\boldsymbol \varepsilon ^\mathbf 2 ) fully polynomial-time approximation scheme (FPTAS) for the fourth variant. In this paper, we provide an alternative O ( n ^\mathbf 4 ) algorithm to solve the first variant and an O ( n ^\mathbf 5/\boldsymbol \varepsilon ) FPTAS for the fourth variant, which are more efficient than those developed by Shabtay from a theoretical perspective. However, when the size of each batch is bounded by a given number b~\boldsymbol >1 , the corresponding time complexities of our algorithms for the first and fourth variants reduce to O (bn ^\mathbf 3 ) and O (bn ^\mathbf 4/\boldsymbol \varepsilon ), respectively. [ABSTRACT FROM AUTHOR]

Aimed at the tremendous challenge of attribute reduction for big data mining and knowledge discovery, we propose a new attribute equilibrium dominance reduction accelerator (DCCAEDR) based on the distributed coevolutionary cloud model. First, the framework of N -populations distributed coevolutionary MapReduce model is designed to divide the entire population into N subpopulations, sharing the reward of different subpopulations’ solutions under a MapReduce cloud mechanism. Because the adaptive balancing between exploration and exploitation can be achieved in a better way, the reduction performance is guaranteed to be the same as those using the whole independent data set. Second, a novel Nash equilibrium dominance strategy of elitists under the N bounded rationality regions is adopted to assist the subpopulations necessary to attain the stable status of Nash equilibrium dominance. This further enhances the accelerator’s robustness against complex noise on big data. Third, the approximation parallelism mechanism based on MapReduce is constructed to implement rule reduction by accelerating the computation of attribute equivalence classes. Consequently, the entire attribute reduction set with the equilibrium dominance solution can be achieved. Extensive simulation results have been used to illustrate the effectiveness and robustness of the proposed DCCAEDR accelerator for attribute reduction on big data. Furthermore, the DCCAEDR is applied to solve attribute reduction for traditional Chinese medical records and to segment cortical surfaces of the neonatal brain 3-D-MRI records, and the DCCAEDR shows the superior competitive results, when compared with the representative algorithms. [ABSTRACT FROM AUTHOR]