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This paper presents the integration of reinforcement learning-based differential evolution (DE) with the cooperative coevolution (R-CCDE) method in a compensatory neuro-fuzzy controller (CNFC). The CNFC model employs compensatory fuzzy operations, which increase the adaptability and effectiveness of the controller. The R-CCDE method was used to determine an adequate control policy for nonlinear system problems. The evolution of a population involved the use of DE with cooperative coevolution to adjust CNFC parameters, and the fitness function of the R-CCDE method is used by a reinforcement signal to determine the controller that can be used to solve the control problem. This paper identified the best performing controller to solve nonlinear system problems. The simulation results of the proposed R-CCDE method were compared with those of various DE methods and the performance of the proposed R-CCDE method was superior to that of the other methods. [ABSTRACT FROM AUTHOR]

Active learning (AL) is a machine-learning approach for reducing the data labeling effort. Given a pool of unlabeled samples, it tries to select the most useful ones to label so that a model built from them can achieve the best possible performance. This paper focuses on pool-based sequential AL for regression (ALR). We first propose three essential criteria that an ALR approach should consider in selecting the most useful unlabeled samples: informativeness, representativeness, and diversity, and compare four existing ALR approaches against them. We then propose a new ALR approach using passive sampling, which considers both the representativeness and the diversity in both the initialization and subsequent iterations. Remarkably, this approach can also be integrated with other existing ALR approaches in the literature to further improve the performance. Extensive experiments on 11 University of California, Irvine, Carnegie Mellon University StatLib, and University of Florida Media Core data sets from various domains verified the effectiveness of our proposed ALR approaches. [ABSTRACT FROM AUTHOR]

Linear discriminant analysis (LDA) is a well-known technique for linear classification, feature extraction, and dimension reduction. To improve the accuracy of LDA under the high dimension low sample size (HDLSS) settings, shrunken estimators, such as Graphical Lasso, can be used to strike a balance between biases and variances. Although the estimator with induced sparsity obtains a faster convergence rate, however, the introduced bias may also degrade the performance. In this paper, we theoretically analyze how the sparsity and the convergence rate of the precision matrix (also known as inverse covariance matrix) estimator would affect the classification accuracy by proposing an analytic model on the upper bound of an LDA misclassification rate. Guided by the model, we propose a novel classifier, $\mathcal {DBSDA}$ , which improves classification accuracy through debiasing. Theoretical analysis shows that $\mathcal {DBSDA}$ possesses a reduced upper bound of misclassification rate and better asymptotic properties than sparse LDA (SDA). We conduct experiments on both synthetic datasets and real application datasets to confirm the correctness of our theoretical analysis and demonstrate the superiority of $\mathcal {DBSDA}$ over LDA, SDA, and other downstream competitors under HDLSS settings. [ABSTRACT FROM AUTHOR]

Most learning methods contain optimization as a substep, where the nondifferentiability and multimodality of objectives push forward the interplay of evolutionary optimization algorithms and machine learning models. The recently emerged evolutionary multimodal optimization (MMOP) technique enables the learning of diverse sets of effective parameters for the models simultaneously, providing new opportunities to the applications requiring both accuracy and diversity, such as ensemble, interactive, and interpretive learning. Targeting at locating multiple optima simultaneously in the multimodal landscape, this paper develops an efficient neighborhood-based niching algorithm. Bare-bones differential evolution is used as the baseline. Further, using Gaussian mutation with local mean and standard deviations, the neighborhoods capture niches that match well with the contours of peaks in the landscape. To increase diversity and enhance global exploration, the proposed algorithm embeds a diversity preserving operator to reinitialize converged or overlapped neighborhoods. The experimental results verify that the proposed algorithm has superior and consistent performance for a wide range of MMOP problems. Further, the algorithm has been successfully applied to train neural network ensembles, which validates its effectiveness and benefits of learning multimodal parameters. [ABSTRACT FROM AUTHOR]

This paper considers the consensus behavior of a spatially distributed 3-D dynamical network composed of heterogeneous agents: leaders and followers, in which the leaders have the preferred information about the destination, while the followers do not have. All followers move in a 3-D Euclidean space with a given speed and with their headings updated according to the average velocity of the corresponding neighbors. Compared with the 2-D model, a key point lies in how to analyze the dynamical behavior of a “linear” nonhomogeneous equation where the nonhomogeneous term strongly nonlinearly depends on the states of all agents. Using the network structure and the estimation of some characteristics for the initial states, we present a proper decaying rate for the nonhomogeneous term and then establish lower bounds on the ratio of the number of leaders to the number of followers that is needed for the expected consensus by considering two cases: 1) fixed speed and neighborhood radius and 2) variable speed and neighborhood radius with respect to the population size. Some simulation examples are given to justify the theoretical results. [ABSTRACT FROM PUBLISHER]

Nonnegative matrix factorization (NMF) is an advanced method for nonnegative feature extraction, with widespread applications. However, the NMF solution often entails to solve a global optimization problem with a nonconvex objective function and nonnegativity constraints. This paper presents a collective neurodynamic optimization (CNO) approach to this challenging problem. The proposed collective neurodynamic system consists of a population of recurrent neural networks (RNNs) at the lower level and a particle swarm optimization (PSO) algorithm with wavelet mutation at the upper level. The RNNs act as search agents carrying out precise local searches according to their neurodynamics and initial conditions. The PSO algorithm coordinates and guides the RNNs with updated initial states toward global optimal solution(s). A wavelet mutation operator is added to enhance PSO exploration diversity. Through iterative interaction and improvement of the locally best solutions of RNNs and global best positions of the whole population, the population-based neurodynamic systems are almost sure able to achieve the global optimality for the NMF problem. It is proved that the convergence of the group-best state to the global optimal solution with probability one. The experimental results substantiate the efficacy and superiority of the CNO approach to bound-constrained global optimization with several benchmark nonconvex functions and NMF-based clustering with benchmark data sets in comparison with the state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

Effective hashing for large-scale image databases is a popular research area, attracting much attention in computer vision and visual information retrieval. Several recent methods attempt to learn either graph embedding or semantic coding for fast and accurate applications. In this paper, a novel unsupervised framework, termed evolutionary compact embedding (ECE), is introduced to automatically learn the task-specific binary hash codes. It can be regarded as an optimization algorithm that combines the genetic programming (GP) and a boosting trick. In our architecture, each bit of ECE is iteratively computed using a weak binary classification function, which is generated through GP evolving by jointly minimizing its empirical risk with the AdaBoost strategy on a training set. We address this as greedy optimization by embedding high-dimensional data points into a similarity-preserved Hamming space with a low dimension. We systematically evaluate ECE on two data sets, SIFT 1M and GIST 1M, showing the effectiveness and the accuracy of our method for a large-scale similarity search. [ABSTRACT FROM PUBLISHER]

Pairwise-interaction graphical games have been widely used in the study and design of strategic interaction in multiagent systems. With regard to this issue, one entitative problem is actually to understand how the interaction structure of agents affects the strategy configuration of Nash equilibria. This paper intends to study the effect of interaction networks on Nash equilibria in pairwise-interaction graphical games. We first show that interaction networks may induce new strategy equilibria in pairwise-interaction graphical games and then provide graphical conditions for the existence of these network-induced equilibria. Furthermore, to determine Nash equilibria of pairwise-interaction graphical games, a graphical replicator dynamics model is formulated, and its connection with graphical games is established. In detail, it is shown that every Nash equilibrium of the graphical games corresponds to a fixed point of the graphical replicator dynamics and that every asymptotically stable fixed point of the graphical replicator dynamics corresponds to a strict pure Nash equilibrium of the graphical games. The obtained results are applied in understanding coordination in complex networks and determination of structural conflicts in signed graphs. This work may provide new insights into understanding and designing strategy equilibria and dynamics in games on networks. [ABSTRACT FROM AUTHOR]

In dynamic optimization problems (DOPs), as the environment changes through time, the optima also dynamically change. How to adapt to the dynamic environment and quickly find the optima in all environments is a challenging issue in solving DOPs. Usually, a new environment is strongly relevant to its previous environment. If we know how it changes from the previous environment to the new one, then we can transfer the information of the previous environment, e.g., past solutions, to get new promising information of the new environment, e.g., new high-quality solutions. Thus, in this paper, we propose a neural network (NN)-based information transfer method, named NNIT, to learn the transfer model of environment changes by NN and then use the learned model to reuse the past solutions. When the environment changes, NNIT first collects the solutions from both the previous environment and the new environment and then uses an NN to learn the transfer model from these solutions. After that, the NN is used to transfer the past solutions to new promising solutions for assisting the optimization in the new environment. The proposed NNIT can be incorporated into population-based evolutionary algorithms (EAs) to solve DOPs. Several typical state-of-the-art EAs for DOPs are selected for comprehensive study and evaluated using the widely used moving peaks benchmark. The experimental results show that the proposed NNIT is promising and can accelerate algorithm convergence. [ABSTRACT FROM AUTHOR]

Collaboration enables weak species to survive in an environment where different species compete for limited resources. Cooperative coevolution (CC) is a nature-inspired optimization method that divides a problem into subcomponents and evolves them while genetically isolating them. Problem decomposition is an important aspect in using CC for neuroevolution. CC employs different problem decomposition methods to decompose the neural network training problem into subcomponents. Different problem decomposition methods have features that are helpful at different stages in the evolutionary process. Adaptation, collaboration, and competition are needed for CC, as multiple subpopulations are used to represent the problem. It is important to add collaboration and competition in CC. This paper presents a competitive CC method for training recurrent neural networks for chaotic time-series prediction. Two different instances of the competitive method are proposed that employs different problem decomposition methods to enforce island-based competition. The results show improvement in the performance of the proposed methods in most cases when compared with standalone CC and other methods from the literature. [ABSTRACT FROM PUBLISHER]

Recently, Dufrenois and Noyer proposed a one class Fisher’s linear discriminant to isolate normal data from outliers. In this paper, a kernelized version of their criterion is presented. Originally on the basis of an iterative optimization process, alternating between subspace selection and clustering, I show here that their criterion has an upper bound making these two problems independent. In particular, the estimation of the label vector is formulated as an unconstrained binary linear problem (UBLP) which can be solved using an iterative perturbation method. Once the label vector is estimated, an optimal projection subspace is obtained by solving a generalized eigenvalue problem. Like many other kernel methods, the performance of the proposed approach depends on the choice of the kernel. Constructed with a Gaussian kernel, I show that the proposed contrast measure is an efficient indicator for selecting an optimal kernel width. This property simplifies the model selection problem which is typically solved by costly (generalized) cross-validation procedures. Initialization, convergence analysis, and computational complexity are also discussed. Lastly, the proposed algorithm is compared with recent novelty detectors on synthetic and real data sets. [ABSTRACT FROM PUBLISHER]

The multivalued neuron with periodic activation function (MVN-P) was proposed by Aizenberg for solving classification problems. The boundaries between two distinct categories are crisply specified in MVN-P, which may result in slow convergence or being unable to converge at all in the learning process. In this paper, we propose a revised model of MVN-P based on the idea of unsharp boundaries. In this revised model, a fuzzy buffer is provided around a boundary between two distinct categories, allowing incorrect assignments with membership degree less than a threshold to be tolerated in the training phase. Genetic algorithms are applied to derive optimal values for the parameters involved in this model, alleviating the burden of setting them manually by the user. Besides, MVN-P has difficulties solving the classification problems having a large number of categories. A tree structure is developed to overcome these difficulties. Simulation results demonstrate the effectiveness of our proposed ideas. [ABSTRACT FROM AUTHOR]

Feature extraction is the first and most critical step in image classification. Most existing image classification methods use hand-crafted features, which are not adaptive for different image domains. In this paper, we develop an evolutionary learning methodology to automatically generate domain-adaptive global feature descriptors for image classification using multiobjective genetic programming (MOGP). In our architecture, a set of primitive 2-D operators are randomly combined to construct feature descriptors through the MOGP evolving and then evaluated by two objective fitness criteria, i.e., the classification error and the tree complexity. After the entire evolution procedure finishes, the best-so-far solution selected by the MOGP is regarded as the (near-)optimal feature descriptor obtained. To evaluate its performance, the proposed approach is systematically tested on the Caltech-101, the MIT urban and nature scene, the CMU PIE, and Jochen Triesch Static Hand Posture II data sets, respectively. Experimental results verify that our method significantly outperforms many state-of-the-art hand-designed features and two feature learning techniques in terms of classification accuracy. [ABSTRACT FROM AUTHOR]

This paper presents a Gaussian classifier-based evolutionary strategy (GCES) to solve multimodal optimization problems. An evolutionary technique for them must answer two crucial questions to guarantee its success: how to distinguish among the different basins of attraction and how to safeguard the already discovered good-quality solutions including both global and local optima. In GCES, multimodal optimization problems are regarded as classification ones, and Gaussian mixture models are employed to save the locations and basins of already and presently identified local or global optima. A sequential estimation technique for the covariance of a Gaussian model is introduced into GCES. To best adjust the global step size, a strategy named top-ranked sample selection is introduced, and a classification method instead of a common but problematic radius-triggered manner is proposed. Experiments are performed on a series of benchmark test functions to compare GCES with the state-of-the-art multimodal optimization approaches. The results show that GCES is not only simple to program and understand, but also provides better and consistent performance. [ABSTRACT FROM AUTHOR]

This paper presents an enhanced rank-order-based learning algorithm, called SpikeTemp, for spiking neural networks (SNNs) with a dynamically adaptive structure. The trained feed-forward SNN consists of two layers of spiking neurons: 1) an encoding layer which temporally encodes real-valued features into spatio-temporal spike patterns and 2) an output layer of dynamically grown neurons which perform spatio-temporal classification. Both Gaussian receptive fields and square cosine population encoding schemes are employed to encode real-valued features into spatio-temporal spike patterns. Unlike the rank-order-based learning approach, SpikeTemp uses the precise times of the incoming spikes for adjusting the synaptic weights such that early spikes result in a large weight change and late spikes lead to a smaller weight change. This removes the need to rank all the incoming spikes and, thus, reduces the computational cost of SpikeTemp. The proposed SpikeTemp algorithm is demonstrated on several benchmark data sets and on an image recognition task. The results show that SpikeTemp can achieve better classification performance and is much faster than the existing rank-order-based learning approach. In addition, the number of output neurons is much smaller when the square cosine encoding scheme is employed. Furthermore, SpikeTemp is benchmarked against a selection of existing machine learning algorithms, and the results demonstrate the ability of SpikeTemp to classify different data sets after just one presentation of the training samples with comparable classification performance. [ABSTRACT FROM PUBLISHER]

An accurate and noninvasive stress assessment from human physiology is a strenuous task. In this paper, a pattern recognition system to learn complex correlates between heart rate variability (HRV) features and salivary stress biomarkers is proposed. Using the Trier social stress test, heart rate and salivary measurements were obtained from volunteers under varying levels of stress induction. Measurements of salivary alpha-amylase and cortisol were used as objective measures of stress, and were correlated with the HRV features using fuzzy ARTMAP (FAM). In improving the predictive ability of the ARTMAPs, techniques, such as genetic algorithms for parameter optimization and voting ensembles, were employed. The ensemble of FAMs can be used for predicting stress responses of salivary alpha-amylase or cortisol using heart rate measurements as the input. Using alpha-amylase as the stress indicator, the ensemble was able to classify stress from heart rate features with 75% accuracy, and 80% accuracy when cortisol was used. [ABSTRACT FROM AUTHOR]

The increasing liberalization of European electricity markets, the growing proportion of intermittent renewable energy being fed into the energy grids, and also new challenges in the patterns of energy consumption (such as electric mobility) require flexible and intelligent power grids capable of providing efficient, reliable, economical, and sustainable energy production and distribution. From the supplier side, particularly, the integration of renewable energy sources (e.g., wind and solar) into the grid imposes an engineering and economic challenge because of the limited ability to control and dispatch these energy sources due to their intermittent characteristics. Time-series prediction of wind speed for wind power production is a particularly important and challenging task, wherein prediction intervals (PIs) are preferable results of the prediction, rather than point estimates, because they provide information on the confidence in the prediction. In this paper, two different machine learning approaches to assess PIs of time-series predictions are considered and compared: 1) multilayer perceptron neural networks trained with a multiobjective genetic algorithm and 2) extreme learning machines combined with the nearest neighbors approach. The proposed approaches are applied for short-term wind speed prediction from a real data set of hourly wind speed measurements for the region of Regina in Saskatchewan, Canada. Both approaches demonstrate good prediction precision and provide complementary advantages with respect to different evaluation criteria. [ABSTRACT FROM PUBLISHER]

In this article, we study the problem of guaranteed display ads (GDAs) allocation, which requires proactively allocate display ads to different impressions to fulfill their impression demands indicated in the contracts. Existing methods for this problem either assume the impressions that are static or solely consider a specific ad’s benefits. Thus, it is hard to generalize to the industrial production scenario where the impressions are dynamical and large-scale, and the overall allocation optimality of all the considered GDAs is required. To bridge this gap, we formulate this problem as a sequential decision-making problem in the scope of multiagent reinforcement learning (MARL), by assigning an allocation agent to each ad and coordinating all the agents for allocating GDAs. The inputs are the states (e.g., the demands of the ad and the remaining time steps for displaying the ads) of each ad and the impressions at different time steps, and the outputs are the display ratios of each ad for each impression. Specifically, we propose a novel hierarchical MARL (HMARL) method that creates hierarchies over the agent policies to handle a large number of ads and the dynamics of impressions. HMARL contains: 1) a manager policy to navigate the agent to choose an appropriate subpolicy and 2) a set of subpolicies that let the agents perform diverse conditioning on their states. Extensive experiments on three real-world data sets from the Tencent advertising platform with tens of millions of records demonstrate significant improvements of HMARL over state-of-the-art approaches. [ABSTRACT FROM AUTHOR]

The evolutionarily stable strategy (ESS) of networked evolutionary games (NEGs) is studied. Analyzing the ESS of infinite popular evolutionary games and comparing it with networked games, a new verifiable definition of ESS for NEGs is proposed. Then, the fundamental evolutionary equation (FEE) is investigated and used to construct the strategy profile dynamics (SPDs) of homogeneous NEGs. Two ways for verifying the ESS are proposed: 1) using the SPDs to verify it directly. The SPDs provides complete information about the NEGs, and then necessary and sufficient conditions are revealed. It can be used for NEGs with small size and 2) some sufficient conditions are proposed to verify the ESS of NEGs via their FEEs. This method is particularly suitable for large scale networks. Some illustrative examples are included to demonstrate the theoretical results. [ABSTRACT FROM AUTHOR]

Federated learning (FL) is currently the most widely adopted framework for collaborative training of (deep) machine learning models under privacy constraints. Albeit its popularity, it has been observed that FL yields suboptimal results if the local clients’ data distributions diverge. To address this issue, we present clustered FL (CFL), a novel federated multitask learning (FMTL) framework, which exploits geometric properties of the FL loss surface to group the client population into clusters with jointly trainable data distributions. In contrast to existing FMTL approaches, CFL does not require any modifications to the FL communication protocol to be made, is applicable to general nonconvex objectives (in particular, deep neural networks), does not require the number of clusters to be known a priori, and comes with strong mathematical guarantees on the clustering quality. CFL is flexible enough to handle client populations that vary over time and can be implemented in a privacy-preserving way. As clustering is only performed after FL has converged to a stationary point, CFL can be viewed as a postprocessing method that will always achieve greater or equal performance than conventional FL by allowing clients to arrive at more specialized models. We verify our theoretical analysis in experiments with deep convolutional and recurrent neural networks on commonly used FL data sets. [ABSTRACT FROM AUTHOR]

Studies of structural connectivity at the synaptic level show that in synaptic connections of the cerebral cortex, the excitatory postsynaptic potential (EPSP) in most synapses exhibits sub-mV values, while a small number of synapses exhibit large EPSPs (≳ 1.0 [mV]). This means that the distribution of EPSP fits a log-normal distribution. While not restricting structural connectivity, skewed and long-tailed distributions have been widely observed in neural activities, such as the occurrences of spiking rates and the size of a synchronously spiking population. Many studies have been modeled this long-tailed EPSP neural activity distribution; however, its causal factors remain controversial. This study focused on the long-tailed EPSP distributions and interlateral synaptic connections primarily observed in the cortical network structures, thereby having constructed a spiking neural network consistent with these features. Especially, we constructed two coupled modules of spiking neural networks with excitatory and inhibitory neural populations with a log-normal EPSP distribution. We evaluated the spiking activities for different input frequencies and with/without strong synaptic connections. These coupled modules exhibited intermittent intermodule-alternative behavior, given moderate input frequency and the existence of strong synaptic and intermodule connections. Moreover, the power analysis, multiscale entropy analysis, and surrogate data analysis revealed that the long-tailed EPSP distribution and intermodule connections enhanced the complexity of spiking activity at large temporal scales and induced nonlinear dynamics and neural activity that followed the long-tailed distribution. [ABSTRACT FROM AUTHOR]

We analyze the learning problem of one-hidden-layer nonoverlapping convolutional neural networks with the rectified linear unit (ReLU) activation function from the perspective of model estimation. The training outputs are assumed to be generated by the neural network with the unknown ground-truth parameters plus some additive noise, and the objective is to estimate the model parameters by minimizing a nonconvex squared loss function of the training data. Assuming that the training set contains a finite number of samples generated from the Gaussian distribution, we prove that the accelerated gradient descent (GD) algorithm with a proper initialization converges to the ground-truth parameters (up to the noise level) with a linear rate even though the learning problem is nonconvex. Moreover, the convergence rate is proved to be faster than the vanilla GD. The initialization can be achieved by the existing tensor initialization method. In contrast to the existing works that assume an infinite number of samples, we theoretically establish the sample complexity of the required number of training samples. Although the neural network considered here is not deep, this is the first work to show that accelerated GD algorithms can find the global optimizer of the nonconvex learning problem of neural networks. This is also the first work that characterizes the sample complexity of gradient-based methods in learning convolutional neural networks with the nonsmooth ReLU activation function. This work also provides the tightest bound so far of the estimation error with respect to the output noise. [ABSTRACT FROM AUTHOR]

In this article, a new deep neural network based on sparse filtering and manifold regularization (DSMR) is proposed for feature extraction and classification of polarimetric synthetic aperture radar (PolSAR) data. DSMR uses a novel deep neural network (DNN) to automatically learn features from raw SAR data. During preprocessing, the spatial information between pixels on PolSAR images is exploited to weight each data sample. Then, in the pretraining and fine-tuning, DSMR uses the population sparsity and the lifetime sparsity (dual sparsity) to learn the global features and preserves the local structure of data by neighborhood-based manifold regularization. The dual sparsity only needs to tune a few parameters, and the manifold regularization cuts down the number of training samples. Experimental results on synthesized and real PolSAR data sets from different SAR systems show that DSMR can improve classification accuracy compared with conventional DNNs, even for data sets with a large angle of incidence. [ABSTRACT FROM AUTHOR]

A new evolutionary-learning algorithm is proposed to learn a decision maker (DM)’s best solution on a conflicting multiobjective space. Given the exemplary pairwise comparisons of solutions by a DM, we learn an ideal point (for the DM) that is used to evolve toward a better set of solutions. The process is repeated to get the DM’s best solution. The comparison of solutions in pairs facilitates the process of eliciting training information for the proposed learning model. Experimental study on standard multiobjective data sets shows that the proposed method accurately identifies a DM’s preferred zone in relatively a few generations and with a small number of preferences. Besides, it is found to be robust to inconsistencies in the preference statements. The results obtained are validated through a variant of the established NSGA-2 algorithm. [ABSTRACT FROM AUTHOR]

Population coding is a method to represent stimuli using the collective activities of a number of neurons. Nevertheless, it is difficult to extract information from these population codes with the noise inherent in neuronal responses. Moreover, it is a challenge to identify the right parameter of the decoding model, which plays a key role for convergence. To address the problem, a population decoding model is proposed for parameter selection. Our method successfully identified the key conditions for a nonzero continuous attractor. Both the theoretical analysis and the application studies demonstrate the correctness and effectiveness of this strategy. [ABSTRACT FROM PUBLISHER]

We consider the task of performing prediction with neural networks (NNs) on the basis of uncertain input data expressed in the form of intervals. We aim at quantifying the uncertainty in the prediction arising from both the input data and the prediction model. A multilayer perceptron NN is trained to map interval-valued input data onto interval outputs, representing the prediction intervals (PIs) of the real target values. The NN training is performed by nondominated sorting genetic algorithm-II, so that the PIs are optimized both in terms of accuracy (coverage probability) and dimension (width). Demonstration of the proposed method is given in two case studies: 1) a synthetic case study, in which the data have been generated with a 5-min time frequency from an autoregressive moving average model with either Gaussian or Chi-squared innovation distribution and 2) a real case study, in which experimental data consist of wind speed measurements with a time step of 1 h. Comparisons are given with a crisp (single-valued) approach. The results show that the crisp approach is less reliable than the interval-valued input approach in terms of capturing the variability in input. [ABSTRACT FROM PUBLISHER]

Information processing in the nervous system involves the activity of large populations of neurons. It is difficult to extract information from these population codes because of the noise inherent in neuronal responses. We propose a divisive normalization model to read the population codes. The dynamics of the model are analyzed by continuous attractor theory. Under certain conditions, the model possesses continuous attractors. Moreover, the explicit expressions of the continuous attractors are provided. Simulations are employed to illustrate the theory. [ABSTRACT FROM AUTHOR]