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This paper presents a new evolutionary approach called the hybrid evolutionary artificial neural network (HEANN) for simultaneously evolving an artificial neural networks (ANNs) topology and weights. Evolutionary algorithms (EAs) with strong global search capabilities are likely to provide the most promising region. However, they are less efficient in fine-tuning the search space locally. HEANN emphasizes the balancing of the global search and local search for the evolutionary process by adapting the mutation probability and the step size of the weight perturbation. This is distinguishable from most previous studies that incorporate EA to search for network topology and gradient learning for weight updating. Four benchmark functions were used to test the evolutionary framework of HEANN. In addition, HEANN was tested on seven classification benchmark problems from the UCI machine learning repository. Experimental results show the superior performance of HEANN in fine-tuning the network complexity within a small number of generations while preserving the generalization capability compared with other algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we consider a new periodic activation function for the multivalued neuron (MVN). The MVN is a neuron with complex-valued weights and inputs/output, which are located on the unit circle. Although the MVN outperforms many other neurons and MVN-based neural networks have shown their high potential, the MVN still has a limited capability of learning highly nonlinear functions. A periodic activation function, which is introduced in this paper, makes it possible to learn nonlinearly separable problems and non-threshold multiple-valued functions using a single multivalued neuron. We call this neuron a multivalued neuron with a periodic activation function (MVN-P). The MVN-Ps functionality is much higher than that of the regular MVN. The MVN-P is more efficient in solving various classification problems. A learning algorithm based on the error-correction rule for the MVN-P is also presented. It is shown that a single MVN-P can easily learn and solve those benchmark classification problems that were considered unsolvable using a single neuron. It is also shown that a universal binary neuron, which can learn nonlinearly separable Boolean functions, and a regular MVN are particular cases of the MVN-P. [ABSTRACT FROM AUTHOR]

Support vector machines (SVMs) have been extensively used. However, it is known that SVMs face difficulty in solving large complex problems due to the intensive computation involved in their training algorithms, which are at least quadratic with respect to the number of training examples. This paper proposes a new, simple, and efficient network architecture which consists of several SVMs each trained on a small subregion of the whole data sampling space and the same number of simple neural quantizer modules which inhibit the outputs of all the remote SVMs and only allow a single local SVM to fire (produce actual output) at any time. In principle, this region-computing based modular network method can significantly reduce the learning time of SYM algorithms without sacrificing much generalization performance. The experiments on a few real large complex bench- mark problems demonstrate that our method can be significantly faster than single SVMs without losing much generalization performance. [ABSTRACT FROM AUTHOR]

In a recent paper, De Jesús et al. proposed a general frame-work for describing dynamic neural networks. Gradient and Jacobian calculations were discussed based on backpropagation-through-time (BPTT) algorithm and real-time recurrent learning (RTRL). Some errors in the paper of De Jesús et al. bring difficulties for other researchers who want to implement the algorithms. This comments paper shows the critical parts of the publication and gives errata to facilitate understanding and implementation. [ABSTRACT FROM AUTHOR]

In this paper, we analyze a model of recurrent kernel associative memory (RKAM) recently proposed by Garcia and Moreno. We show that this model consists in a kernelization of the recurrent correlation associative memory (RCAM) of Chiueh and Goodman. In particular, using an exponential kernel, we obtain a generalization of the well-known exponential correlation associative memory (ECAM), while using a polynomial kernel, we obtain a generalization of higher order Hopfield networks with Hebbian weights. We show that the RKAM can outperform the aforementioned associative memory models, becoming equivalent to them when a dominance condition is fulfilled by the kernel matrix. To ascertain the dominance condition, we propose a statistical measure which can be easily computed from the probability distribution of the interpattern Hamming distance or directly estimated from the memory vectors. The RKAM can be used below saturation to realize associative memories with reduced dynamic range with respect to the ECAM and with reduced number of synaptic coefficients with respect to higher order Hopfield networks. [ABSTRACT FROM AUTHOR]

The hierarchical graph neuron (HGN) implements a single cycle memorization and recall operation through a novel algorithmic design. The HGN is an improvement on the already published original graph neuron (GN) algorithm. In this improved approach, it recognizes incomplete/noisy patterns. It also resolves the crosstalk problem, which is identified in the previous publications, within closely matched patterns. To accomplish this, the HGN links multiple GN networks for filtering noise and crosstalk out of pattern data inputs. Intrinsically, the HGN is a lightweight in-network processing algorithm which does not require expensive floating point computations; hence, it is very suitable for real-time applications and tiny devices such as the wireless sensor networks. This paper describes that the HGN's pattern matching capability and the small response time remain insensitive to the increases in the number of stored patterns. Moreover, the HGN does not require definition of rules or setting of thresholds by the operator to achieve the desired results nor does it require heuristics entailing iterative operations for memorization and recall of patterns. [ABSTRACT FROM AUTHOR]

In this paper, we present an incremental method for model selection and learning of Gaussian mixtures based on the recently proposed variational Bayes approach. The method adds components to the mixture using a Bayesian splitting test procedure: a component is split into two components and then variational update equations are applied only to the parameters of the two components. As a result, either both components are retained in the model or one of them is found to be redundant and is eliminated from the model. In our approach, the model selection problem is treated locally, in a region of the data space, so we can set more informative priors based on the local data distribution. A modified Bayesian mixture model is presented to implement this approach, along with a learning algorithm that iteratively applies a splitting test on each mixture component. Experimental results and comparisons with two other techniques testify for the adequacy of the proposed approach. [ABSTRACT FROM AUTHOR]

Two backpropagation algorithms with momentum for feedforward neural networks with a single hidden layer are considered. It is assumed that the training samples are supplied to the network in a cyclic or an almost-cyclic fashion in the learning procedure, i.e., in each training cycle, each sample of the training set is supplied in a fixed or a stochastic order respectively to the network exactly once. A restart strategy for the momentum is adopted such that the momentum coefficient is set to zero at the beginning of each training cycle. Corresponding weak and strong convergence results are then proved, indicating that the gradient of the error function goes to zero and the weight sequence goes to a fixed point, respectively. The convergence conditions on the learning rate, the momentum coefficient, and the activation functions are much relaxed compared with those of the existing results. [ABSTRACT FROM AUTHOR]

Presents a systematic approach for construction reformulated radial basis function (RBF) neural networks, which was developed to facilitate their training by supervised learning algorithms based on gradient descent. Admissibility conditions for RBF; Estimation of the free parameters of RBF; Experimental results.

Neural network algorithms such as multilayer perceptrons (MLPs) and radial basis function networks (RBFNets) have been used to construct learners which exhibit strong predictive performance. Two data related issues that can have a detrimental impact on supervised learning initiatives are class imbalance and labeling errors (or class noise). Imbalanced data can make it more difficult for the neural network learning algorithms to distinguish between examples of the various classes, and class noise can lead to the formulation of incorrect hypotheses. Both class imbalance and labeling errors are pervasive problems encountered in a wide variety of application domains. Many studies have been performed to investigate these problems in isolation, but few have focused on their combined effects. This study presents a comprehensive empirical investigation using neural network algorithms to learn from imbalanced data with labeling errors. In particular, the first component of our study investigates the impact of class noise and class imbalance on two common neural network learning algorithms, while the second component considers the ability of data sampling (which is commonly used to address the issue of class imbalance) to improve their performances. Our results, for which over two million models were trained and evaluated, show that conclusions drawn using the more commonly studied C4.5 classifier may not apply when using neural networks. [ABSTRACT FROM AUTHOR]

As a typical data visualization technique, self-organizing map (SOM) has been extensively applied to data clustering, image analysis, dimension reduction, and so forth. In a conventional adaptive SOM, it needs to choose an appropriate learning rate whose value is monotonically reduced over time to ensure the convergence of the map, meanwhile being kept large enough so that the map is able to gradually learn the data topology. Otherwise, the SOM's performance may seriously deteriorate. In general, it is nontrivial to choose an appropriate monotonically decreasing function for such a learning rate. In this letter, we therefore propose a novel rival-model penalized self-organizing map (RPSOM) learning algorithm that, for each input, adaptively chooses several rivals of the best-matching unit (BMU) and penalizes their associated models, i.e., those parametric real vectors with the same dimension as the input vectors, a little far away from the input. Compared to the existing methods, this RPSOM utilizes a constant learning rate to circumvent the awkward selection of a monotonically decreased function for the learning rate, but still reaches a robust result. The numerical experiments have shown the efficacy of our algorithm. [ABSTRACT FROM AUTHOR]