A hierarchical method for finding optimal architecture and weights using evolutionary least square based learning

In this paper, we present a novel approach of implementing a combination methodology to find appropriate neural network architecture and weights using an evolutionary least square based algorithm (GALS).1 This paper focuses on aspects such as the heuristics of updating weights using an evolutionary least square based algorithm, finding the number of hidden neurons for a two layer feed forward neural network, the stopping criterion for the algorithm and finally some comparisons of the results with other existing methods for searching optimal or near optimal solution in the multidimensional complex search space comprising the architecture and the weight variables. We explain how the weight updating algorithm using evolutionary least square based approach can be combined with the growing architecture model to find the optimum number of hidden neurons. We also discuss the issues of finding a probabilistic solution space as a starting point for the least square method and address the problems involving fitness breaking. We apply the proposed approach to XOR problem, 10 bit odd parity problem and many real-world benchmark data sets such as handwriting data set from CEDAR, breast cancer and heart disease data sets from UCI ML repository. The comparative results based on classification accuracy and the time complexity are discussed.     

Short-term prediction of chaotic time series by using RBF network with regression weights

We propose a framework for constructing and training a radial basis function (RBF) neural network. The structure of the gaussian functions is modified using a pseudo-gaussian function (PG) in which two scaling parameters sigma are introduced, which eliminates the symmetry restriction and provides the neurons in the hidden layer with greater flexibility with respect to function approximation. We propose a modified PG-BF (pseudo-gaussian basis function) network in which the regression weights are used to replace the constant weights in the output layer. For this purpose, a sequential learning algorithm is presented to adapt the structure of the network, in which it is possible to create a new hidden unit and also to detect and remove inactive units. A salient feature of the network systems is that the method used for calculating the overall output is the weighted average of the output associated with each receptive field. The superior performance of the proposed PG-BF system over the standard RBF are illustrated using the problem of short-term prediction of chaotic time series.     

基于人工神经网络的非线性拟合方法ⅡBP学习算法中各因素的影响

本文研究了人工神经网络BP学习算法中动量因子、隐节点数、学习速率、激活因子等对网络学习速度有影响的几个因素,并且找出了最佳值．     

An improvement of extreme learning machine for compact single-hidden-layer feedforward neural networks

Recently, a novel learning algorithm called extreme learning machine (ELM) was proposed for efficiently training single-hidden-layer feedforward neural networks (SLFNs). It was much faster than the traditional gradient-descent-based learning algorithms due to the analytical determination of output weights with the random choice of input weights and hidden layer biases. However, this algorithm often requires a large number of hidden units and thus slowly responds to new observations. Evolutionary extreme learning machine (E-ELM) was proposed to overcome this problem; it used the differential evolution algorithm to select the input weights and hidden layer biases. However, this algorithm required much time for searching optimal parameters with iterative processes and was not suitable for data sets with a large number of input features. In this paper, a new approach for training SLFNs is proposed, in which the input weights and biases of hidden units are determined based on a fast regularized least-squares scheme. Experimental results for many real applications with both small and large number of input features show that our proposed approach can achieve good generalization performance with much more compact networks and extremely high speed for both learning and testing.     

Instabilities and oscillation in the deterministic Boltzmann machine

Simulations indicate that the deterministic Boltzmann machine, unlike the stochastic Boltzmann machine from which it is derived, exhibits unstable behavior during contrastive Hebbian learning of nonlinear problems, including oscillation in the learning algorithm and extreme sensitivity to small weight perturbations. Although careful choice of the initial weight magnitudes, the learning rate, and the annealing schedule will produce convergence in most cases, the stability of the resulting solution depends on the parameters in a complex and generally indiscernible way. We show that this unstable behavior is the result of over parameterization (excessive freedom in the weights), which leads to continuous rather than isolated optimal weight solution sets. This allows the weights to drift without correction by the learning algorithm until the free energy landscape changes in such a way that the settling procedure employed finds a different minimum of the free energy function than it did previously and a gross output error occurs. Because all the weight sets in a continuous optimal solution set produce exactly the same network outputs, we define reliability, a measure of the robustness of the network, as a new performance criterion.     

Implementing Gaussian process inference with neural networks

Gaussian processes compare favourably with backpropagation neural networks as a tool for regression, and Bayesian neural networks have Gaussian process behaviour when the number of hidden neurons tends to infinity. We describe a simple recurrent neural network with connection weights trained by one-shot Hebbian learning. This network amounts to a dynamical system which relaxes to a stable state in which it generates predictions identical to those of Gaussian process regression. In effect an infinite number of hidden units in a feed-forward architecture can be replaced by a merely finite number, together with recurrent connections.     

Emergence of clusters in the hidden layer of a dynamic recurrent neural network

The neural integrator of the oculomotor system is a privileged field for artificial neural network simulation. In this paper, we were interested in an improvement of the biologically plausible features of the Arnold-Robinson network. This improvement was done by fixing the sign of the connection weights in the network (in order to respect the biological Dale's Law). We also introduced a notion of distance in the network in the form of transmission delays between its units. These modifications necessitated the introduction of a general supervisor in order to train the network to act as a leaky integrator. When examining the lateral connection weights of the hidden layer, the distribution of the weights values was found to exhibit a conspicuous structure: the high-value weights were grouped in what we call clusters. Other zones are quite flat and characterized by low-value weights. Clusters are defined as particular groups of adjoining neurons which have strong and privileged connections with another neighborhood of neurons. The clusters of the trained network are reminiscent of the small clusters or patches that have been found experimentally in the nucleus prepositus hypoglossi, where the neural integrator is located. A study was conducted to determine the conditions of emergence of these clusters in our network: they include the fixation of the weight sign, the introduction of a distance, and a convergence of the information from the hidden layer to the motoneurons. We conclude that this spontaneous emergence of clusters in artificial neural networks, performing a temporal integration, is due to computational constraints, with a restricted space of solutions. Thus, information processing could induce the emergence of iterated patterns in biological neural networks. Received: 18 September 1996 / Accepted in revised form: 7 January 1997     

Rule extraction from minimal neural networks for credit card screening

While feedforward neural networks have been widely accepted as effective tools for solving classification problems, the issue of finding the best network architecture remains unresolved, particularly so in real-world problem settings. We address this issue in the context of credit card screening, where it is important to not only find a neural network with good predictive performance but also one that facilitates a clear explanation of how it produces its predictions. We show that minimal neural networks with as few as one hidden unit provide good predictive accuracy, while having the added advantage of making it easier to generate concise and comprehensible classification rules for the user. To further reduce model size, a novel approach is suggested in which network connections from the input units to this hidden unit are removed by a very straightaway pruning procedure. In terms of predictive accuracy, both the minimized neural networks and the rule sets generated from them are shown to compare favorably with other neural network based classifiers. The rules generated from the minimized neural networks are concise and thus easier to validate in a real-life setting.     

Artificial neural network based soft estimator for estimation of transducer static nonlinearity

In this work, the development of an Artificial Neural Network (ANN) based soft estimator is reported for the estimation of static-nonlinearity associated with the transducers. Under the realm of ANN based transducer modeling, only two neural models have been suggested to estimate the static-nonlinearity associated with the transducers with quite successful results. The first existing model is based on the concept of a functional link artificial neural network (FLANN) trained with mu-LMS (Least Mean Squares) learning algorithm. The second one is based on the architecture of a single layer linear ANN trained with alpha-LMS learning algorithm. However, both these models suffer from the problem of slow convergence (learning). In order to circumvent this problem, it is proposed to synthesize the direct model of transducers using the concept of a Polynomial-ANN (polynomial artificial neural network) trained with Levenberg-Marquardt (LM) learning algorithm. The proposed Polynomial-ANN oriented transducer model is implemented based on the topology of a single-layer feed-forward back-propagation-ANN. The proposed neural modeling technique provided an extremely fast convergence speed with increased accuracy for the estimation of transducer static nonlinearity. The results of convergence are very stimulating with the LM learning algorithm.     

Cooperative coevolution of neural representations

A genetic algorithm (GA) is used to search for a set of local feature detectors or hidden units. These are in turn employed as a representation of the input data for neural learning in the upper layer of a multilayer perceptron (MLP) which performs an image classification task. Three different methods of encoding hidden unit weights in the chromosome of the GA are presented, including one which coevolves all the feature detectors in a single chromosome, and two which promote the cooperation of feature detectors by encoding them in their own individual chromosomes. The fitness function measures the MLP classification accuracy together with the confidence of the networks.     

Back-Propagation Operation for Analog Neural Network Hardware with Synapse Components Having Hysteresis Characteristics

To realize an analog artificial neural network hardware, the circuit element for synapse function is important because the number of synapse elements is much larger than that of neuron elements. One of the candidates for this synapse element is a ferroelectric memristor. This device functions as a voltage controllable variable resistor, which can be applied to a synapse weight. However, its conductance shows hysteresis characteristics and dispersion to the input voltage. Therefore, the conductance values vary according to the history of the height and the width of the applied pulse voltage. Due to the difficulty of controlling the accurate conductance, it is not easy to apply the back-propagation learning algorithm to the neural network hardware having memristor synapses. To solve this problem, we proposed and simulated a learning operation procedure as follows. Employing a weight perturbation technique, we derived the error change. When the error reduced, the next pulse voltage was updated according to the back-propagation learning algorithm. If the error increased the amplitude of the next voltage pulse was set in such way as to cause similar memristor conductance but in the opposite voltage scanning direction. By this operation, we could eliminate the hysteresis and confirmed that the simulation of the learning operation converged. We also adopted conductance dispersion numerically in the simulation. We examined the probability that the error decreased to a designated value within a predetermined loop number. The ferroelectric has the characteristics that the magnitude of polarization does not become smaller when voltages having the same polarity are applied. These characteristics greatly improved the probability even if the learning rate was small, if the magnitude of the dispersion is adequate. Because the dispersion of analog circuit elements is inevitable, this learning operation procedure is useful for analog neural network hardware.     

Artificial neural network learning of nonstationary behavior in time series

We refine and complement a previously-proposed artificial neural network method for learning hidden signals forcing nonstationary behavior in time series. The method adds an extra input unit to the network and feeds it with the proposed profile for the unknown perturbing signal. The correct time evolution of this new input parameter is learned simultaneously with the intrinsic stationary dynamics underlying the series, which is accomplished by minimizing a suitably-defined error function for the training process. We incorporate here the use of validation data, held out from the training set, to accurately determine the optimal value of a hyperparameter required by the method. Furthermore, we evaluate this algorithm in a controlled situation and show that it outperforms other existing methods in the literature. Finally, we discuss a preliminary application to the real-world sunspot time series and link the obtained hidden perturbing signal to the secular evolution of the solar magnetic field.     

Intelligent scheduling of FMSs with inductive learning capability using neural networks

With the growing uncertainty and complexity in the manufacturing environment, most scheduling problems have been proven to be NP-complete and this can degrade the performance of conventional operations research (OR) techniques. This article presents a system-attribute-oriented knowledge-based scheduling system (SAOSS) with inductive learning capability. With the rich heritage from artificial intelligence (AI), SAOSS takes a multialgorithm paradigm which makes it more intelligent, flexible, and suitable than others for tackling complicated, dynamic scheduling problems. SAOSS employs an efficient and effective inductive learning method, a continuous iterative dichotomister 3 (CID3) algorithm, to induce decision rules for scheduling by converting corresponding decision trees into hidden layers of a self-generated neural network. Connection weights between hidden units imply the scheduling heuristics, which are then formulated into scheduling rules. An FMS scheduling problem is also given for illustration. The scheduling results show that the system-attribute-oriented knowledge-based approach is capable of addressing dynamic scheduling problems.     

Cross-validation of protein structural class prediction using statistical clustering and neural networks.

We present an approach to predicting protein structural class that uses amino acid composition and hydrophobic pattern frequency information as input to two types of neural networks: (1) a three-layer back-propagation network and (2) a learning vector quantization network. The results of these methods are compared to those obtained from a modified Euclidean statistical clustering algorithm. The protein sequence data used to drive these algorithms consist of the normalized frequency of up to 20 amino acid types and six hydrophobic amino acid patterns. From these frequency values the structural class predictions for each protein (all-alpha, all-beta, or alpha-beta classes) are derived. Examples consisting of 64 previously classified proteins were randomly divided into multiple training (56 proteins) and test (8 proteins) sets. The best performing algorithm on the test sets was the learning vector quantization network using 17 inputs, obtaining a prediction accuracy of 80.2%. The Matthews correlation coefficients are statistically significant for all algorithms and all structural classes. The differences between algorithms are in general not statistically significant. These results show that information exists in protein primary sequences that is easily obtainable and useful for the prediction of protein structural class by neural networks as well as by standard statistical clustering algorithms.     

Automatic determination of radial basis functions: an immunity-based approach

The appropriate operation of a radial basis function (RBF) neural network depends mainly upon an adequate choice of the parameters of its basis functions. The simplest approach to train an RBF network is to assume fixed radial basis functions defining the activation of the hidden units. Once the RBF parameters are fixed, the optimal set of output weights can be determined straightforwardly by using a linear least squares algorithm, which generally means reduction in the learning time as compared to the determination of all RBF network parameters using supervised learning. The main drawback of this strategy is the requirement of an efficient algorithm to determine the number, position, and dispersion of the RBFs. The approach proposed here is inspired by models derived from the vertebrate immune system, that will be shown to perform unsupervised cluster analysis. The algorithm is introduced and its performance is compared to that of the random, k-means center selection procedures and other results from the literature. By automatically defining the number of RBF centers, their positions and dispersions, the proposed method leads to parsimonious solutions. Simulation results are reported concerning regression and classification problems.     

A Lempel-Ziv complexity-based neural network pruning algorithm

This paper presents a pruning method for artificial neural networks (ANNs) based on the 'Lempel-Ziv complexity' (LZC) measure. We call this method the 'silent pruning algorithm' (SPA). The term 'silent' is used in the sense that SPA prunes ANNs without causing much disturbance during the network training. SPA prunes hidden units during the training process according to their ranks computed from LZC. LZC extracts the number of unique patterns in a time sequence obtained from the output of a hidden unit and a smaller value of LZC indicates higher redundancy of a hidden unit. SPA has a great resemblance to biological brains since it encourages higher complexity during the training process. SPA is similar to, yet different from, existing pruning algorithms. The algorithm has been tested on a number of challenging benchmark problems in machine learning, including cancer, diabetes, heart, card, iris, glass, thyroid, and hepatitis problems. We compared SPA with other pruning algorithms and we found that SPA is better than the 'random deletion algorithm' (RDA) which prunes hidden units randomly. Our experimental results show that SPA can simplify ANNs with good generalization ability.     

Development of predictive models of laboratory animal growth using artificial neural networks

Traditional regression analysis of body weight growth curvesencounters problems .when the data are extremely variable. Whiletransformations are often employed to meet the criteria of theanalysis, some transformations are inadequate for normalizingthe data. Regression analysis also requires presuppositionsregarding the model to be fit and the techniques to be usedin the analysis. An alternative approach using artificial neuralnetworks is presented which may be suitable for developing predictivemodels of growth. Neural networks are simulators of the processesthat occur in the biological brain during the learning process.They are trained on the data, developing the necessary algorithmswithin their internal architecture, and produce a predictivemodel based on the learned facts. A dataset of Sprague–Dawleyrat (Rattus norvegicus) weights is analyzed by both traditionalregression analysis and neural network training. Predictionsof body weight are made from both models. While both methodsproduce models that adequately predict the body weights, theneural network model is superior in that it combines accuracyand precision, being less influenced by longitudinal variabilityin the data. Thus, the neural network provides another toolfor researchers to analyze growth curve data.     

Comparison of different neural network algorithms in the diagnosis of acute appendicitis

Four different neural network algorithms, binary adaptive resonance theory (ART1), self-organizing map, learning vector quantization and back-propagation, were compared in the diagnosis of acute appendicitis with different parameter groups. The results show that supervised learning algorithms learning vector quantization and back-propagation were better than unsupervised algorithms in this medical decision making problem. The best results were obtained with the learning vector quantization. The self-organizing map algorithm showed good specificity, but this was in conjunction with lower sensitivity. The best parameter group was found to be the clinical signs. It seems beneficial to design a decision support system which uses these methods in the decision making process.     

具有节点偏置的高阶神经网络模型

在汪涛文献基础上提出了一个具有节点偏置的高阶神经网络模型、给出了模型的哈密顿量和学习算法,证明了学习算法的收敛性,该模型能对每一神经元自动引入一个节点偏置使得网络能够存储所有学习图样包括相关图样,其存储容量远高于Hebb—rule—like学习算法下的高阶神经网络模型.对由30个神经元组成的二阶神经网络进行了计算机仿真,结果证实了上述结论.此外,对初始突触强度对学习效果的影响和不同存储图样数目下的平均吸引半径进行了仿真计算并分析了所得结果.新模型的特点使其具有良好的应用前景     

A fast and convergent stochastic MLP learning algorithm

We propose a stochastic learning algorithm for multilayer perceptrons of linear-threshold function units, which theoretically converges with probability one and experimentally exhibits 100% convergence rate and remarkable speed on parity and classification problems with typical generalization accuracy. For learning the n bit parity function with n hidden units, the algorithm converged on all the trials we tested (n=2 to 12) after 5.8 x 4.1(n) presentations for 0.23 x 4.0(n-6) seconds on a 533MHz Alpha 21164A chip on average, which is five to ten times faster than Levenberg-Marquardt algorithm with restarts. For a medium size classification problem known as Thyroid in UCI repository, the algorithm is faster in speed and comparative in generalization accuracy than the standard backpropagation and Levenberg-Marquardt algorithms.