A Structural Learning Algorithm for Neural Networks and Handwritten Zipcode Recognition

This paper presents the development of several efficient learning algorithms for neural networks (ELEANNE). The ELEANNE 1 and ELEANNE 2 are two recursive least-squares learning algorithms, proposed for training single-layered neural networks with analog output. This paper also proposes a new optimization strategy for training single-layered neural networks, which provides the basis for the development of a variety of efficient learning algorithms. This optimization strategy is the source of the ELEANNE 3, a second-order learning algorithm for training single-layered neural networks with binary output. A simplified version of this algorithm, called ELEANNE 4, is also derived on the basis of some simplifying but reasonable assumptions. The two algorithms developed for single-layered neural networks provide the basis for the derivation of ELEANNE 5 and ELEANNE 6, which are proposed for training multilayered neural networks with binary output. The ELEANNE 7 is an efficient algorithm developed for training multilayered neural networks with either binary or analog output. >

The Sixth International Symposium on Neural Networks (ISNN 2009)

Learning algorithm of neural network is always an important research contents in neural network theory research and application field, learning algorithm about the feed-forward neural network has no satisfactory solution in particular for its defects in calculation speed. The paper presents a new Fourier basis functions neural network algorithm and applied it to classify network trade customer. First, 21 customer classification indicators are designed, based on characteristics and behaviors analysis of network trade customer, including customer characteristics type variables and customer behaviors type variables,; Second, Fourier basis functions is used to improve the calculation flow and algorithm structure of original BP neural network algorithm to speed up its convergence and then a new Fourier basis neural network model is constructed. Finally the experimental results show that the problem of convergence speed can been solved, and the accuracy of the customer classification are ensured when the new algorithm is used in network trade customer classification practically. DOI: http://dx.doi.org/10.11591/telkomnika.v11i11.2978 Full Text: PDF

The paper proposes a fast online learning method for neural network structures by using genetic algorithm (GA) and dynamic back propagation algorithm (BP) jointly. GA is used in the coarse tuning process which adjusts interconnection weights of the neural network. The dynamic back propagation algorithm is subsequently applied to achieve fine adjusting of the network weights. The fitness function, based on the squared error between the teaching signal and the network output value, is redefined at every time step and the proposed GA based algorithm solves a nonstationary function optimization task. At every time step the solution with the best fitness function is used for current representation of the neural network weights and biases. It is shown through the simulations and real time temperature control of drying oven that this learning algorithm has faster convergence ability and better performance on reducing mapping error in the online learning neural network structures. This leads to an improvement of the transient response of neuro adaptive systems. The proposed method has the potential to be applied to many practical areas such as system modeling and control, signal processing and pattern recognition.

This paper presents a single-objective and a multiobjective stochastic optimization algorithms for global training of neural networks based on simulated annealing. The algorithms overcome the limitation of local optimization by the conventional gradient-based training methods and perform global optimization of the weights of the neural networks. Especially, the multiobjective training algorithm is designed to enhance generalization capability of the trained networks by minimizing the training error and the dynamic range of the network weights simulataneously. For fast convergence and good solution quality of the algorithms, we suggest the hybrid simulated annealing algorithm with the gradient-based local optimization method. Experimental results show that the performance of the trained networks by the proposed methods is better than that by the gradient-based local training algorithm and, moreover, the generalization capability of the networks is significantly improved by preventing overfitting phenomena.

Fractional calculus has been adopted in the modelling of many scientific processes and systems. Due to the inherent feature of long term memory of fractional derivatives, it has been used in the learning process of neural networks. A fractional order derivative based back propagation learning algorithm in neural networks is proposed in this paper. Specifically, Riemann-Liouville (R-L), Caputo (C) and Caputo Fabrizio (CF) fractional Derivative based on the back propagation algorithms in a three layer feed-forward neural network employed. To get a faster learning rate without oscillation, momentum factor is incorporated. The effect of fractional order and momentum factor is investigated and compared. The performance of these fractional derivatives based algorithms with integer derivatives based algorithm in terms of mean square error (MSE), particularly the salary based on years of experience is predicted. Results demonstrate that fractional derivative based learning algorithms outperform the integer derivatives.

Mapping capabilities of a three-layer feedforward neural network with a finite number of hidden units which have sigmoid functions as their nonlinearities are discussed. It is proved that sigmoid functions of a hidden layer of the network can raise the dimension of the input space up to the number of the hidden units. From this result, it is concluded that a three-layer feedforward neural network with N hidden units can assign arbitrary analog values to N arbitrary input vectors.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A fast and robust algorithm for training feedforward neural networks (FNNs) by using a variable forgetting factor and U-D factorization-based recursive prediction error (RPE) method is proposed. In comparison with the backpropagation (BP) and RPE based learning algorithms, the proposed algorithm, called UD-RPE, can provide much more accurate learning results in fewer iterations with fewer hidden nodes and improve convergence rate and numerical stability (robustness). In addition, it is less sensitive to start-up parameters, such as initial weights and initial covariance matrix, and the randomness in the observed data. It also has good generalization ability and needs less learning time. Simulation results of nonlinear dynamic system modeling and identification show that the algorithm proposed here is an effective and efficient learning algorithm for FNNs.

A fast and robust learning algorithm for feedforward neural networks

At present, deep learning is becoming one of the most popular approach to creation of the artificial intelligences systems such as speech recognition, natural language processing, computer vision and so on. The paper presents a historical overview of deep learning in neural networks. The model of the artificial neural network is described as well as the learning algorithms for neural networks including the error backpropagation algorithm, which is used to train deep neural networks. The development of neural networks architectures is presented including neocognitron, autoencoders, convolutional neural networks, restricted Boltzmann machine, deep belief networks, long short-term memory, gated recurrent neural networks, and residual networks. Training deep neural networks with many hidden layers is impeded by the vanishing gradient problem. The paper describes the approaches to solve this problem that provide the ability to train neural networks with more than hundred layers. An overview of popular deep learning libraries is presented. Nowadays, for computer vision tasks convolutional neural networks are utilized, while for sequence processing, including natural language processing, recurrent networks are preferred solution, primarily long short-term memory networks and gated recurrent neural networks.

Fast Learning Algorithms

Extreme learning machine (ELM) is an easy-to use and effective learning algorithm of single-hidden layer feed-forward neural networks (SLFNs). The classical learning algorithm in neural network, e. g. backpropagation, requires setting several user-defined parameters and may get into local minimum. However, ELM only requires setting the number of hidden neurons and the activation function. It does not require adjusting the input weights and hidden layer biases during the implementation of the algorithm, and it produces only one optimal solution. Therefore, ELM has the advantages of fast learning speed and good generalization performance. In this paper, ELM is introduced in predicting reservoir permeability. By comparing to SVM, we analyze its feasibility and advantages in reservoir permeability prediction. The experimental results show that ELM has similar accuracy compared to SVR, but it has obvious advantages in parameter selection and learning speed.

This paper presents a novel dynamic ensemble learning (DEL) algorithm for designing ensemble of neural networks (NNs). DEL algorithm determines the size of ensemble, the number of individual NNs employing a constructive strategy, the number of hidden nodes of individual NNs employing a constructive–pruning strategy, and different training samples for individual NN’s learning. For diversity, negative correlation learning has been introduced and also variation of training samples has been made for individual NNs that provide better learning from the whole training samples. The major benefits of the proposed DEL compared to existing ensemble algorithms are (1) automatic design of ensemble; (2) maintaining accuracy and diversity of NNs at the same time; and (3) minimum number of parameters to be defined by user. DEL algorithm is applied to a set of real-world classification problems such as the cancer, diabetes, heart disease, thyroid, credit card, glass, gene, horse, letter recognition, mushroom, and soybean datasets. It has been confirmed by experimental results that DEL produces dynamic NN ensembles of appropriate architecture and diversity that demonstrate good generalization ability.

Extreme learning machine (ELM) is a learning algorithm for single-hidden layer feedforward neural networks. In theory, this algorithm is able to provide good generalization capability at extremely fast learning speed. Comparative studies of benchmark function approximation problems revealed that ELM can learn thousands of times faster than conventional neural network (NN) and can produce good generalization performance in most cases. Unfortunately, the research on damage localization using ELM is limited in the literature. In this chapter, the ELM is extended to the domain of damage localization of plate structures. Its effectiveness in comparison with typical neural networks such as back-propagation neural network (BPNN) and least squares support vector machine (LSSVM) is illustrated through experimental studies. Comparative investigations in terms of learning time and localization accuracy are carried out in detail. It is shown that ELM paves a new way in the domain of plate structure health monitoring. Both advantages and disadvantages of using ELM are discussed.

Recent study, the extended Kalman filter (EKF) is applied to the learning algorithm for a feedforward neural network and it is shown that the EKF based learning algorithm has good convergence performances. However, the feedforward neural network could not perform a dynamical signal processing such as time series pattern recognition. On the other hand, the recurrent neural network (RNN) could have dynamical characteristics because the RNN has feedback connections with time delay in the network. The EKF based learning algorithms for the RNN are also reported and some training properties became clear. In this paper, RNN training based on the EKF are applied to the time series signal processing. The connection weights of the RNN can be modified by using the filtering algorithm based on the EKF. Simulation results show that the RNN based on the EKF has good performances of the training for time series patterns generated from sine functions and for some pulse patterns.