Abstract—In some practical applications of neural networks, fast response to external events within an extremely short time is highly demanded and expected. However, the extensively used gradient-descent-based learning algorithms obviously cannot satisfy the real-time learning needs in many applications, especially for large-scale applications and/or when higher generalization performance is required. Based on Huang’s constructive network model, this paper proposes a simple learning algorithm capable of real-time learning which can automatically select appropriate values of neural quantizers and analytically determine the parameters (weights and bias) of the network at one time only. The performance of the proposed algorithm has been systematically investigated on a large batch of benchmark real-world regression and classification problems. The experimental results demonstrate that our algorithm can not only produce good generalization performance but also have real-time learning and prediction capability. Thus, it may provide an alternative approach for the practical applications of neural networks where real-time learning and prediction implementation is required. Index Terms—Backpropagation (BP), extreme learning machine, feedforward networks, generalization performance,-NN, real-time learning, real-time prediction. I.

One of the open problems in neural network research is how to automatically determine network architectures for given applications. In this brief, we propose a simple and efficient approach to automatically determine the number of hidden nodes in generalized single-hidden-layer feedforward networks (SLFNs) which need not be neural alike. This approach referred to as error minimized extreme learning machine (EM-ELM) can add random hidden nodes to SLFNs one by one or group by group (with varying group size). During the growth of the networks, the output weights are updated incrementally. The convergence of this approach is proved in this brief as well. Simulation results demonstrate and verify that our new approach is much faster than other sequential/incremental/growing algorithms with good generalization performance.

Abstract—In this paper, an optimized approximation algorithm (OAA) is proposed to address the overfitting problem in function approximation using neural networks (NNs). The optimized approximation algorithm avoids overfitting by means of a novel and effective stopping criterion based on the estimation of the signal-to-noise-ratio figure (SNRF). Using SNRF, which checks the goodness-of-fit in the approximation, overfitting can be automatically detected from the training error only without use of a separate validation set. The algorithm has been applied to problems of optimizing the number of hidden neurons in a multilayer perceptron (MLP) and optimizing the number of learning epochs in MLP’s backpropagation training using both synthetic and benchmark data sets. The OAA algorithm can also be utilized in the optimization of other parameters of NNs. In addition, it can be applied to the problem of function approximation using any kind of basis functions, or to the problem of learning model selection when overfitting needs to be considered. Index Terms—Function approximation, neural network (NN) learning, overfitting.

is a learning method for two-layer feedforward neural networks, based on sensitivity analysis, that calculates the weights by solving a system of linear equations. Therefore, there is an important saving in computational time which significantly enhances the behavior of this method compared to other learning algorithms. This paper introduces a generalization of the SBLLM by adding a regularization term in the cost function. The theoretical basis for the method is given and its performance is illustrated. 1