A Novel Method of Curve Fitting Based on Optimized Extreme Learning Machine

Abstract

In this article, we present a new method based on extreme learning machine (ELM) algorithm for solving nonlinear curve fitting problems. Curve fitting is a computational problem in which we seek an underlying target function with a set of data points given. We proposed that the unknown target function is realized by an ELM with introducing an additional linear neuron to correct the localized behavior caused by Gaussian type neurons. The number of hidden layer neurons of ELM is a crucial factor to achieve a good performance. An evolutionary computation algorithm–particle swarm optimization (PSO) technique is applied to determine the optimal number of hidden nodes. Several numerical experiments with benchmark datasets, simulated spectral data and measured data from high energy physics experiments have been conducted to test the proposed method. Accurate fitting has been accomplished for various tough curve fitting tasks. Comparing with the results of other methods, the proposed method outperforms the traditional numerical-based technique. This work clearly demonstrates that the classical numerical analysis problem-curve fitting can be satisfactorily resolved via the approach of artificial intelligence.