A Constrained Optimization based Extreme Learning Machine for noisy data regression

Most of the existing Artificial Intelligence (AI) models for data regression commonly assume that the data samples are completely clean without noise or worst yet, only the symmetrical noise is in considerations. However in the real world applications, this is often not the case. This paper addresses a significant note of inefficiency in methods for regression when dealing with outliers, especially for cases with polarity of noise involved (i.e., one sided noise with either only positive noise or negative noise). Using soft margin loss function concept, we propose Constrained Optimization method based Extreme Learning Machine for Regression, hereafter denoted as CO-ELM-R. The proposed method incorporates the two Lagrange multipliers that mimic Support Vector Regression (SVR) into the basis of ELM to cope with infeasible constraints of the regression optimization problem. Thus, CO-ELM-R will complement the recursive iterations of SVR in the training phase due to the fact that ELM is much simpler in structure and faster in implementation. The proposed CO-ELM-R is evaluated empirically on a few benchmark data sets and a real world application of NOx gas emission data set collected from one of the power plant in Malaysia. The obtained results have demonstrated its validity and efficacy in handling noisy data regression problems. (C) 2015 Elsevier B.V. All rights reserved.