Interval LASSO regression based extreme learning machine for nonlinear multivariate calibration of near infrared spectroscopic datasets

Abstract

As a nonlinear multivariate calibration method, extreme learning machine (ELM) has recently received increasing attention for its fast learning speed and excellent generalized performance. However, it is implemented normally under the empirical risk minimization scheme, and is prone to generate a large-scale and over-fitting model. Least absolute shrinkage and selection operator (LASSO) based ELM (LASSO-ELM) is a simple and efficient approach to avoid over-fitting and obtain an appropriate network structure. Unfortunately, when the initial hidden layer output matrix is in a high dimensional feature space, solving the LASSO problem remains a challenge. To improve the efficiency of solving high-dimension LASSO, we propose interval LASSO based ELM (iLASSO-ELM), which is generated by incorporating interval selection of hidden layer output matrix into original LASSO-ELM. The proposed model combines the coarse screening of interval selection and fine screening of LASSO. Thus, it can identify the relevant hidden nodes quickly and prevent over-fitting. A comparison of the proposed iLASSO-ELM with six other models, namely, ELM, partial least square based ELM (PLS-ELM), ridge regression based ELM (RR-ELM), elastic net based ELM (EN-ELM), LASSO-ELM and Least-Squares Support Vector Machines method (LS-SVM), was evaluated on four benchmark-near infrared (NIR) spectroscopic datasets. Additionally, the Wilcoxon signed rank test was used to statistically compare the predictive performance of the two competing calibration models. Experimental results show that iLASSO-ELM has the minimum root mean square errors of predictions and performs, at least statistically, not worse than other models.