Novel Incremental Regularized Extreme Learning Machine Method Based on Improved Particle Swarm Optimization for Nonlinear Multivariate Calibration of Visible and Near-Infrared Spectroscopy

Abstract

Novel incremental regularized extreme learning machine (IR-ELM) based upon improved particle swarm optimization (IPSO-IR-ELM) is reported for the nonlinear multivariate calibration of visible/near-infrared (Vis/NIR) spectroscopy. IR-ELM is employed to construct a nonlinear calibration model for samples. Combined with IPSO, three parts of the IR-ELM algorithm are intelligently optimized. First, the regularization coefficient of the initial network in IR-ELM is optimized by IPSO. Second, IPSO is used again to select the optimal input weights and hidden biases while adding new hidden nodes in IR-ELM. Third, the 2-norm of the output matrix in IR-ELM is introduced as the conditional constraint in IPSO for updating the particle position. The performance of the reported method was tested with two Vis/NIR spectra datasets: blood hemoglobin and water pH. Key spectral variables were selected by successive projections algorithm and employed to establish the calibration models. Compared with partial least squares, ELM, error minimized extreme learning machine, and IR-ELM, IPSO-IR-ELM achieved the highest accuracy and best generalization. For the blood hemoglobin dataset, the RMSEP (root mean square error of prediction) was 0.210 g·dL−1, and the R p 2 (coefficient of determination of prediction) was 0.973. For the water pH dataset, the RMSEP was 0.825, and the R p 2 was 0.899. The results demonstrate that IPSO-IR-ELM is an alternative nonlinear multivariate calibration approach for Vis/NIR spectroscopy.