Combination of activation functions in extreme learning machines for multivariate calibration

The key point in multivariate calibration is to build an accurate regression relationship between the predictors and responses. In this paper, we first use extreme learning machine (ELM) to build spectroscopy regression model. Then, we propose a combinational ELM (CELM) method in which the decision function is represented as a sum of a linear hidden-node output function (activation function) and a nonlinear hidden-node output function. As the output functions map the input spectral signal to linear and nonlinear feature spaces respectively, the proposed method can effectively describe the linear and nonlinear relations existed in spectroscopy regression by the CELM output weights vector which can be simply resolved by ridge least squares or alternative iterative regularization. The proposed method is compared, in terms of RMSEP, to PLS and ELM on simulated and real NIR data sets. Experimental results demonstrate the efficacy and effectiveness of the proposed method. (C) 2012 Elsevier B.V. All rights reserved.