Maximum correntropy criterion based regression for multivariate calibration

- A maximum correntropy criterion based regression model is proposed.
- A nonlinear correntropy-based metric is used to replace the traditional least-squares metric.
- A half-quadratic optimization technique is developed to solve the correntropy-based model.
- The nonlinear Gaussian function in MCC leads to an accurate estimation of the regression relation.
- It outperforms some modified PLS algorithms and robust regression methods.

The least-squares criterion is widely used in the multivariate calibration models. Rather than using the conventional linear least-squares metric, we employ a nonlinear correntropy-based metric to describe the spectra-concentrate relations and propose a maximum correntropy criterion based regression (MCCR) model. To solve the correntropy-based model, a half-quadratic optimization technique is developed to convert a non-convex and nonlinear optimization problem into an iteratively re-weighted least-squares problem. Finally, MCCR can provide an accurate estimation of the regression relation by alternatively updating an auxiliary vector represented as a nonlinear Gaussian function of fitted residuals and a weight computed by a regularized weighted least-squares model. The proposed method is compared to some modified PLS algorithms and robust regression methods on four real near-infrared (NIR) spectra data sets. Experimental results demonstrate the efficacy and effectiveness of the proposed method.