Robustness control in bilinear modeling based on maximum correntropy

Abstract

We present the development of a bilinear regression model for multivariate calibration on the basis of maximum correntropy criteria (MCC) whose robustness can be easily controlled. MCC regression methods can be more effective when the assumption of normality does not hold or when data are contaminated with outliers. These methods are competitive when the degree of robustness against outliers should be controlled. By controlling the robustness, information from candidate outliers can be partially retained rather than completely included or discarded during calibration. Within the context of bilinear regression models, an MCC approach using statistically inspired modification of the partial least squares (SIMPLS) is proposed, which is named maximum correntropy‐weighted partial least squares (MCW‐PLS). Thanks to the controllable robustness of MCC models, observations are upweighted or downweighted during the calibration process, rendering robust models with soft discrimination of samples. Such a weighting represents an important advantage, especially for cases when samples are not drawn from a normal distribution. Applications to three real case studies are presented. These applications uncovered three main features of MCW‐PLS: robustness control between SIMPLS and robust SIMPLS (RSIMPLS), improvements in prediction performance of bilinear calibration models, and the possibility to detect the most informative samples in a calibration set.

Cost-efficient unsupervised sample selection for multivariate calibration

“…The effectiveness of the type of bilinear models that are widely used for NIR applications has been reported by many researchers. Unless the spectral values have a strong nonlinear relationship with chemical reference values, bilinear models for regression tasks such as partial least squares regression (PLSR) or principal component regression (PCR) remain the workhorse model architectures [16]. Most of the work that can be found addressing the current problem of interest provides answers about the minimum required sample size using PLSR models [5,1,10,17].…”