Locally-weighted-RoBoost-PLS: a multivariate calibration approach to simultaneously cope with non-linearities and outliers.

Background: Partial Least Squares regression (PLS) is a widely used tool for predictive modelling, particularly when dealing with multivariate datasets with dependent variables exhibiting strong collinearities. However, when relationships between variables are non-linear or atypical data points have to be coped with, PLS calibration models may face challenges. In recent years, different variants of the original PLS algorithm have been proposed to overcome these limitations. On the one hand, several robust regression methods that down-weigh outlying observations during the model training phase like RoBoost-PLS have been developed to reduce the detrimental effect of outliers on the performance of PLS. On the other hand, local modelling approaches, like K-Nearest-Neighbours-Locally-Weighted-PLS (KNN-LW-PLS), have been designed to handle non-linearities by fitting for each new incoming sample a separate linear calibration model considering only its nearest-neighbours. Unfortunately, none of these strategies can address the two aforementioned problems simultaneously. This paper introduces a novel approach named Locally-Weighted-RoBoost-PLS (LW-RoBoost-PLS), that combines the strengths of both local and robust modelling methodologies in order to deal with non-linearities while mitigating at the same time the influence of outliers.

Results: The performance of LW-RoBoost-PLS was evaluated on simulated and real industrial data (with this latter resulting from a continuous Acrylonitrile-Butadiene-Styrene ABS production process conducted at Versalis S.p.A.), both characterised by the simultaneous presence of outliers and non-linear relationships among measured variables. In the two case-studies investigated here, LW-RoBoost-PLS outperformed RoBoost-PLS and KNN-LW-PLS, achieving considerable reductions in the prediction error and prediction bias, which demonstrates that this technique permits to effectively overcome the limitations of the other approaches.

Significance: This paper describes a novel multivariate calibration approach named LW-RoBoost-PLS, which provides a solution for predictive modelling in scenarios where outliers and non-linearities co-exist. LW-RoBoost-PLS simultaneously handles non-linearities and outliers by combining local and robust modelling strategies, leading to improved prediction accuracy and reduced bias.