Iterative re-weighted multilinear partial least squares modelling for robust predictive modelling

Higher order data are commonly encountered in the domain of chemometrics, often generated by advanced analytical instruments. Due to the multilinear nature of the data, higher order data require different regression approaches compared with traditional two-way data for predictive modelling. The main aim is usually to extract the rich multilinear information, which is often lost if the data are simply analysed in unfolded form. A common algorithm for multilinear predictive modelling is N-way partial least squares (NPLS). However, a limitation of NPLS is that it inherently does not handle outlying observations, which can be detrimental to the model. This work presents a new robust multilinear predictive modelling approach based on iterative down-weighting of the outlier observations in both predictor and response space. A key benefit of the method is that it only requires a single extra parameter to tune. In this work, the algorithm is described, and the method is demonstrated on three real multilinear data sets. In all cases, the presented method outperformed the traditional NPLS modelling regarding the root mean squared error of prediction.