The canonical partial least squares approach to analysing multiway datasets—N-CPLS

Multiway datasets arise in various situations, typically from specialised measurement technologies, as a result of measuring data over varying conditions in multiple dimensions or simply as sets of possibly multichannel images. When such measurements are intended for predicting some external properties, the amount of methods available is limited. The multilinear partial least squares (PLS) is among the few available options. In the present work, we generalise the canonical partial least squares framework to handle multiway data. We demonstrate the resulting multiway data analysis method to be capable of building parsimonious models, encompassing continuous and categorical responses—both single and multiple—in a unifying framework. This also enables inclusion of additional responses/information that can contribute to more parsimonious models. Finally, we achieve a considerable advantage in computational speed without sacrificing numerical precision by deflating the responses and orthogonalising scores rather than the more costly deflations of the predictor data.