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

Abstract

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.

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

“…The modification to deal with multiple responses can be achieved by implementing the multilinear canonical PLS approach. 14 The extension of multilinear canonical PLS is simple and can be achieved by replacing the following steps for loading weight estimation. At first, candidate loading weights are estimated as W ¼ X t Y.…”

Swiss knife covariates selection: A unified algorithm for covariates selection in single block, multiblock, multiway, multiway multiblock cases including multiple responses

“…The responses Y are also assumed to be mean centred. The tensor notation, , is associated with the tensor dot product exemplified in Liland et al 30 …”

“…The responses Y are also assumed to be mean centred. The tensor notation, B, is associated with the tensor dot product exemplified in Liland et al 30 * Calculation of projection for score predictions R ð Þ assumes winning loadings and loading weights stacked with matrices of zeros for the loosing blocks.…”

Insight into the Recent Application of Chemometrics in Quality Analysis and Characterization of Bee Honey during Processing and Storage

“…For the geographical origin, identification of the highest accuracy is obtained through autoscale, variance (std) scaling and class centroid centering and scaling. For the botanical origin, the highest accuracy is obtained through the variance (std) scaling data pre-treatment [149]; o Unfolded PLS-DA UPLS-DA combines unfolded PLS [150] which decompose the sample spectra to extract the relevant information with DA; o Multilinear PLS-DA MPLS-DA combines multilinear PLS [151,152] which can use multidimensional data as input with DA.…”