Swiss knife partial least squares (SKPLS): One tool for modelling single block, multiblock, multiway, multiway multiblock including multi-responses and meta information under the ROSA framework

Abstract

In the domain of chemometrics and multivariate data analysis, partial least squares (PLS) modelling is a widely used technique. PLS gains its beauty by handling the high collinearity found in multivariate data by replacing highly covarying variables with common subspaces spanned by orthogonal latent variables. Furthermore, all can be achieved with simple steps of linear algebra requiring minimal computation power and time usage compared to current high-end computing and substantial hyperparameter tuning required by methods such as deep learning. PLS can be used for a wide variety of tasks, for example, single block modelling, multiblock modelling, multiway data modelling and for task such as regression and classification. Furthermore, new PLS based approaches can also incorporate meta information to improve the PLS subspace extraction. However, in the current scenario, there is a wide range of separate tools and codes available to perform different PLS tasks. Often when the user needs to perform a new PLS task, they need to start with a separate mathematical implementation of the PLS techniques. This study aims to provide a single solution, i.e., the Swiss knife PLS (SKPLS) modelling approach to enable a single mathematical implementation to perform analyses of single block, multiblock, multiway, multiblock multiway, multi-response, and incorporation of meta information in PLS modelling. It contains all that is needed for any PLS practitioner to perform both classification and regression tasks. The SKPLS backbone is the stepwise PLS strategy called response oriented sequential alternation (ROSA) which we generalize to enable all the mentioned analysis possibilities. The basic structure of the algorithm is highlighted, and some example cases of performing single block, multiblock, multiway, multiblock multiway, multi-response PLS modelling and the incorporation of meta information in PLS modelling are included.