Sparse N-way Partial Least Squares by L1-penalization

Abstract N -PLS, as the natural extension of PLS to N -way structures, tries to maximize the covariance between an X and a Y N -way data arrays. It provides a useful framework for fitting prediction models to N -way data. However, N-PLS by itself does not perform variable selection, which indeed can facilitate interpretation in different situations (e.g. the so-called “–omics” data). In this work, we propose a method for variable selection within N -PLS by introducing sparsity in the weights matrices W J and W K by means of L1-penalization. The sparse version of N -PLS is able to provide lower prediction errors by filtering all the noise variables and to further improve interpretability and usability of the N -PLS results. To test Sparse N- PLS performance two different simulated data sets were used, whereas to show its utility in a biological context a real time course metabolomics data set was used.