Generalization of Powered-Partial-Least-Squares

Indahl originally proposed a variant to Wold's PLS1 algorithm in which weight coefficients were all modified by an exponent coefficient. This led to Powered-PLS (P-PLS). The aim of this paper is to revisit Indahi's P-PLS algorithm in order to make a robust and fast regression methodology calculating easy to interpret models. We first demonstrate that P-PLS is in fact a regression based on correlation maximization, but constrained by weight coefficients originally calculated in standard PLS1. From that, we propose a generalization of P-PLS by replacing the power transformation function by beta Cumulative Density Functions (beta-CDFs), leading to our proposed regression methodology called beta-PLS. With two public datasets, we demonstrate that P-PLS and even more beta-PIS regressions outperform standard PLS1 in terms of cross-validation performances in the case where the number of calibration observations is largely lower than the number of variables in X.