Much faster cross-validation in PLSR-modelling by avoiding redundant calculations

Abstract

A novel formulation of the wide kernel algorithm for partial least squares regression (PLSR) is proposed. We show how the elimination of redundant calculations in the traditional applications of PLSR helps in speeding up any choice of cross-validation strategy by utilizing precalculated lookup matrices. The proposed lookup approach is combined with some additional computational shortcuts resulting in highly effective and numerically accurate cross-validation results. The computational advantages of the proposed method are demonstrated by comparisons to the classical NIPALS and the bidiag2 algorithms for calculating cross-validated PLSR models. Problems including both one and several responses, double/nested cross-validated, and one-vs-all classification are among the considered applications.