The geometry of PLS1 explained properly: 10 key notes on mathematical properties of and some alternative algorithmic approaches to PLS1 modelling

The insight from, and conclusions of this paper motivate efficient and numerically robust ‘new’ variants of algorithms for solving the single response partial least squares regression (PLS1) problem. Prototype MATLAB code for these variants are included in the Appendix. The analysis of and conclusions regarding PLS1 modelling are based on a rich and nontrivial application of numerous key concepts from elementary linear algebra. The investigation starts with a simple analysis of the nonlinear iterative partial least squares (NIPALS) PLS1 algorithm variant computing orthonormal scores and weights.

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