A Comparison of Numerical Stability of PLS1 Algorithms

Andersson (2009) evaluated nine PLS1 algorithms in terms of their numerical stability and their speed. Inspired by his work, seven PLS1 algorithms were compared in terms of their numerical stability in this paper. They were (1) NIPALS algorithm by Wold, (2) Nonorthogonalized scores algorithm by Martens, (3) SIMPLS algorithm by de Jong, (4) Improved SIMPLS algorithm by Faber and Ferre, (5) Improved Kernel Algorithm by Dayal and MacGregor, (6) Direct-scores algorithm by Andersson, and (7) A new algorithm. A measure of numerical stability was proposed, and six data sets were used to compare the numerical stability of the seven algorithms. The new algorithm developed in this paper gave the best performance for all the data sets considered.