On the numerical stability of two widely used PLS algorithms

Ideally, the score vectors numerically computed by an orthogonal scores partial least squares (PLS) algorithm should be orthogonal close to machine precision. However, this is not ensured without taking special precautions. The progressive loss of orthogonality with increasing number of components is illustrated for two widely used PLS algorithms, i.e., one that can be considered as a standard PLS algorithm, and SIMPLS. It is shown that the original standard PLS algorithm outperforms the original SIMPLS in terms of numerical stability. However, SIMPLS is confirmed to perform much better in terms of speed. We have investigated reorthogonalization as the special precaution to ensure orthogonality close to machine precision. Since the increase of computing time is relatively small for SIMPLS, we therefore recommend SIMPLS with reorthogonalization. Copyright © 2008 John Wiley & Sons, Ltd.