Multivariate partial least squares method, which has been widely used in chemometrics, has been mainly introduced as algorithms. Since they are of iterative forms and different authors use different symbols for the algorithms it often leads to a sea o...
Multivariate partial least squares method, which has been widely used in chemometrics, has been mainly introduced as algorithms. Since they are of iterative forms and different authors use different symbols for the algorithms it often leads to a sea of confusion. In the literature, usually PLS1 algorithm is introduced first and PLS2 is explained as an extension of PLS1. In this paper we have introduced a principle of the partial least squares method and developed several PLS2 algorithms according to the principle, and verified the equivalence of the algorithms. We have then induced PLS1 algorithm as a special case of PLS2. SAS/IML codes for the developed algorithms are listed in the appendix.