| Abstract
| - Traditionally the partial least-squares (PLS) algorithm, commonly used in chemistry for ill-conditionedmultivariate linear regression, has been derived (motivated) and presented in terms of data matrices. In thiswork the PLS algorithm is derived probabilistically in terms of stochastic variables where sample estimatescalculated using data matrices are employed at the end. The derivation, which offers a probabilistic motivationto each step of the PLS algorithm, is performed for the general multiresponse case and without reference toany latent variable model of the response variable and also without any so-called “inner relation”. On thebasis of the derivation, some theoretical issues of the PLS algorithm are briefly considered: the complexityof the original motivation of PLS regression which involves an “inner relation”; the original motivationbehind the prediction stage of the PLS algorithm; the relationship between uncorrelated and orthogonallatent variables; the limited possibilities to make natural interpretations of the latent variables extracted.
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