Algorithms
A number of variants of PLS exist for estimating the factor and loading matrices and . Most of them construct estimates of the linear regression between and as . Some PLS algorithms are only appropriate for the case where is a column vector, while others deal with the general case of a matrix . Algorithms also differ on whether they estimate the factor matrix as an orthogonal, an orthonormal matrix or not. The final prediction will be the same for all these varieties of PLS, but the components will differ.
Read more about this topic: Partial Least Squares Regression