Analysis of two partial-least-squares algorithms for multivariate calibration

Manne, R., 1987. Analysis of two partial-least-squares algorithms for multivariate calibration. Chemometrics and Intelligent Laboratory Systems, 2: 187-197. Two algorithms for multivariate calibration are analysed in terms of standard linear regression theory. The matrix inversion problem of linear regression is shown to be solved by transformations to a bidiagonal form in PLS1 and to a triangular form in PLS2. PLS1 gives results identical with the bidiagonalization algorithm by Golub and Kahan, similar to the method of conjugate gradients. The general efficiency of the algorithms is discussed.