@inbook{e8c321410c954c5c973ccc502adaf9e2,

title = "On the PLS algorithm for multiple regression (PLS1)",

abstract = "Partial least squares (PLS) was first introduced byWold in the mid 1960s as a heuristic algorithm to solve linear least squares (LS) problems. No optimality property of the algorithm was known then. Since then, however, a number of interesting properties have been established about the PLS algorithm for regression analysis (called PLS1). This paper shows that the PLS estimator for a specific dimensionality S is a kind of constrained LS estimator confined to a Krylov subspace of dimensionality S. Links to the Lanczos bidiagonalization and conjugate gradient methods are also discussed from a somewhat different perspective from previous authors.",

keywords = "Conjugate gradients, Constrained principal component analysis (CPCA), Krylov subspace, Lanczos bidiagonalization, NIPALS, PLS1 algorithm",

author = "Yoshio Takane and Sebastien Loisel",

year = "2016",

month = oct,

day = "16",

doi = "10.1007/978-3-319-40643-5_2",

language = "English",

isbn = "9783319406411",

series = "Springer Proceedings in Mathematics & Statistics",

publisher = "Springer",

pages = "17--28",

booktitle = "The Multiple Facets of Partial Least Squares and Related Methods",

}