Abstract
Over‒fitting in multivariate regression is often viewed as the consequence of the number of variables. However, it is almost counterintuitive that the number of variables used to fit a regression model increases the risk of over‒fitting instead of adding useful information. In this paper, we will be discussing the source of over‒fitting and ways of reducing it during the computation of partial least squares (PLS) components. A close look at the linear algebra used for PLS component calculation will highlight hints of the origin of over‒fitting. Simulation of multivariate datasets will explore the influence of noise, number of variables and complexity of the underlying latent variable structure on over‒fitting. A tentative solution to overcome the identified problem will be presented, and a new PLS algorithm will be proposed. Finally, the properties of this new algorithm will be explored. Copyright © 2014 JohnWiley & Sons, Ltd.
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