Spectral preconditioning of Krylov spaces: Combining PLS and PC regression

Authors:
Athanassios Kondylis;Joe Whittaker
Affiliations:
Institute of Statistics, University of Neuchítel, Switzerland;Department of Mathematics and Statistics, Lancaster University, UK
Venue:
Computational Statistics & Data Analysis
Year:
2008

Citing 6
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Abstract

In regularized regression the vectors that lie in Krylov and eigen subspaces, formed in PLS and PC regressions respectively, provide useful low dimensional approximations for the LS regression coefficient vector. By preconditioning the LS normal equations we provide a framework in which to combine these methods, and so exploit both of their respective advantages. The link between the proposed method to orthogonal signal correction and to cyclic subspace regression is made. The performance of the proposed solution in reducing the dimension of the regression problem, and the shrinkage properties of the resulting coefficient vector, are both examined.