Selection of principal variables through a modified Gram–Schmidt process with and without supervision

Summary

In various situations requiring empirical model building from highly multivariate measurements, modelling based on partial least squares regression (PLSR)
may often provide efficient low-dimensional model solutions. In unsupervised
situations, the same may be true for principal component analysis (PCA). In
both cases, however, it is also of interest to identify subsets of the measured
variables useful for obtaining sparser but still comparable models without significant loss of information and performance. In the present paper, we propose
a voting approach for sparse overall maximisation of variance analogous to
PCA and a similar alternative for deriving sparse regression models influenced
closely related to the PLSR method. Both cases yield pivoting strategies for a
modified Gram–Schmidt process and its corresponding (partial) QRfactorisation of the underlying data matrix to manage the variable selection
process. The proposed methods include score and loading plot possibilities that
are acknowledged for providing efficient interpretations of the related PCA
and PLS models in chemometric applications.

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DOI : doi.org/10.1002/cem.3510
NVA : hdl.handle.net/11250/3084015