G-CovSel: Covariance oriented variable clustering

Abstract

Dimensionality reduction is an essential step in the processing of analytical chemistry data. When this reduction is carried out by variable selection, it can enable the identification of biochemical pathways. CovSel has been developed to meet this requirement, through a parsimonious selection of non-redundant variables. This article presents the g-CovSel method, which modifies the CovSel algorithm to produce highly complementary groups containing highly correlated variables. This modification requires the theoretical definition of the groups' construction and of the deflation of the data with respect to the selected groups. Two applications, on two extreme case studies, are presented. The first, based on near-infrared spectra related to four chemicals, demonstrates the relevance of the selected groups and the method's ability to handle highly correlated variables. The second, based on genomic data, demonstrates the method's ability to handle very highly multivariate data. Most of the groups formed can be interpreted from a functional point of view, making g-CovSel a tool of choice for biomarker identification in omics. Further work will be carried out to generalize g-CovSel to multi-block and multi-way data.