Selecting groups of covariates in the elastic net

This paper introduces a novel method to select groups of variables in sparse regression and classication settings. The groups are formed based on the correlations between covariates and ensure that for example spatial or spectral relations are preserved without explicitly coding for these. The preservation of relations gives increased interpretability. The method is based on the elastic net and adaptively selects highly correlated groups of variables and does therefore not waste time in grouping irrelevant variables for the problem at hand. The method is illustrated on a simulated data set and on regression of moisture content in multispectral images of sand. In both cases, the predictions were better or similar to existing regression and classication algorithms and the interpretation was enhanced using the grouping method. On top of that, the grouping method more consistently selects the important variables.