Group-wise partial least square regression

This paper introduces the group-wise partial least squares (GPLS) regression. GPLS is a new sparse PLS technique where the sparsity structure is defined in terms of groups of correlated variables, similarly to what is done in the related group-wise principal component analysis. These groups are found in correlation maps derived from the data to be analyzed. GPLS is especially useful for exploratory data analysis, because suitable values for its metaparameters can be inferred upon visualization of the correlation maps. Following this approach, we show GPLS solves an inherent problem of sparse PLS: its tendency to confound the data structure because of setting its metaparameters using standard approaches for optimizing prediction, like cross-validation. Results are shown for both simulated and experimental data.