Unravelling the geometry of data matrices: effects of water stress regimes on winemaking

A new method is proposed for unravelling the patterns between a set of experiments and the features that characterize those experiments. The aims are to extract these patterns in the form of a coupling between the rows and columns of the corresponding data matrix and to use this geometry as a support for model testing. These aims are reached through two key steps, namely application of an iterative geometric approach to couple the metric spaces associated with the rows and columns, and use of statistical physics to generate matrices that mimic the original data while maintaining their inherent structure, thereby providing the basis for hypothesis testing and statistical inference. The power of this new method is illustrated on the study of the impact of water stress conditions on the attributes of 'Cabernet Sauvignon' Grapes, Juice, Wine and Bottled Wine from two vintages. The first step, named data mechanics, de-convolutes the intrinsic effects of grape berries and wine attributes due to the experimental irrigation conditions from the extrinsic effects of the environment. The second step provides an analysis of the associations of some attributes of the bottled wine with characteristics of either the matured grape berries or the resulting juice, thereby identifying statistically significant associations between the juice pH, yeast assimilable nitrogen, and sugar content and the bottled wine alcohol level.