A method to propagate the uncertainty of measurements in principal component analysis applied to the elemental composition of cooking salts measured by instrumental neutron activation analysis

Cooking salt is one of the most diffused food commodities, with high relevance both for flavour exaltation and food preservation. In commerce are present peculiar cooking salts with a high commercial value due to their colour and organoleptic characteristics, which are subjected to fraud and adulteration. The elemental composition of different cooking salts from different geographical origins was investigated with instrumental neutron activation analysis (INAA), as a calibrated and validated multi-element technique, suitable for the accurate determination of trace concentration of most natural elements. The elemental fingerprint differences between samples were explored by principal component analysis (PCA), which was expanded with a simple data augmentation method called "Data explosion" with the scope of propagating the uncertainty budget associated with the raw data in the PCA model, using a Monte Carlo simulation. The PCA models with and without considering the uncertainty of measurement were compared using common figures of merit, attesting that, in the absence of the uncertainty regions associated with the scores, erroneous conclusion about sample similarities and differences could be drawn.