Gaussianization of LA-ICP-MS features to improve calibration in forensic glass comparison

The forensic comparison of glass aims to compare a glass sample of an unknown source with a control glass sample of a known source. In this work, we use multi-elemental features from Laser Ablation Inductively Coupled Plasma with Mass Spectrometry (LA-ICP-MS) to compute a likelihood ratio. This calculation is a complex procedure that generally requires a probabilistic model including the within-source and between-source variabilities of the features. Assuming the within-source variability to be normally distributed is a practical premise with the available data. However, the between-source variability is generally assumed to follow a much more complex distribution, typically described with a kernel density function. In this work, instead of modeling distributions with complex densities, we propose the use of simpler models and the introduction of a data pre-processing step consisting on the Gaussianization of the glass features. In this context, to obtain a better fit of the features with the Gaussian model assumptions, we explore the use of different normalization techniques of the LA-ICP-MS glass features, namely marginal Gaussianization based on histogram matching, marginal Gaussianization based on Yeo-Johnson transformation and a more complex joint Gaussianization using normalizing flows. We report an improvement in the performance of the Likelihood Ratios computed with the previously Gaussianized feature vectors, particularly relevant in their calibration, which implies a more reliable forensic glass comparison.