Information-theoretical feature selection using data obtained by scanning electron microscopy coupled with and energy dispersive X-ray spectrometer for the classification of glass traces

In this work, a selection of the best features for multivariate forensic glass classification using Scanning Electron Microscopy coupled with an Energy Dispersive X-ray spectrometer (SEM-EDX) has been performed. This has been motivated by the fact that the databases available for forensic glass classification are sparse nowadays, and the acquisition of SEM-EDX data is both costly and time-consuming for forensic laboratories. The database used for this work consists of 278 glass objects for which 7 variables, based on their elemental compositions obtained with SEM-EDX, are available. Two categories are considered for the classification task, namely containers and car/building windows, both of them typical in forensic casework. A multivariate model is proposed for the computation of the likelihood ratios. The feature selection process is carried out by means of an exhaustive search, with an Empirical Cross-Entropy (ECE) objective function. The ECE metric takes into account not only the discriminating power of the model in use, but also its calibration, which indicates whether or not the likelihood ratios are interpretable in a probabilistic way. Thus, the proposed model is applied to all the 63 possible univariate, bivariate and trivariate combinations taken from the 7 variables in the database, and its performance is ranked by its ECE. Results show remarkable accuracy of the best variables selected following the proposed procedure for the task of classifying glass fragments into windows (from cars or buildings) or containers, obtaining high (almost perfect) discriminating power and good calibration. This allows the proposed models to be used in casework. We also present an in-depth analysis which reveals the benefits of the proposed ECE metric as an assessment tool for classification models based on likelihood ratios.