Enhancing counterfeit and illicit medicines grouping via feature selection and X-ray fluorescence spectrometry

In this paper, we propose a novel framework to select the most relevant X-Ray Fluorescence (XRF) energy values (i.e., features) to enhance the clustering (grouping) of counterfeit and illicit medical tablets. The framework is based on the integration of multidimensional scaling (MDS) and Procrustes analysis (PA) multivariate techniques. MDS provides a projection of the original data into a lower dimension, while PA finds a projection matrix from the original data. Such outputs give rise to a feature importance index that guides an iterative feature selection process; after each feature is inserted in the subset, an optimization procedure based on a greedy search method is carried out to maximize the clustering quality assessed through the Silhouette Index (SI). The inorganic chemical fingerprinting of 41 commercial samples (Viagra®, Cialis®, Lazar®, Libiden®, Maxfil®, Plenovit®, Potent 75®, Rigix®, V-50®, Vimax® and Pramil®) and 56 seized counterfeit samples (Viagra and Cialis) was used to validate the proposed framework. From the original 2048 data points in the full spectra, we identified a subset comprised of 41 energy values that substantially improved clustering quality; the obtained groups were assessed by visual inspection of the PCA plots.