Cluster analysis for the selection of potential discriminatory variables and the identification of subgroups in archaeometry

In this article, three variable selection methods based on Gaussian mixture models were compared to find a subset of variables that provided the "best" clustering. The use of an appropriate transformation for composi-tional data, whose geometric space is the Simplex, is emphasized. The comparison revealed the ability of the models to cluster data in multiple phases, showing to be more convenient to select the relevant variables than to perform an analysis based on 2D plots or by simultaneously including all the available variables in a multivariate analysis. Once the informative variables for the clustering were obtained, we used a method called Databionic Swarm (DBS). This method uses unsupervised machine learning, taking advantage of emergence and swarm intelligence applied to find natural chemical groups in the input data space. DBS can visualize high-dimensional distances in the projection through a 3D topographic map with hypsometric tints. The results were compared in terms of accuracy, both in the selection of the variables and in the classification, using a supervised accuracy index for clustering and two unsupervised indexes (the Heatmap and the Silhouette plot). The concepts and methods were illustrated by applying them to two published archaeological glass data sets. The first set consisted of 245 Romano-British glass vessels and the second set of 180 glass vessels from the 15th-17th century in Antwerp. In these applications, it was found that the methods for the selection of variables increased the ac-curacy of the classification compared to traditional methods.