Variable selection study using Procrustes analysis

Several analytical techniques are often used in archaeometric studies, and when used in combination, these techniques can be used to assess 30 or more elements. Multivariate statistical methods are frequently used to interpret archaeometric data, but their applications can be problematic or difficult to interpret due to the large number of variables. In general, the analyst first measures several variables, many of which may be found to be uninformative, this is naturally very time consuming and expensive. In subsequent studies the analyst may wish to measure fewer variables while attempting to minimize the loss of essential information. Such multidimensional data sets must be closely examined to draw useful information. This paper aims to describe and illustrate a stopping rule for the identification of redundant variables, and the selection of variables subsets, preserving multivariate data structure using Procrustes analysis, selecting those variables that are in some senses adequate for discrimination purposes. We provide an illustrative example of the procedure using a data set of 40 samples in which were determined the concentration of As, Ce, Cr, Eu, Fe, Hf, La, Na, Nd, Sc, Sm, Th, and U obtained via instrumental neutron activation analysis (INAA) on archaeological ceramic samples. The results showed that for this data set, only eight variables (As, Cr, Fe, Hf, La, Nd, Sm, and Th) are required to interpret the data without substantial loss information.