A nonlinear principal component analysis to study archeometric data

Abstract

Statistical techniques, when applied to data obtained by chemical investigations on ancient artworks, are usually expected to recognize groups of objects to classify the archeological finds, to attribute the provenance of items compared with earlier investigated ones, or to determine whether an archaelogical attribution is possible or not. The statistical technique most frequently used in archeometry is the principal component analysis (PCA), because of its simplicity in theory and implementation. However, the application of PCA to archeometric data showed severe limitations because of its linear feature. Indeed, PCA is inadequate to classify data whose behavior describe a curve or a curved subspace of the original data space. As a consequence of it, an amount of information is lost because the multi-dimensional data space is compressed into a lower-dimensional subspace including principal components. The aim of this work is then to test a novel statistical technique for archeometry. We propose a nonlinear PCA method to extract maximum chemical information by plotting data on the smallest number of principal components and to answer archeological questions. The higher accuracy and effectiveness of nonlinear PCA approach with respect to standard PCA for the analysis of archeometric data are shown through the study of Apulian red figured pottery (fifth–fourth century BC) coming from some of the most relevant archeological sites of ancient Apulia (Monte Sannace (Gioia del Colle), Egnatia (Fasano), Canosa, Altamura, Conversano, and Arpi(Foggia)). Copyright © 2016 John Wiley & Sons, Ltd

The Distinctive Role of Chemical Composition in Archaeometry. The Case of Apulian Red Figure Pottery

“…The multivariate statistical treatments proposed in this paper are NLPCA (nonlinear principal component analysis) and DA (discriminant analysis). NLPCA and DA are techniques based on the transformation of the original data [75,88]. NLPCA ignores class labels and finds directions of maximal variance and is used as an exploratory approach.…”

“…PCA graphic takes place plotting the score and loading vectors of the different parameters in the subplane of the first two or three principal components. However, the application of PCA to characterize data showed severe limitations because of its linear feature [75]. In this case, a nonlinear generalization of standard PCA by replacing linear surfaces with curved ones can be the right answer.…”

“…In this work, we consider hierarchical NLPCA based on Auto-Associative Neural network models. This method was already successfully tested on some Apulian red figure pottery [75]. To evaluate how good the model fits the data, two fitting parameters are considered: R 2 and the Lack of Fit (Lof).…”

“…Fewer studies are available on pottery production in Magna Graecia and in Puglia particularly. Most part of them are devoted to assessing the provenance of finds [14,64,[73][74][75][76][77][78][79] and fewer to identify technological features [8,11,[28][29][30][31][32]36,56,78,[80][81][82][83][84]. Often the items investigated were museum objects or seized material examined to verify their authenticity [27,85,86].…”