Multivariate Mixture of Normals With Unknown Number of Components: An Application to Cluster Neolithic Ceramics From Aegean and Asia Minor Using Portable Xrf*

Abstract

Multivariate techniques and especially cluster analysis have been commonly used in Archaeometry. Exploratory and model-based techniques of clustering have been applied in geochemical (continuous) data of archaeological artifacts for provenance studies. Model-based clustering techniques like classification maximum-likelihood and mixture maximum likelihood had been used in a lesser extent in this context and although they seem to be suitable for such data, they either present practical difficulties-like high dimensionality of the data-or their performance give no evidence to support that they prevail on the standard methods (Papageorgiou et al., 2001). In this paper standard statistical methods (hierarchical clustering, principal components analysis) and the recently developed one of the multivariate mixture of normals with unknown number of components (see Dellaportas and Papageorgiou, 2005) in the category of the model-based ones, are applied and compared. The data set comprises of chemical compositions in 188 ceramic samples derived from the Aegean islands and surrounding areas.

Portable XRF of Archaeological Artifacts: Current Research, Potentials and Limitations

“…Stressed here is the tactic of using real peak shapes in the fitting function as there are typically large amounts of low-energy tails on peaks, which must be fitted accurately in order to get reliable peak area data. Similar findings on the importance of including peak distortions are reported by Kondrashov et al (2000) who also recommended the use of least moduli rather than least squares (Papageorgiou and Liritzis 2007) method when fitting peaks with high peak-to-background ratio. It is well known that, no matter how good the peak fitting algorithm, the overall performance can only be as good as the detector response function, and while detector function is improved, peak fitting algorithms are crucial in reducing error.…”

“…But nowadays due to the improvement in the elemental range measured by PXRF, the use of portable applications can be increasingly seen in the literature. PXRF has been applied extensively to archaeological materials such as ceramics, clays, soils, focused on clay provenance, clay fabric similarities, and trade exchange issues processing the data by clustering techniques, for example, Mantzourani and Liritzis (2006), Papadopoulou et al (2006), Papageorgiou and Liritzis (2007), Liritzis et al (2002, Liritzis (2005), Pappalardo et al (2003).…”

“…Complementary methods that contribute to this problem include PCA, correspondence and discriminant analysis, and model-based multivariate mixture of normals (Papageorgiou and Liritzis 2007).…”

Non‐destructive analysis using PXRF: methodology and application to archaeological ceramics

“…These potential interferences may preclude the use of PXRF for a particular sample or necessitate changes to data evaluation, such as restricting elements of interest to heavy trace elements. Some recent studies reverted to physically destructive sample preparation methods (samples were sectioned to expose a flat surface or ground into a fine powder and pelletised) to mitigate such effects 16–20. PXRF has a higher background in relation to peaks of interest than stationery XRF21 and poorer detection limits (LDL) than techniques such as NAA and ICP‐MS.…”

Historical Survey and Chronology of Bonajuto Chapel in Catania, Italy

“…Table 4 shows the concentrations of the major elements (10) and of the minor and trace elements (25 in total) that were selected for the characterization of the samples. The multivariate analysis (agglomerative hierarchical clustering) was used as a statistical discriminant approach in artefact groupings (Liritzis et al, 2008;Mantzourani and Liritzis, 2006;Papageorgiou and Liritzis, 2007). The results are presented as a dendrogram, showing the order and level of clustering, as well as the distance between individual samples.…”