Compositional data analysis for elemental data in forensic science.

Discrimination of material based on elemental composition was achieved within a compositional data (CoDa) analysis framework in a form appropriate for use in forensic science. The methods were carried out on example data from New Zealand nephrite. We have achieved good separation of the in situ outcrops of nephrite from within a well-defined area. The most significant achievement of working within the CoDa analysis framework is that the implications of the constraints on the data are acknowledged and dealt with, not ignored. The full composition was reduced based on collinearity of elements, principal components analysis (PCA) and scalings from a backwards linear discriminant analysis (LDA). Thus, a descriptive subcomposition was used for the final discrimination, using LDA, and proved to be more successful than using the full composition. The classification based on the LDA model showed a mean error rate of 2.9% when validated using a 10 repeat, three-fold cross-validation. The methods presented lend objectivity to the process of interpretation, rather than relying on subjective pattern matching type approaches.