This article describes a method for performing discriminant analysis in the presence of interfering background signal.
The method is based on performing target factor analysis on a data set comprised of contributions from analyte(s) and interfering components. A library of data from representative analyte classes is tested for possible contributing factors by performing oblique rotations of the principal factors to obtain the best match, in a least-squares sense, between test and predicted vectors. The degree of match between the test and predicted vectors is measured by the Pearson correlation coefficient, r, and the distribution of r for each class is determined. A Bayesian soft classifier is used to calculate the posterior probability based on the distributions of r for each class, which assist the analyst in assessing the presence of one or more analytes. The method is demonstrated by analyses performed on spectra obtained by laser induced breakdown spectroscopy (LIBS). Single and multiple bullet jacketing transfers to steel and porcelain substrates were analyzed to identify the jacketing materials. Additionally, the metal surrounding bullet holes was analyzed to identify the class of bullet jacketing that passed through a stainless steel plate. Of 36 single sample transfers, the copper jacketed (CJ) and non-jacketed (NJ) class on porcelain had an average posterior probability of the metal deposited on the substrate of 1.0. Metal jacketed (MJ) bullet transfers to steel and porcelain were not detected as successfully. Multiple transfers of CJ/NJ and CJ/MJ on the two substrates resulted in posterior probabilities that reflected the presence of both jacketing materials. The MJ/NJ transfers gave posterior probabilities that reflected the presence of the NJ material, but the MJ component was mistaken for CJ on steel, while non-zero probabilities were obtained for both CJ and MJ on porcelain. Jacketing transfer from a bullet to steel as the projectile passed through the steel also proved difficult to analyze. Over 50 percent of the samples left insufficient transfer to be identified. Transfer from NJ and CJ jacketing was successfully identified by posterior probabilities greater than 0.8. (publisher abstract modified)