Development and optimization of piecewise linear discriminants for the automated detection of chemical species

Signal processing and pattern recognition methods for the remote, airborne detection of radioisotopes by gamma-ray spectroscopy

“…In the work described here, the patterns in the active data class are generated synthetically from the modulation of a single laboratory-collected spectrum. [44][45][46][47][48] These spectra are then overlaid with backgrounds collected from a broad range of locations around the nation, in order to simulate any theoretical scenario the ASPECT program may encounter from high to low intensity sources. This collection of synthetic active spectra is supplemented by a second set of inactive spectra drawn from a separate pool of backgrounds collected from multiple vetted locations.…”

“…Recall that this method will attempt to generate a discriminant somewhere between the two classes, making the assumption that the data belong to a multivariate normal distribution. 45 This initialization step is making the assumption that the data follow a Gaussian distribution, but this is not likely the case. Therefore, this initial Bayesian step is merely designed to place an initial discriminant somewhere approximating the border region between the inactive and active classes.…”

“…3-48 through 3-50 in conjunction with the Bayesian discriminant vector generation assures that the first discriminant generated should lie somewhere along the boundary between the inactive and other classes. 45,47,77 This initial discriminant generation method is only useful in the first step as this parametric method would be an ineffective procedure in finalizing a nonparametric data discriminant. More importantly, it ensures that NSS discriminants are penalized at the initialization step which should reduce the number of false detections as the discriminant is further optimized in the following steps.…”

“…The literature has been thorough on querying various different simplex methods and response functions, with the presented equations and methods being the demonstrated best thus far for the applications in this thesis. 45,47 The resulting weight vector(s) are declared the optimal discriminants for a given set of patterns and classifier parameters, which are subsequently carried forward to a validation step that verifies the simplex optimization of the discriminant(s). 45,47,77…”

“…Once computed, the classification model is applicable to other sets of data processed in the same fashion, assuming the target analyte remains the same. [44][45][46][47][48] The specifics of the implementation of PLDA for the thesis work will be described section 3.4.…”