Discriminant analysis techniques for the identification of atmospheric pollutants from passive Fourier transform infrared interferograms

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

“…This second set of patterns should be characteristically similar to the training patterns, in order to assess in a controlled environment whether the discriminant optimization was isolated to the training set alone or can be applied to multiple sets of data. 36,77,83 By defining the classes as active and inactive, similar to the training set, the discriminants can be applied to the new set of monitoring data. By assessing how the discriminants separate the classes, the performance of the simplex optimization can be determined.…”

“…Even if the initial training results are poor, it is expected that the discriminant applied to a monitoring set would result in a similar separation of the classes. 36,77,83 If the discriminant is identified as having been poorly optimized, a review of the simplex optimization parameters can be done. In some cases, the spanning constant of the vertices may need to be reassessed in order to free the optimization from an anomalous pattern cluster.…”

“…If this discriminant is NSS, it is corrected using a fixed-increment perceptron algorithm, pushing the discriminant in increments until all of the inactive patterns are correctly classified. 40,77 In summary, this correction algorithm is designed to move the projected discriminant so that it becomes single-sided.…”

“…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.…”

“…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…”