Improved response function for the Simplex optimization of piecewise linear discriminants

Response functions are investigated that improve the performance of piecewise linear discriminants computed with Simplex optimization. Employing data from Fourier transform infrared (FTIR) remote sensing measurements of sulfur hexafluoride, methanol, acetone, and 2-butanone, piecewise linear discriminants are computed that allow automated detection decisions to be made regarding the presence of each analyte. In this application, the limit of detection of an analyte is determined by the degree to which the discriminants are optimally positioned in the data space formed from digitally filtered segments of the FTIR interferogram data. When Simplex optimization is used to guide the discriminant placement, a response function is required whose value correlates with the degree to which the discriminant is optimally positioned in the data space. This work investigates the requirements for a successful response function and tests 20 possible components of this function. From this evaluation, a response function is constructed that includes the logarithmically scaled summation of the discriminant scores of the currently misclassified analyte-active interferograms. This response function is evaluated by correlating the function values with the classification performance of optimized piecewise linear discriminants. Regression analysis is used to quantify this correlation for cases in which the discriminants are applied to test data not included in the original discriminant optimizations. The new response function is observed to perform significantly better than functions used previously in terms of the absolute classification performance of the computed discriminants and the degree of correlation between the function values and classification performance.