Genetic algorithms for the optimization of piecewise linear discriminants

Abstract

The application of genetic algorithms (GAs) to the optimization of piecewise linear discriminants is described. Piecewise linear discriminant analysis (PLDA) is a supervised pattern recognition technique employed in this work for the automated classification of Fourier transform infrared (FTIR) remote sensing data. PLDA employs multiple linear discriminants to approximate a nonlinear separating surface between data categories defined in a vector space. The key to the successful implementation of PLDA is the positioning of the individual discriminants that comprise the piecewise linear discriminant. For the remote sensing application, the discriminant optimization is challenging due to the large number of input variables required and the corresponding tendency for local optima to occur on the response surface of the optimization. In this work, three implementations of GAs are configured and evaluated: a binary-coded GA (GAB), a real-coded GA (GAR), and a Simplex-GA hybrid (SGA). GA configurations are developed by use of experimental design studies, and piecewise linear discriminants for acetone, methanol, and sulfur hexafluoride are optimized (trained). The training and prediction classification results indicate that GAs area viable approach for discriminant optimization. On average, the best piecewise linear discriminant optimized by a GA is observed to classify 11% more analyte-active patterns correctly in prediction than an unoptimized piecewise linear discriminant. Discriminant optimization problems not used in the experimental design study are employed to test the stability of the GA configurations. For these cases, the best piecewise linear discriminant optimized by SGA is shown to classify 19% more analyte-active patterns correctly in prediction than an unoptimized discriminant. These results also demonstrate that the two real number coded GAs (GAR and SGA) perform better than the GAB. Real number coded GAs are also observed to execute faster and are simpler to implement.