Abstract
Kernel methods, as alternatives to component analysis, are mathematical tools that provide a higher dimensional representation, for feature recognition and image analysis problems. In machine learning, the kernel trick is a method for converting a linear classification learning algorithm into non-linear one, by mapping the original observations into a higher-dimensional space so that the use of a linear classifier in the new space is equivalent to a non-linear classifier in the original space. In this dissertation we present the performance results of several continuous distribution function kernels, lattice oscillation model kernels, Kelvin function kernels, and orthogonal polynomial kernels on select benchmarking databases. In addition, we develop methods to analyze the use of these kernels for projection analysis applications; principal component analysis, independent component analysis, and optimal projection analysis. We compare the performance results with known kernel methods on several benchmarks. Empirical results show that several of these kernels outperform other previously suggested kernels on these data sets.
Additionally, we develop a genetic algorithm-based kernel optimal projection analysis method which, through extensive testing, demonstrates a ten percent average improvement in performance on all data sets over the kernel principal component analysis projection. We also compare our kernels methods for kernel eigenface representations with previous techniques. Finally, we analyze the benchmark databases used here to determine whether we can aid in the selection of a particular kernel that would perform optimally based on the statistical characteristics of each database.
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