A performance analysis of lattice oscilation model kernels and KPCA

Kernel methods are mathematical tools that provide higher dimensional representation of given data set in feature space for pattern recognition and data analysis problems. Typically, the kernel trick is thought of as a method for converting a linear classification learning algorithm into non-linear one, by mapping the original observations into a higher-dimensional non-linear space so that linear classification in the new space is equivalent to non-linear classification in the original space. Moreover, optimal kernels can be designed to capture the natural variation present in the data. In this paper we present the standalone performance results of Einstein and Debye kernel functions and their respective performance for kernel principle component analysis on select databases. Empirical results show that these kernels perform well and some even better than existing kernels on these databases.