An appointment with Reproducing Kernel Hilbert Space generated by Generalized Gaussian RBF as $L^2-$measure

Abstract

Gaussian Radial Basis Function (RBF) Kernels are the most-often-employed kernels in artificial intelligence and machine learning routines for providing optimally-best results in contrast to their respective counter-parts. However, a little is known about the application of the Generalized Gaussian Radial Basis Function on various machine learning algorithms namely, kernel regression, support vector machine (SVM) and pattern-recognition via neural networks. The results that are yielded by Generalized Gaussian RBF in the kernel sense outperforms in stark contrast to Gaussian RBF Kernel, Sigmoid Function and ReLU Function. This manuscript demonstrates the application of the Generalized Gaussian RBF in the kernel sense on the aforementioned machine learning routines along with the comparisons against the aforementioned functions as well.