Machine Learning Application of Generalized Gaussian Radial Basis Function and Its Reproducing Kernel Theory

Himanshu Singh ()
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Himanshu Singh: Department of Mathematics, The University of Texas at Tyler, Tyler, TX 75799, USA

Mathematics, 2024, vol. 12, issue 6, 1-28

Abstract: Gaussian Radial Basis Function Kernels are the most-often-employed kernel function in artificial intelligence for providing the optimal results in contrast to their respective counterparts. However, our understanding surrounding the utilization of the Generalized Gaussian Radial Basis Function across different machine learning algorithms, such as kernel regression, support vector machines, and pattern recognition via neural networks is incomplete. The results delivered by the Generalized Gaussian Radial Basis Function Kernel in the previously mentioned applications remarkably outperforms those of the Gaussian Radial Basis Function Kernel, the Sigmoid function, and the ReLU function in terms of accuracy and misclassification. This article provides a concrete illustration of the utilization of the Generalized Gaussian Radial Basis Function Kernel as mentioned earlier. We also provide an explicit description of the reproducing kernel Hilbert space by embedding the Generalized Gaussian Radial Basis Function as an L 2 − measure, which is utilized in implementing the analysis support vector machine. Finally, we provide the conclusion that we draw from the empirical experiments considered in the manuscript along with the possible future directions in terms of spectral decomposition of the Generalized Gaussian Radial Basis Function.

Keywords: Gaussian Radial Basis Function; reproducing kernel Hilbert space; support vector machine; neural network; ReLU; Generalized Hypergeometric Function; Pochhammer symbol; Hermite polynomials (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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