Although Gaussian RBF kernels are one of the most often used kernels in modern machine learning methods such as support vector machines (SVMs), almost nothing is known about the structure of their reproducing kernel Hilbert spaces (RKHSs). In this work we give two distinct explicit descriptions of the RKHSs corresponding to Gaussian RBF kernels and discuss some consequences. Furthermore, we present an orthonormal system for these spaces. Finally we discuss how our results can be used for analyzing the learning performance of SVMs.
I. Steinwart, D. Hush, and C. Scovel, An Explicit Description of the Reproducing Kernel Hilbert Spaces of Gaussian RBF Kernels Kernels. IEEE Transactions on Information Theory, Vol. 52, pp. 4635-4643, 2006. Los Alamos National Laboratory Technical Report LA-UR-04-8274. [ Abstract | PDF (244 KB) ]
