Abstract
Kernel methods play an important role in machine learning, pattern recognition and data mining. Although the kernel functions are the central part of the kernel methods, little is known about the structure of its reproducing kernel Hilbert spaces (RKHS) and the eigenvalues of the integral operator. In this paper, we first give the definition of the extended Gaussian kernel which includes the Gaussian kernel as its special case. Then, through a generalization form of the Weyl inner product, we present an explicit description of the RKHS of the extended Gaussian kernel. Furthermore, using the Funk-Hecke formula, we get the eigenvalues and eigenfunctions of the integral operator on the unit sphere.
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Liu, Y., Liao, S. (2013). An Explicit Description of the Extended Gaussian Kernel. In: Washio, T., Luo, J. (eds) Emerging Trends in Knowledge Discovery and Data Mining. PAKDD 2012. Lecture Notes in Computer Science(), vol 7769. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36778-6_8
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DOI: https://doi.org/10.1007/978-3-642-36778-6_8
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