Abstract
For the construction of support vector machines so-called Mercer kernels are of considerable importance. Since the conditions of Mercer’s theorem are hard to verify some mathematical results arising from semi-simple Lie groups are collected here to provide concrete examples of Mercer kernels for the real line. Besides an interesting connection to Furstenberg’s theory of noncommuting random products comes to light. These results have, in essence, been known for quite some time but are rather technical in nature. Hence a concise treatment is offered here to make them accessible to Neural Network researchers.
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Falkowski, BJ. (2003). Mercer Kernels and 1-Cohomology of Certain Semi-simple Lie Groups. In: Palade, V., Howlett, R.J., Jain, L. (eds) Knowledge-Based Intelligent Information and Engineering Systems. KES 2003. Lecture Notes in Computer Science(), vol 2773. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45224-9_44
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DOI: https://doi.org/10.1007/978-3-540-45224-9_44
Publisher Name: Springer, Berlin, Heidelberg
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