Geodesic
Some methods of constructing kernels in statistical learning
Discussiones Mathematicae. Probability and Statistics, Tome 30 (2010) no. 2, pp. 179-201

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This paper is a collection of numerous methods and results concerning a design of kernel functions. It gives a short overview of methods of building kernels in metric spaces, especially R^n and S^n. However we also present a new theory. Introducing kernels was motivated by searching for non-linear patterns by using linear functions in a feature space created using a non-linear feature map.
Keywords: positive definite kernel, dot product kernel, statistical kernel, SVM, kPCA 
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Górecki, Tomasz; Łuczak, Maciej. Some methods of constructing kernels in statistical learning. Discussiones Mathematicae. Probability and Statistics, Tome 30 (2010) no. 2, pp. 179-201. http://geodesic.mathdoc.fr/item/DMPS_2010_30_2_a1/