Radial basis function kernel: Difference between revisions

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In [[machine learning]], the ('''Gaussian''') '''[[radial basis function]] kernel''', or '''RBF kernel''', is a popular [[Positive-definite kernel|kernel function]] used in various [[kernel method|kernelized]] learning algorithms. In particular, it is commonly used in [[support vector machine]] [[statistical classification|classification]].<ref name="Chang2010">Yin-Wen Chang, Cho-Jui Hsieh, Kai-Wei Chang, Michael Ringgaard and Chih-Jen Lin (2010). [http://jmlr.org/papers/v11/chang10a.html "Training and testing low-degree polynomial data mappings via linear SVM"]. ''J. Machine Learning Research'' '''11''':1471–1490.</ref>

The RBF kernel on two samples '''x''' and '''x'''', represented as feature vectors in some ''input space'', is defined as<ref name="primer">Vert, Jean-Philippe, Koji Tsuda, and Bernhard Schölkopf (2004). [http://cbio.ensmp.fr/~jvert/publi/04kmcbbook/kernelprimer.pdf "A primer on kernel methods".] ''Kernel Methods in Computational Biology''.</ref>