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 [[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). ''Training and testing low-degree polynomial data mappings via linear SVM''. J. Machine Learning Research '''11''':1471–1490.</ref>

The RBF kernel applied 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). "A primer on kernel methods." Kernel Methods in Computational Biology.</ref>

:<math>K(\mathbf{x}, \mathbf{x'}) = \exp\left(-\frac{||\mathbf{x} - \mathbf{x'}||_2^2}{2\sigma^2}\right)</math>