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The basic classification SVM creates a maximum-margin hyperplane that lies in a transformed input space. Given training examples labeled either "yes" or "no", a maximum-margin hyperplane splits the "yes" and "no" training examples, such that the distance from the closest examples (the margin) to the hyperplane is maximized. The use of the maximum-margin hyperplane is motivated by Vapnik Chervonenkis theory, which provides a probabilistic test error bound which is minimized when the margin is maximized. The parameters of the maximum-margin hyperplane are derived by solving a quadratic programming (QP) optimization problem. There exist several specialized algorithms for quickly solving the QP problem that arises from SVMs.

The original optimal hyperplane algorithm proposed by Vladimir Vapnik in 1963 was a linear classifier. However, in 1992, Bernhard Boser , Isabelle Guyon and Vapnik suggested applying the kernel trick (originally proposed by Aizerman) to maximum-margin hyperplanes. The resulting algorithm is formally similar, except that every dot product is replaced by a non-linear kernelIn analysis, consider an integral transform T which transforms a function f into a function Tf given by the integral formula : The function k ''x ''y that appears in this formula is the kernel of the operator T''. See also Dirichlet kernel convolution ker function. This causes the linear algorithm to operate in a different space. Using the kernel trick makes the maximum margin hyperplane be fit in a feature space. The feature space is a non-linear map from the original input space, usually of much higher dimensionality than the original input space. In this way, non-linear classifiers can be created. If the kernel used is a radial basis function , the corresponding feature space is a Hilbert spaceIn mathematics, a Hilbert space is an inner product space that is complete with respect to the norm defined by the inner product. Hilbert spaces serve to clarify and generalize the concept of Fourier expansion, certain linear transformations such as the F of infinite dimension. Maximum margin classifiers are well regularizedThe mathematical term regularization has two main meanings, both associated with making a function more `regular' or smooth. Regularization in physics In physics, especially particle physics, regularization is a method of dealing with infinite, divergent,, so the infinite dimension does not spoil the results. In 19951995 was a common year starting on Sunday (see link for calendar). It has a Golden number of 1, and was the first year of the International Decade of the World's Indigenous People (1995- 2005): http://www. org/culture/indigenous . Events January events Ja, Corinna Cortes and Vapnik suggested a modified maximum margin idea that allows for mislabeled examples. If there exists no hyperplane that can split the "yes" and "no" examples, the Soft Margin method will choose a hyperplane that splits the examples as cleanly as possible, while still maximizing the distance to the nearest cleanly split examples. This work popularized the expression Support Vector Machine or SVM.

A version of a SVM for regression was proposed in 19971997 was a common year starting on Wednesday (see link for calendar), and was designated the International Year of the Reef''. Events January January 3 NBC's Today Show Bryant Gumbel signs off for the last time January 8 Mister Rogers receives a star on t by Vapnik, Steven Golowich , and Alex Smola . This method is called Support Vector Regression (SVR). The model produced by Support Vector Classification (as described above) only depends on a subset of the training data, because the cost function for building the model does not care about training points that lie beyond the margin. Analogously, the model produced by Support Vector Regression only depends on a subset of the training data, because the cost function for building the model ignores any training data that is close (within a threshold ) to the model prediction.