Vapnik Chervonenkis theory

Vapnik Chervonenkis theory (also known as VC theory) was developed during 1960-1990 by Vladimir Vapnik and Alexey Chervonenkis. The theory is a form of computational learning theory, which attempts to explains the learning process from a statistical point of view. VC theory is also referred to as statistical learning theory by Vapnik and his close colleagues. VC theory covers four parts (as explained in The Nature of Statistical Learning Theory): Theory of consistency of learning process ...

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The concept of shattering of a set of points plays an important role in Vapnik Chervonenkis theory, also known as VC-theory. Shattering and VC-theory are used in the study of empirical processes as well as in statistical computational learning theory. Shattering - Definition. A class of sets, C, shatters a set A if and only if, for all there exists some such that , that is, if and only if For ...

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• Shattering - Definition

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When used for classification, the SVM algorithm creates a hyperplane that separates the data into two classes with the maximum-margin. Given training examples labeled either "yes" or "no", a maximum-margin hyperplane is identified which splits the "yes" from the "no" training examples, such that the distance between the hyperplane and the closest examples (the margin) is maximized. The use of the maximum-margin hyperplane is motivated by Vapnik Chervonenkis theory, which provides a probabilistic test error bound that is minimized when ...

See also:

Support vector machine, Support vector machine - Linear classification, Support vector machine - Non-linear classification with the kernel trick, Support vector machine - Soft margin, Support vector machine - Regression, Support vector machine - Software

Read more here: » Support vector machine: Encyclopedia II - Support vector machine - Linear classification

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 a way to create non-linear classifiers by 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 kernel function. This allows the algorithm to fit the maximum-margin hyperplane in the transformed feature space. The transformation may b ...

See also:

Support vector machine, Support vector machine - Linear classification, Support vector machine - Non-linear classification with the kernel trick, Support vector machine - Soft margin, Support vector machine - Regression, Support vector machine - Software

Read more here: » Support vector machine: Encyclopedia II - Support vector machine - Non-linear classification with the kernel trick