Problem Definition
In 1992 Vapnik and coworkers [1] proposed a supervised algorithm for classification that has since evolved into what are now known as Support Vector Machines (SVMs) [2]: a class of algorithms for classification, regression and other applications that represent the current state of the art in the field. Among the key innovations of this method were the explicit use of convex optimization, statistical learning theory, and kernel functions.
Classification
Given a training set \( { S=\{(\mathbf{x}_1,y_1), \dots , (\mathbf{x}_\ell, y_\ell)\} } \) of data points \( { \mathbf{x}_i } \) from \( { X \subseteq \mathbb{R}^n } \) with corresponding labels y i from \( { Y = \{-1, +1 \} } \), generated from an unknown distribution, the task of classification is to learn a function \( { g: X \rightarrow Y } \) that correctly classifies new examples \( { (\mathbf{x}, y) } \) (i. e. such that \( { g(\mathbf{x})=y } \)) generated from the same underlying distribution as the training...
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Recommended Reading
Boser, B., Guyon, I., Vapnik, V.: AÂ training algorithm for optimal margin classifiers. In: Proceedings of the Fifth Annual Workshop on Computational Learning Theory, Pittsburgh (1992)
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Cristianini, N., Ricci, E. (2008). Support Vector Machines. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30162-4_415
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DOI: https://doi.org/10.1007/978-0-387-30162-4_415
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