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Support Vector Machines

1992; Boser, Guyon, Vapnik

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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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  • DOI: 10.1007/978-0-387-30162-4_415
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Figure 1

Recommended Reading

  1. Boser, B., Guyon, I., Vapnik, V.: A training algorithm for optimal margin classifiers. In: Proceedings of the Fifth Annual Workshop on Computational Learning Theory, Pittsburgh (1992)

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  2. Cristianini, N., Shawe-Taylor, J.: An Introduction to Support Vector Machines and other kernel-based learning methods. Cambridge University Press, Cambrigde, Book website: www.support-vector.net (2000)

  3. Vapnik, V.: The Nature of Statistical Learning Theory. Springer, New York (1995)

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  4. Cortes, C., Vapnik, V.: Support-vector network. Mach. Learn. 20, 273–297 (1995)

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  5. Hastie, T., Rosset, S., Tibshirani, R., Zhu, J.: The entire regularization path for the support vector machine. J. Mach. Learn. Res. 5, 1391–1415 (2004)

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  6. Drucker, H., Burges, C.J.C., Kaufman, L., Smola, A., Vapnik, V.: Support Vector Regression Machines. Adv. Neural. Inf. Process. Syst. (NIPS) 9, 155–161 MIT Press (1997)

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  7. Platt, J.: Fast training of support vector machines using sequential minimal optimization. In: Schölkopf, B., Burges, C.J.C., Smola, A.J. (eds.) Advances in Kernel Methods Support Vector Learning. pp 185–208. MIT Press, Cambridge (1999)

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  8. Shawe-Taylor, J., Cristianini, N.: Kernel Methods for Pattern Analysis. Cambridge University Press, Cambridge. Book website: www.kernel-methods.net (2004)

  9. Scholkopf, B., Smola, A.J.: Learning with Kernels. MIT Press, Cambridge (2002)

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  10. Lanckriet, G.R.G., Cristianini, N., Bartlett, P., El Ghaoui, L., Jordan, M.I.: Learning the Kernel Matrix with Semidefinite Programming. J. Mach. Learn. Res. 5, 27–72 (2004)

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  11. Joachims, T.: Text categorization with support vector machines. In: Proceedings of European Conference on Machine Learning (ECML) Chemnitz (1998)

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  12. Dumais, S., Platt, J., Heckerman, D., Sahami, M.: Inductive learning algorithms and representations for text categorization. In: 7th International Conference on Information and Knowledge Management (1998)

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  13. LeCun, Y., Jackel, L.D., Bottou, L., Brunot, A., Cortes, C., Denker, J.S., Drucker, H., Guyon, I., Muller, U.A., Sackinger, E., Simard, P., Vapnik, V.: Comparison of learning algorithms for handwritten digit recognition. In: Fogelman-Soulie F., Gallinari P. (eds.), Proceedings International Conference on Artificial Neural Networks (ICANN) 2, 5360. EC2 (1995)

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  14. Jaakkola, T.S., Haussler, D.: Probabilistic kernel regression models. In: Proceedings of the 1999 Conference on AI and Statistics Fort Lauderdale (1999)

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  15. Brown, M., Grundy, W., Lin, D., Cristianini, N., Sugnet, C., Furey, T., Ares Jr., M., Haussler, D.: Knowledge-based analysis of mircoarray gene expression data using support vector machines. In: Proceedings of the National Academy of Sciences 97(1), 262–267 (2000)

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© 2008 Springer-Verlag

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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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