Ellipsoidal Support Vector Machines

Michinari Momma, Kohei Hatano, Hiroki Nakayama
Proceedings of 2nd Asian Conference on Machine Learning, PMLR 13:31-46, 2010.

Abstract

This paper proposes the ellipsoidal SVM (e-SVM) that uses an ellipsoid center, in the version space, to approximate the Bayes point. Since SVM approximates it by a sphere center, e-SVM provides an extension to SVM for better approximation of the Bayes point. Although the idea has been mentioned before (Ruján, 1997), no work has been done for formulating and kernelizing the method. Starting from the maximum volume ellipsoid problem, we successfully formulate and kernelize it by employing relaxations. The resulting e-SVM optimization framework has much similarity to SVM; it is naturally extendable to other loss functions and other problems. A variant of the sequential minimal optimization is provided for efficient batch implementation. Moreover, we provide an online version of linear, or primal, e-SVM to be applicable for large-scale datasets.

Cite this Paper

BibTeX
@InProceedings{pmlr-v13-momma10a, title = {Ellipsoidal Support Vector Machines}, author = {Momma, Michinari and Hatano, Kohei and Nakayama, Hiroki}, booktitle = {Proceedings of 2nd Asian Conference on Machine Learning}, pages = {31--46}, year = {2010}, editor = {Sugiyama, Masashi and Yang, Qiang}, volume = {13}, series = {Proceedings of Machine Learning Research}, address = {Tokyo, Japan}, month = {08--10 Nov}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v13/momma10a/momma10a.pdf}, url = {https://proceedings.mlr.press/v13/momma10a.html}, abstract = {This paper proposes the ellipsoidal SVM (e-SVM) that uses an ellipsoid center, in the version space, to approximate the Bayes point. Since SVM approximates it by a sphere center, e-SVM provides an extension to SVM for better approximation of the Bayes point. Although the idea has been mentioned before (Ruján, 1997), no work has been done for formulating and kernelizing the method. Starting from the maximum volume ellipsoid problem, we successfully formulate and kernelize it by employing relaxations. The resulting e-SVM optimization framework has much similarity to SVM; it is naturally extendable to other loss functions and other problems. A variant of the sequential minimal optimization is provided for efficient batch implementation. Moreover, we provide an online version of linear, or primal, e-SVM to be applicable for large-scale datasets.} }
Endnote
%0 Conference Paper %T Ellipsoidal Support Vector Machines %A Michinari Momma %A Kohei Hatano %A Hiroki Nakayama %B Proceedings of 2nd Asian Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2010 %E Masashi Sugiyama %E Qiang Yang %F pmlr-v13-momma10a %I PMLR %P 31--46 %U https://proceedings.mlr.press/v13/momma10a.html %V 13 %X This paper proposes the ellipsoidal SVM (e-SVM) that uses an ellipsoid center, in the version space, to approximate the Bayes point. Since SVM approximates it by a sphere center, e-SVM provides an extension to SVM for better approximation of the Bayes point. Although the idea has been mentioned before (Ruján, 1997), no work has been done for formulating and kernelizing the method. Starting from the maximum volume ellipsoid problem, we successfully formulate and kernelize it by employing relaxations. The resulting e-SVM optimization framework has much similarity to SVM; it is naturally extendable to other loss functions and other problems. A variant of the sequential minimal optimization is provided for efficient batch implementation. Moreover, we provide an online version of linear, or primal, e-SVM to be applicable for large-scale datasets.
RIS
TY - CPAPER TI - Ellipsoidal Support Vector Machines AU - Michinari Momma AU - Kohei Hatano AU - Hiroki Nakayama BT - Proceedings of 2nd Asian Conference on Machine Learning DA - 2010/10/31 ED - Masashi Sugiyama ED - Qiang Yang ID - pmlr-v13-momma10a PB - PMLR DP - Proceedings of Machine Learning Research VL - 13 SP - 31 EP - 46 L1 - http://proceedings.mlr.press/v13/momma10a/momma10a.pdf UR - https://proceedings.mlr.press/v13/momma10a.html AB - This paper proposes the ellipsoidal SVM (e-SVM) that uses an ellipsoid center, in the version space, to approximate the Bayes point. Since SVM approximates it by a sphere center, e-SVM provides an extension to SVM for better approximation of the Bayes point. Although the idea has been mentioned before (Ruján, 1997), no work has been done for formulating and kernelizing the method. Starting from the maximum volume ellipsoid problem, we successfully formulate and kernelize it by employing relaxations. The resulting e-SVM optimization framework has much similarity to SVM; it is naturally extendable to other loss functions and other problems. A variant of the sequential minimal optimization is provided for efficient batch implementation. Moreover, we provide an online version of linear, or primal, e-SVM to be applicable for large-scale datasets. ER -
APA
Momma, M., Hatano, K. & Nakayama, H.. (2010). Ellipsoidal Support Vector Machines. Proceedings of 2nd Asian Conference on Machine Learning, in Proceedings of Machine Learning Research 13:31-46 Available from https://proceedings.mlr.press/v13/momma10a.html.

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