May 07 2007
Minimum Bounding Sphere SVM Formulation
La formulazione con sfera a minimo raggio è stata introdotta dallo stesso Vapnik per problemi di classificazione multipla. Successivamente è stata adoperata per problemi di One-class classification e per problemi di regressione. Infine per il Support Vector Clustering.
Approfondire:
-
B. Schölkopf, C. Burges, and V. Vapnik, "Extracting support data for a given task," in First International Conference on Knowledge Discovery & Data Mining, Menlo Park, 1995.
@inproceedings{sch95extracting, Address = {Menlo Park},
Author = {B. Sch”olkopf and C. Burges and V. Vapnik},
Booktitle = {First International Conference on Knowledge Discovery & Data Mining},
Date-Added = {2007-05-07 12:59:25 +0200},
Date-Modified = {2007-06-19 11:32:17 +0200},
Editor = {U. M. Fayyad and R. Uthurusamy},
Keywords = {svm},
Publisher = {AAAI Press},
Title = {Extracting support data for a given task},
Url = {http://citeseer.ist.psu.edu/sch95extracting.html},
Year = {1995},
Bdsk-File-1 = {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},
Bdsk-Url-1 = {http://citeseer.ist.psu.edu/sch95extracting.html}
}
-
D. M. J. Tax and R. P. W. Duin, "Data Domain Description using Support Vectors," in European Symposium on Artificial Neural Network, Bruges (Belgium), 1999, pp. 251-256.
@inproceedings{es1999, Address = {Bruges (Belgium)},
Author = {David M. J. Tax and Robert P. W. Duin},
Booktitle = {European Symposium on Artificial Neural Network},
Date-Added = {2007-05-07 12:55:54 +0200},
Date-Modified = {2007-06-23 08:24:18 +0200},
Keywords = {SVM, domain description, SVDD, novelty detection, one-class},
Month = {April},
Pages = {251–256},
Title = {Data Domain Description using Support Vectors},
Url = {http://www.dice.ucl.ac.be/Proceedings/esann/esannpdf/es1999-458.pdf},
Year = {1999},
Bdsk-File-1 = {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},
Bdsk-Url-1 = {http://www.dice.ucl.ac.be/Proceedings/esann/esannpdf/es1999-458.pdf}
}
-
J. Wang, P. Neskovic, and L. N. Cooper, "Pattern Classification Based on Minimum Bounding Spheres," in International Conference on Intelligent Computing, 2005, pp. 1969-1978.
@inproceedings{icic05,
author = {Jigang Wang and Predrag Neskovic and Leon N. Cooper},
Booktitle = {International Conference on Intelligent Computing},
Date-Added = {2007-05-07 13:10:15 +0200},
Date-Modified = {2007-06-19 18:44:37 +0200},
Keywords = {svm},
Pages = {1969–1978},
Title = {Pattern Classification Based on Minimum Bounding Spheres},
Url = {http://www.physics.brown.edu/physics/userpages/faculty/Predrag_Neskovic/Publications/icic05-mbs.PDF},
Year = {2005},
Bdsk-File-1 = {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},
Bdsk-Url-1 = {http://www.physics.brown.edu/physics/userpages/faculty/Predrag_Neskovic/Publications/icic05-mbs.PDF}
}
