Feature selection algorithm in classification learning using support vector machines
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 7, pp. 1318-1336 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

An algorithm for selecting features in the classification learning problem is considered. The algorithm is based on a modification of the standard criterion used in the support vector machine method. The new criterion adds to the standard criterion a penalty function that depends on the selected features. The solution of the problem is reduced to finding the minimax of a convex-concave function. As a result, the initial set of features is decomposed into three classes – unconditionally selected, weighted selected, and eliminated features.
@article{ZVMMF_2008_48_7_a14,
     author = {Yu. V. Goncharov and I. B. Muchnik and L. V. Shvartser},
     title = {Feature selection algorithm in classification learning using support vector machines},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1318--1336},
     year = {2008},
     volume = {48},
     number = {7},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_7_a14/}
}
TY  - JOUR
AU  - Yu. V. Goncharov
AU  - I. B. Muchnik
AU  - L. V. Shvartser
TI  - Feature selection algorithm in classification learning using support vector machines
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2008
SP  - 1318
EP  - 1336
VL  - 48
IS  - 7
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_7_a14/
LA  - ru
ID  - ZVMMF_2008_48_7_a14
ER  - 
%0 Journal Article
%A Yu. V. Goncharov
%A I. B. Muchnik
%A L. V. Shvartser
%T Feature selection algorithm in classification learning using support vector machines
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2008
%P 1318-1336
%V 48
%N 7
%U http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_7_a14/
%G ru
%F ZVMMF_2008_48_7_a14
Yu. V. Goncharov; I. B. Muchnik; L. V. Shvartser. Feature selection algorithm in classification learning using support vector machines. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 7, pp. 1318-1336. http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_7_a14/

[1] Vapnik V. N., Chervonenkis A. Ya., Teoriya raspoznavaniya obrazov, Nauka, M., 1974 | MR | Zbl

[2] Vapnik V. N., Vosstanovlenie zavisimostei po empiricheskim dannym, Nauka, M., 1979 | MR | Zbl

[3] Vapnik V. N., The nature of statistical learning theory, Springer, New York, 1995 | MR

[4] Cortes C., Vapnik V., “Support vector networks”, Machine Learning, 20:3 (1995), 273–297 | Zbl

[5] Burges C. J. C., “A tutorial on support vector machines for pattern recognition”, Knowledge Discovery and Data Mining, 2:4 (1998), 121–167 | DOI

[6] Bennett K. P., Campbell C., “Support vector machines: Hype or hallelujah?”, SIGKDD Explorations, 2:2 (2000), 1–13 | DOI

[7] Aizerman M. A., Bravermann E. M., Rozonoer L. I., Metod potentsialnykh funktsii v teorii obucheniya mashin, Nauka, M., 1970

[8] Molina L., Belanche L., Nebot A., Feature selection algorithms: A survey and experimental evaluation, ICDM, 2002, 306–313 pp.

[9] Goncharov Y., Muchnik L., Shvartser L., Simultaneous feature selection and margin maximization using saddle point approach, DIMACS Techn. 2004. no 2004-08

[10] Rokafellar P., Vypuklyi analiz, Mir, M., 1973

[11] Errou K. Dzh., Gurvits L., Udzava X., Issledovanie po lineinomu i nelineinomu programmirovaniyu, Izd-vo inostr. lit., M., 1962

[12] Antipin A. C., “Upravlyaemye proksimalnye differentsialnye sistemy dlya resheniya sedlovykh zadach”, Differents. ur-niya, 28:11 (1992), 1846–1861 | MR | Zbl

[13] Golshtein E. G., Tretyakov N. V., Modifitsirovannye funktsii Lagranzha, Nauka, M., 1989 | MR

[14] Korpelevich G. M., “Ekstragradientnyi metod dlya otyskaniya sedlovykh tochek i drugikh zadach”, Ekonomika i matem. metody, 12 (1976), 560–565

[15] Antipin A. C., “Metod gradientnogo tipa dlya otyskaniya sedlovoi tochki modifitsirovannoi funktsii Lagranzha”, Ekonomika i matem. metody, 13 (1977), 756 | MR

[16] Antipin A. S., “From optima to equilibria”, Proc. Inst. Systems Analys. “Dynamics of non-homogeneous systems”, v. 3, Moscow, 2000, 35–64

[17] Censor Y., Computational acceleration of projection algorithms for the linear best approximation problem, Techn. Rept., May, Dept. Math., Univ. Haifa, Israel, 2005

[18] Bauschke H. H., Borwein J. M., “Dykstra's alternating projection algorithm for two sets”, J. Approximat. Theory, 79:3 (1994), 418–443 | DOI | MR | Zbl

[19] Gaffke N., Mathar R., “A cyclic projection algorithm via duality”, Metrika, 36:1 (1989), 29–54 | DOI | MR | Zbl

[20] Joachims T., “Optimizing search engines using clickthrough data”, ACM SIGKDD Conf. Knowledge Discovery and Data Mining (KDD), 2002, 133–142

[21] Joachims T., “Estimating the generalization performance of an SVM-Efficiently”, Proc. ICML-00, 17th Internat. Conf. Mach. Learning, 2000, 431–438

[22] Anghelescu A. V., Muchnik I. B., “Optimization of SVM in a space of two parameters: weak margin and intercept”, DIMACS Working Group on Monitoring Message Streams, May, 2003

[23] Goncharov Y., Muchnik I., Shvartser L., Saddle point feature selection in SVM regression, DIMACS Techn. Rept. no 2007-08, 2007