Geodesic
Minimax feature selection problem for constructing a classifier using support vector machines
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 5, pp. 967-976 
Yu. V. Goncharov. Minimax feature selection problem for constructing a classifier using support vector machines. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 5, pp. 967-976. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_5_a13/
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Voir la notice de l'article provenant de la source Math-Net.Ru

A minimax feature selection problem for constructing a classifier using support vector machines is considered. Properties of the solutions of this problem are analyzed. An improvement of the saddle point search algorithm based on extending the bound for the step parameter is proposed. A new nondifferential optimization algorithm is developed that, together with the saddle point search algorithm, forms a hybrid feature selection algorithm. The efficiency of the algorithm for computing Dykstra’s projections as applied for the feature selection problem is experimentally estimated.

[1] Goncharov Yu. V., Muchnik I. B., Shvartser L. V., “Algoritm vybora priznakov v zadache obucheniya klassifikatsii metodom opornykh vektorov”, Zh. vychisl. matem. i matem. fiz., 48:7 (2008), 1318–1336

[2] Demyanov V. F., Malozemov V. N., Vvedenie v minimaks, Nauka, M., 1972 | MR

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

[4] Polyak B. T., Vvedenie v optimizatsiyu, Nauka, M., 1983 | MR

[5] Combettes P., Luo J., “An adaptive level set method for nondifferentiable constrained image recovery”, IEEE Trans. Image Processing, 11 (2002), 1295–1304 | DOI | MR

[6] 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

[7] Izmailov A. F., Solodov M. F., Chislennye metody optimizatsii, Fizmatlit, M., 2005 | Zbl

[8] Weston J., Mukherjee S., Chapelle O. et al., “Feature selection for SVMs”, Advances in Neural Information Processing Systems, 13, 2000, 668–674