Support vector machines with adaptive Lq penalty

Computational Statistics and Data Analysis

Volumn 51, Issue 12, 2007, Pages 6380-6394

  Liu, Yufeng ^a   Helen Zhang, Hao ^b   Park, Cheolwoo ^c   Ahn, Jeongyoun ^c  

^a UNIVERSITY OF NORTH CAROLINA   (United States)

^b NORTH CAROLINA STATE UNIVERSITY   (United States)

^c UNIVERSITY OF GEORGIA   (United States)

Author keywords

Adaptive penalty; Classification; Shrinkage; Support vector machine; Variable selection

Indexed keywords

ADAPTIVE ALGORITHMS; ADAPTIVE SYSTEMS; CLASSIFICATION (OF INFORMATION); ITERATIVE METHODS;

ADAPTIVE PENALTY; DATA APPLICATIONS; ITERATIVE ALGORITHMS; VARIABLE SELECTION;

SUPPORT VECTOR MACHINES;

EID: 34547234238     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2007.02.006     Document Type: Article

References (23)

1. Antoniadis A., and Fan J. Regularization of wavelets approximations. J. Amer. Statist. Assoc. 96 (2001) 939-967
2. Boser, B., Guyon, I., Vapnik, V.N., 1992. A training algorithm for optimal margin classifiers. In: The Fifth Annual Conference on Computational Learning Theory. ACM, Pittsburgh, pp. 142-152.
3. Bradley P., and Mangasarian O. Feature selection via concave minimization and support vector machines. In: Shavlik J. (Ed). ICML'98 (1998), Morgan Kaufmann, Los Altos, CA
4. Chen S., Donoho D.L., and Saunders M.A. Atomic decomposition by basis pursuit. SIAM J. Sci. Comput. 20 1 (1999) 33-61
5. Crammer K., and Singer Y. On the algorithmic implementation of multiclass kernel-based vector machines. J. Mach. Learning Res. 2 (2001) 265-292
6. Donoho D., and Johnstone I. Ideal spatial adaptation by wavelet shrinkage. Biometrika 81 (1994) 425-455
7. Efron B., Hastie T., Johnstone I., and Tibshirani R. Least angle regression. Ann. Statist. 32 2 (2004) 407-499
8. Fan J., and Li R. Variable selection via nonconcave penalized likelihood and its oracle properties. J. Amer. Statist. Assoc. 96 456 (2001) 1348-1360
9. Frank I.E., and Friedman J.H. An statistical view of some chemometrics regression tools. Technometrics 35 (1993) 109-135
10. Fu W.J. Penalized regressions: the bridge vs the lasso. J. Comput. Graphical Statist. 7 3 (1998) 397-416
11. Ikeda K., and Murata N. Geometrical properties of ν support vector machines with different norms. Neural Comput. 17 11 (2005) 2508-2529
12. Knight K., and Fu W.J. Asymptotics for lasso-type estimators. Ann. Statist. 28 5 (2000) 1356-1378
13. Lee Y., Lin Y., and Wahba G. Multicategory support vector machines, theory, and application to the classification of microarray data and satellite radiance data. J. Amer. Statist. Assoc. 99 465 (2004) 67-81
14. Lin Y. Support vector machines and the Bayes rule in classification. Data Mining and Knowledge Discovery 6 (2002) 259-275
15. Lin Y., Lee Y., and Wahba G. Support vector machines for classification in nonstandard situations. Mach. Learning 46 (2002) 191-202
16. Tibshirani R.J. Regression shrinkage and selection via the Lasso. J. Roy. Statist. Soc. Ser. B 58 (1996) 267-288
17. Vapnik V. Statistical Learning Theory (1998), Wiley, New York
18. Wahba G. Support vector machines, reproducing kernel Hilbert spaces, and randomized GACV. In: Schölkopf B., Burges C.J.C., and Smola A.J. (Eds). Advances in Kernel Methods. Support Vector Learning (1998), MIT Press, Cambridge, MA 125-143
19. Wahba G., Gu C., Wang Y., and Chappell R. Soft Classification, a.k.a. risk estimation, via penalized log likelihood and smoothing spline analysis of variance. In: Petsche T. (Ed). Computational Learning Theory and Natural Learning Systems vol. 3 (1995), MIT Press, Cambridge, MA 127-158
20. Wang L., and Shen X. Multi-category support vector machines, feature selection, and solution path. Statist. Sinica 16 (2006) 617-633
21. Weston J., and Watkins C. Support vector machines for multi-class pattern recognition. Proceedings of the Seventh European Symposium on Artificial Neural Networks (1999)
22. Zhu J., Hastie T., Rosset S., and Tibshirani R. 1-norm support vector machines. Neural Inform. Process. Systems 16 (2003)
23. Zou H., and Hastie T. Regularization and variable selection via the elastic net. J. Roy. Statist. Soc. Ser. B 67 (2005) 301-320