Feature selection combining linear support vector machines and concave optimization

Optimization Methods and Software

Volumn 25, Issue 1, 2010, Pages 117-128

  Rinaldi, F ^a,b   Sciandrone, M ^a,b  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

^b UNIVERSITY OF FLORENCE   (Italy)

Author keywords

Concave programming; Frank Wolfe method; Support vector machines; Zero norm

Indexed keywords

CLASSIFICATION ACCURACY; CONCAVE OPTIMIZATION; CONCAVE PROGRAMMING; FEATURE SELECTION; FUNCTIONAL DEPENDENCY; INPUT SPACE; INPUT VARIABLES; LINEAR CLASSIFIERS; LINEAR MACHINES; LINEAR MODEL; LINEAR SUPPORT VECTOR MACHINES; PREDICTION CAPABILITY; REAL-WORLD APPLICATION; SPARSE SOLUTIONS; WOLFE METHOD;

BIOLOGY; CLASSIFIERS; COMPUTATIONAL EFFICIENCY; VECTORS;

SUPPORT VECTOR MACHINES;

EID: 77949543342     PISSN: 10556788     EISSN: 10294937     Source Type: Journal    
DOI: 10.1080/10556780903139388     Document Type: Article

References (15)

1. U.Alon, N. Barkai, D.A. Notterman, K. Gish, S.Ybarra, D. Mack, and A.J. Levine, Broad patterns of gene expression revealed by clustering analysis of tumor and normal colon tissues probed by oligonucleotide arrays, Cell Biol. 96 (1999), pp. 6745-6750.
2. E. Amaldi and V. Kann, On the approximability of minimizing nonzero variables or unsatisfied relations in linear systems, Theore. Comput. Sci. 209 (1998), pp. 237-260.
3. P.S. Bradley and O.L. Mangasarian, Feature selection via concave minimization and support vector machines, in Machine Learning Proceedings of the Fifteenth International Conference(ICML '98), J. Shavlik, ed., Morgan Kaufmann, San Francisco, California, 1998, pp. 82-90.
4. K.-W. Chang, C.-J. Hsieh, and C.-J. Lin, Coordinate descent method for large-scale L2-loss linear SVM, J. Mach. Learn. Res. 9 (2008), pp. 1369-1398.
5. R.-E. Fan, K.-W. Chang, C.-J. Hsieh, X.-R.Wang, and C.-J. Lin, LIBLINEAR:A library for large linear classification, J. Mach. Learn. Res. 9 (2008), pp. 1871-1874.
6. M. Frank and P.Wolfe, An algorithm for quadratic programming, Naval Res. Logist. Quart. 3 (1956), pp. 95-110.
7. T.R. Golub, D.K. Slonim, P. Tamayo, C. Huard, M. Gaasenbeek, J.P. Mesirov, H. Coller, M.L. Loh, J.R. Downing, M.A. Caligiuri, C.D. Bloomfield, and E.S. Lander, Molecular classification of cancer: class discovery and class prediction by gene expression monitoring, Science 531, 286(5439) 1999, p. 531.
8. I. Guyon and A. Elisseeff, An introduction to variable and feature selection, J. Mach. Learn. Res. 3 (2003), pp. 1157-1182.
9. I. Guyon, J. Weston, S. Barnhill, and V. Vapnik, Gene selection for cancer classification using support vector machines, Mach. Learn. 46 (2002), pp. 389-422.
10. O.L. Mangasarian, Machine learning via polyhedral concave minimization, in Applied Mathematics and Parallel Computing - Festschrift for Klaus Ritter, H. Fischer, B. Riedmueller, and S. Schaeffler, eds., Physica-Verlag, Germany, 1996, pp. 175-188.
11. F. Rinaldi, F. Schoen, and M. Sciandrone, Concave programming for minimizing the zero-norm over polyhedral sets, Tech. Rep. RT 2/2008, Dipartimento Sistemi e Informatica, Università di Firenze, Comput. Optim. Appl., 2008, DOI: 10.1007/s10589-008-9202-9.
12. V.N. Vapnik, The Nature of Statistical Learning Theory, Springer-Verlag, NewYork, 1995.
13. M. West, C. Blanchette, H. Dressman, E. Huang, S. Ishida, R. Spang, H. Zuzan, J.A. Olson, Jr., J.R. Marks, and J.R. Nevins, Predicting the clinical status of human breast cancer by using gene expression profiles, Proc. Natl Acad. Sci. 17, 98 (2001), pp. 11462-11467.
14. J.Weston, A. Elisseef, B. Schölkopf, and M. Tipping, Use of the zero-norm with linear models and kernel methods, J. Mach. Learn. Res. 3 (2003), pp. 1439-1461.
15. J.Weston, A. Elisseef, G. Baklr, and F. Sinz, The spider. Available at http://www.kyb.tuebingen.mpg.de/bs/people/ spider/.