Support vector machines for interval discriminant analysis

Neurocomputing

Volumn 71, Issue 7-9, 2008, Pages 1220-1229

  Angulo, C ^a   Anguita, D ^b   Gonzalez Abril, L ^c   Ortega, J A ^c  

^a UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

^b UNIVERSITY OF GENOA   (Italy)

^c UNIVERSITY OF SEVILLE   (Spain)

Author keywords

Classification; Convex optimization; Interval analysis; Kernel machines

Indexed keywords

DATA PROCESSING; DISCRIMINANT ANALYSIS; OPTIMIZATION;

CONVEX OPTIMIZATION THEORY; INTERVAL DISCRIMINANT ANALYSIS;

SUPPORT VECTOR MACHINES;

ARTICLE; BREAST CANCER; DATA ANALYSIS; DISCRIMINANT ANALYSIS; INTERVAL DISCRIMINANT ANALYSIS; KERNEL METHOD; LINEAR SYSTEM; PRIORITY JOURNAL; PROCESS OPTIMIZATION; PROGNOSIS; STATISTICAL ANALYSIS; SUPPORT VECTOR MACHINE;

EID: 40649093975     PISSN: 09252312     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.neucom.2007.12.025     Document Type: Article

References (28)

1. H.H. Bock, Analysis of Symbolic Data: Exploratory Methods for Extracting Statistical Information from Complex Data, Springer, New York, Secaucus, NJ, USA, 2000.
2. Cristianini N., and Shawe-Taylor J. An Introduction to Support Vector Machines and Other Kernel-based Learning Methods (2000), Cambridge University Press, Cambridge
3. Do T.-N., and Poulet F. Kernel methods and visualization for interval data mining. Proceedings of the International Symposium on Applied Stochastic Models and Data Analysis (2005), Brest, France 345-354
4. G. Fung, O.L. Mangasarian, J. Shavlik, Knowledge-based support vector machine classifiers, Technical Report 01-09, Data Mining Institute, Computer Sciences Department, University of Wisconsin, Madison, Wisconsin, November 2001.
5. Fung G.M., Mangasarian O.L., and Shavlik J.W. Knowledge-based support vector machine classifiers. In: Becker S.T.S., and Obermayer K. (Eds). Advances in Neural Information Processing Systems vol. 15 (2003), MIT Press, Cambridge, MA 521-528
6. L. González, F. Velasco, F. Cuberos, J.A. Ortega, C. Angulo, A kernel to use with a discretization of continuous features, in: Proceedings of Learning'04, Elche, Spain, 2004.
7. González L., Angulo C., Velasco F., and Catala A. Dual unification of bi-class support vector machine formulations. Pattern Recognition 39 7 (2006) 1325-1332
8. L. Gonzalez-Abril, C. Angulo, F. Velasco, J. Ortega, A note on the bias in SVMs for multi-classification, IEEE Trans. on Neural Networks, accepted for publication, doi:10.1109/TNN.2007.914138.
9. Hansen E. Global Optimization using Interval Analysis (1992), Marcel Dekker, New York
10. Hebrich R. Learning Kernel Classifiers: Theory and Algorithms (2002), MIT Press, Cambridge, MA
11. Hong D.H., and Hwang C. Interval regression analysis using quadratic loss support vector machine. IEEE Trans. Fuzzy Systems 13 2 (2005) 229-237
12. Hwang C., Hong D.H., and Seok K.H. Support vector interval regression machine for crisp input and output data. Fuzzy Sets and Systems 157 8 (2006) 1114-1125
13. Jaulin L., Kieffer M., Didrit O., and Walter E. Applied Interval Analysis (2001), Springer, London
14. Kreinovich V., Modave F., Starks S.A., and Xiang G. Towards real world applications: interval-related talks at nafips'05. Reliable Comput. 12 1 (2006) 73-77
15. Mangasarian O.L. Nonlinear Programming (1994), SIAM, Philadelphia, PA
16. T. Martinetz, K. Schulten, A "neural gas" network learns topologies, Artificial Neural Networks, Elsevier, Amsterdam, 1991, pp. 397-402.
17. Moore R.E. Interval Analysis (1966), Prentice-Hall, Englewood Cliffs
18. C.B.D.J. Newman, S. Hettich, C. Merz, UCI repository of machine learning databases 〈http://www.ics.uci.edu/∼mlearn/MLRepository.html〉.
19. P. Nivlet, F. Fournier, J. Royer, Interval discriminant analysis: an efficient method to integrate errors in supervised pattern recognition, in: 2nd International Symposium on Imprecise Probabilities and their Applications, 2001.
20. Ohta Y. Nonconvex polygon interval arithmetic as a tool for the analysis and design of robust control systems. Reliable Comput. 6 (2000) 247-279
21. Palumbo F. Editorial. Comput. Stat. 21 2 (2006) 183-185
22. S. Pikorski, L. Lacassagne, M. Kieffer, D. Etiemble, Efficient 16-bit floating point interval processor for embedded systems and applications, in: 12th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics, 2006.
23. X. Rovira, N. Agell, M. Sánchez, F. Prats, X. Parra, An approach to qualitative radial basis function networks over orders of magnitude, in: Proceedings of the 18th International Workshop on Qualitative Reasoning (QR'04), Evanston, Illinois, USA, 2004.
24. F.J. Ruiz, N. Agell, C. Angulo, A kernel intersection defined on intervals, in: Recent Advances in Artificial Intelligence Research and Development, vol. 113, in: Frontiers in Artificial Intelligence and Applications, IOS Press, 2004, pp. 103-110.
25. Tanaka H., and Lee H. Interval regression analysis by quadratic programming approach. IEEE Trans. Fuzzy Systems 6 4 (1998) 473-481
26. G.G. Towell, J.W. Shavlik, M.O. Noordenier, Refinement of Approximate Domain Theories by Knowledge Based Neural Network, vol. 2, 1990, pp. 861-866.
27. Vapnik V. Statistical Learning Theory (1998), Wiley, New York
28. Y. Zhao, Q. Chen, Q. He, An interval set classification based on support vector machines, in: Proceedings of the Joint International Conference on Autonomic and Autonomous Systems 2005/International Conference on Networking and Services 2005 (ICAS/ICNS 2005), IEEE Computer Society, Papeete, Tahiti, 2005, pp. 81-86.