New results on error correcting output codes of kernel machines

IEEE Transactions on Neural Networks

Volumn 15, Issue 1, 2004, Pages 45-54

  Passerini, Andrea ^a   Pontil, Massimiliano ^b   Frasconi, Paolo ^a  

^a UNIVERSITY OF FLORENCE   (Italy)

^b UNIVERSITY COLLEGE LONDON   (United Kingdom)

Author keywords

Error correcting output codes (ECOC); Machine learning; Statistical learning theory; Support vector machines

Indexed keywords

BINARY CODES; CODING ERRORS; DECODING; ERROR CORRECTION; LEARNING ALGORITHMS; MATHEMATICAL MODELS; NEURAL NETWORKS; PARAMETER ESTIMATION; PROBABILITY; STATISTICAL METHODS;

BINARY CLASSIFIERS; ERROR CORRECTING OUTPUT CODES; MULTICLASS CLASSIFICATION; STATISTICAL LEARNING THEORY; SUPPORT VECTOR MACHINES;

LEARNING SYSTEMS;

ARTICLE; ARTIFICIAL NEURAL NETWORK; METHODOLOGY;

NEURAL NETWORKS (COMPUTER); RESEARCH DESIGN;

EID: 1242263799     PISSN: 10459227     EISSN: None     Source Type: Journal    
DOI: 10.1109/TNN.2003.820841     Document Type: Article

References (35)

1. H. Akaike, "Information theory and an extension of the maximum likelihood principle," in Proc. 2nd Int. Symp. Information Theory, 1973, pp. 267-281.
2. E. L. Allwein, R. E. Schapire, and Y. Singer, "Reducing multiclass to binary: a unifying approach for margin classifiers," in Proc. 17th Int. Conf. Machine Learning. San Francisco, CA: Morgan Kaufmann, 2000, pp. 9-16.
3. N. Aronszajn, "Theory of reproducing kernels," Trans. Amer. Math. Soc., vol. 686, pp. 337-404, 1950.
4. P. Bartlett and J. Shawe-Taylor, "Generalization performance of support vector machine and other patern classifiers," in Advances in Kernel Methods - Support Vector Learning, B. Scholkopf and C. Burges, Eds. Cambridge, MA: MIT Press, 1998.
5. Y. Bengio, "Gradient-based optimization of hyper-parameters," Neural Computation, vol. 12, no. 8, pp. 1889-1900, 2000.
6. C. L. Blake and C. J. Merz, UCI Repository of Machine Learning Databases, 1998.
7. R. C. Bose and D. K. Ray-Chaudhuri, "On a class of error correcting binary group codes," Inform. Contr., vol. 3, pp. 68-79, Mar. 1960.
8. O. Bousquet and A. Elisseeff, "Stability and generalization," J. Machine Learning Res., vol.2, pp. 499-526, 2002.
9. P. Burman, "A comparative study of ordinary cross validation, 5-fold cross validation, and the repeated learning testing methods," Biometrica, vol. 76, no. 3, pp. 503-514, 1989.
10. O. Chapelle, V. Vapnik, O. Bousquet, and S. Mukherjee, "Choosing kernel parameters for support vector machines," Machine Learning, vol. 46, no. 1-3, pp. 131-159, 2002.
11. C. Cortes and V. Vapnik, "Support vector networks," Machine Learning, vol. 20, pp. 1-25, 1995.
12. K. Crammer and Y. Singer, "On the learnability and design of output codes for multiclass problems," in Computat. Learning Theory, 2000, pp. 35-46.
13. P. Craven and G. Wahba, "Smoothing noisy data with spline functions: estimating the correct degree of smoothing by the method of generalized cross validation," Numer. Math, vol. 31, pp. 377-403, 1979.
14. N. Cristianini and J. Shawe-Taylor, An Introduction to Support Vector Machines. Cambridge, U.K.: Cambridge Univ. Press, 2000.
15. F. Cucker and S. Smale, "On the mathematical foundations of learning," Bulletin (New Series) of the Amer. Math. Soc., vol. 39, no. 1, pp. 1-49, 2001.
16. T. G. Dietterich and G. Bakiri, "Solving multiclass learning problems via error-correcting output codes," J. Artific. Intell. Res., vol. 2, pp. 263-286, 1995.
17. A. Elisseeff and M. Pontil et al., "Leave-one-out error and stability of learning algorithms with applications," in NATO-ASI Series on Learning Theory and Practice, J. Suykens et al., Eds: IOS Press, 2002.
18. T. Evgeniou, M. Pontil, and T. Poggio, "Regularization networks and support vector machines," Adv. Computat. Math., vol. 13, pp. 1-50, 2000.
19. C. H. FitzGerald, C. A. Micchelli, and A. Pinkus, "Functions that preserves families of positive definite functions," Linear Alg. its Applicat., vol. 221, pp. 83-102, 1995.
20. Y. Freund and R. E. Schapire, "Large margin classification using the perceptron algorithm," in Computat. Learning Theory, 1998, pp. 209-217.
21. J. H. Friedman, "Another approach to polychotomous classification," Dept. Statistics, Stanford Univ., Tech. Rep., 1996.
22. J. Fürnkranz, "Round robin classification," J. Machine Learning Research, vol. 2, pp. 721-747, 2002.
23. Y. Guermeur, A. Elisseeff, and H. Paugam-Mousy, "A new multi-class SVM based on a uniform convergence result," in Proc. IEEE IJCNN - Int. Joint Conf. Neural Networks, 2000.
24. T. Hastie, R. Tibshirani, and J. Friedman, "The elements of statistical learning: data mining, inference, and prediction," in Springer Series in Statistics. New York: Springer-Verlag, 2002.
25. T. Jaakkola and D. Haussler, "Exploiting generative models in discriminative classifiers," in Proc. Neural Information Processing Conf., 1998.
26. J. Kwok, "Moderating the outputs of support vector machine classifiers," IEEE Trans. Neural Networks, vol. 10, pp. 1018-1031, 1999.
27. C. A. Micchelli, "Interpolation of scattered data: distance matrices and conditionally positive definite functions," Construct. Approximat., vol. 2, pp. 11-22, 1986.
28. J. Platt, "Probabilistic outputs for support vector machines and comparison to regularized likelihood methods," in Advances in Large Margin Classiers, A. Smola, P. Bartlett, B. Scholkopf, and D. Schurmans, Eds. Cambridge, MA: MIT Press, 1999.
29. J. D. M. Rennie and R. Rifkin, "Improving multiclass text classification with the support vector machine," MIT, Tech. Rep. 2001-026, 2001.
30. F. Rosenblatt, "The perceptron: a probabilistic model for information storage and organization in the brain," Psycholog. Rev., vol. 65, pp. 386-408, 1958.
31. B. Schoelkopf and A. J. Smola, Learning With Kernels. Cambridge, MA: MIT Press, 2002.
32. V. N. Vapnik, Estimation of Dependences Based on Empirical Data. Berlin, Germany: Springer-Verlag, 1982.
33. ____, Statistical Learning Theory. New York: Wiley, 1998.
34. G. Wahba, "Splines models for observational data," in Series in Applied Mathematics. Philadelphia, PA: SIAM, 1990, vol. 59.
35. T. Joachims, "Making large-scale (SVM) learning practical," in Advances in Kernel Methods - Support Vector Learning, B. Schölkopf, C. Burges, and A. Smola, Eds. Cambridge, MA: MIT Press, 1998, ch. 11, pp. 169-185.