Pattern classification with class probability output network

IEEE Transactions on Neural Networks

Volumn 20, Issue 10, 2009, Pages 1659-1673

  Park, Woon Jeung ^a   Kil, Rhee Man ^a  

^a Korea Advanced Institute of Science and Technology (KAIST)   (South Korea)

Author keywords

Bayes decision; Beta distribution; Classification; Probabilistic scaling; Support vector machine (SVM)

Indexed keywords

BAYES DECISION; BETA DISTRIBUTION; CLASSIFICATION; PROBABILISTIC SCALING; SUPPORT VECTOR MACHINE (SVM);

CLASSIFIERS; DISTRIBUTION FUNCTIONS; IMAGE RETRIEVAL; SUPPORT VECTOR MACHINES;

PROBABILITY;

ALGORITHM; ARTICLE; ARTIFICIAL NEURAL NETWORK; AUTOMATED PATTERN RECOGNITION; COMPUTER SIMULATION; FEEDBACK SYSTEM; METHODOLOGY; STATISTICAL MODEL;

ALGORITHMS; COMPUTER SIMULATION; FEEDBACK; MODELS, STATISTICAL; NEURAL NETWORKS (COMPUTER); PATTERN RECOGNITION, AUTOMATED;

EID: 70350341225     PISSN: 10459227     EISSN: None     Source Type: Journal    
DOI: 10.1109/TNN.2009.2029103     Document Type: Article

References (34)

1. K. Fukunaga and D. Kessell, "Nonparametric bayes error estimation using unclassified samples," IEEE Trans. Inf. Theory, vol. IT-19, no. 4, pp. 434-439, Jul. 1973.
2. N. Glick, "Additive estimators for probabilities of correct classification," Pattern Recognit., vol. 10, pp. 211-222, 1978.
3. J. Kittler and P. Devijver, "An efficient estimator of pattern recognition system error probability," Pattern Recognit., vol. 13, pp. 245-249, 1981.
4. A. G. Curieses, J. C. Sueiro, R. A. Rodriguez, and A. R. Vidal, "Local estiamtion of posterior class probabilities to minimize classification errors," IEEE Trans. Neural Netw., vol. 15, no. 2, pp. 309-317, Mar. 2004.
5. E. Parzen, "On the estimation of a probability density function and mode," Ann. Math. Statist., vol. 33, pp. 1065-1076, 1962.
6. V. Vapnik, Statistical Learning Theory. New York: Wiley, 1998.
7. G. Wahba, "Advances in kernel methods," in Support Vector Learning, Reproducing Kernel Hilbert Spaces and the Randomized GACV. Cambridge, MA: MIT Press, 1999, pp. 69-88.
8. T. S. Jaakkola and D. Haussler, "Probabilistic kernel regression models," in Proc. Conf. Artif. Intell. Statist., 1999.
9. V. Roth, "Probabilistic discriminative kernel classifiers for multi-class problems," in Lecture Notes in Computer Science. Berlin, Germany: Springer-Verlag, 2001, vol. 2191, pp. 246-253.
10. J. Zhu and T. Hastie, "Kernel logistic regression and the import vector machine," J. Comput. Graph. Statist., vol. 14, no. 1, pp. 185-205, 2005.
11. G. Wahba, "Multivariate function and operator estimation, based on smoothing splines and reproducing kernels," in Proceedings of the Sciences of Complexity, M. Casdagli and S. Eubandk, Eds. Reading, MA: Addison-Wesley, 1992, vol. 12, pp. 95-112.
12. J. C. Platt, "Probabilistic outputs for support vector machines and comparisons to regularized likelihood methods," in Advances in Large-Margin Classifers, P. J. Bartlett, B. Schölkopf, D. Schuurmans, and A. Smola, Eds. Cambridge, MA: MIT Press, 2000, pp. 61-74.
13. T. Hastie and R. Tibshirani, "Classification by pairwise coupling," Anal. Statist., vol. 26, no. 2, pp. 451-471, Apr. 1998.
14. V. K. Rohatgi and A. K. M. E. Saleh, "Nonparametric statistical Inference," in An Introduction to Probability and Statistics, 2nd ed. New York: Wiley-Interscience, 2001, pp. 608-633.
15. P. M. Murphy and D. W. Aha, UCI Repository of Machine Learning Databases, Univ. California at Irvine, Irvine, CA, 1994 [Online]. Available: Http://www.archive.ics.uci.edu/ml/
16. Y. Lee, Y. Lin, and G. Wahba, "Multicategory support vector machines, theory, and application to the classification of microarray data and satellite radiance data," J. Amer. Statist. Assoc., vol. 99, pp. 67-81, 2004.
17. Y. Lee, G. Wahba, and S. Ackerman, "Classification of satellite radiance data by multicategory support vector machines," Dept. Statist., Univ.Wisconsin-Madison, Madison, WI, Tech. Rep. 1075, Feb. 2003.
18. Y. Lee, Multicategory Support Vector Machines (MSVM), Sep. 2003 [Online]. Available: Http://www.stat.wisc.edu/~yklee/sharecode.html
19. X. Shen, G. Tseng, X. Zhang, and W.Wong, "On ψ-learning," J. Amer. Statist. Assoc., vol. 98, no. 462, pp. 724-734, 2003.
20. Y. Liu, X. Shen, and H. Doss, "Multicategory ψ-learning and support vector machine: Computational tools," J. Amer. Statist. Assoc., vol. 14, pp. 219-236, 2005.
21. D. Luenberger, Optimization by Vector Space Method. New York: Wiley, 1969.
22. M. Guignard, "Generalized kuhn-tucker conditions for mathematical programming problems in banach space," SIAM J. Control, vol. 7, pp. 232-241, 1969.
23. A. B. Tal and J. Zowe, "A unified theory of first and second order conditions for extremum problems in topological vector space," Math. Programm. Study, vol. 19, pp. 39-76, 1982.
24. T. Hastie, R. Tibshirani, and J. Friedman, "Linear methods for classification," in The Elements of Statistical Learning. NewYork: Springer-Verlag, 2002, pp. 95-105.
25. P. M. Wiliams, "Bayesian regularization and pruning using a Laplace prior," Neural Comput., vol. 7, pp. 117-143, 1995.
26. B. Schölkopf, R. Herbrich, and A. J. Smola, "A generalized representer theorem," in Lecture Notes in Computer Science. Berlin, Germany: Springer-Verlag, 2001, vol. 2111, pp. 416-426.
27. D. Luenberger, Introduction to Linear and Nonlinear Programming. Reading, MA: Addison-Wesley, 1973.
28. R. Gnanadeskan, R. S. Pinkham, and L. P. Hughes, "Maximum likelihood estimation of the parameters of the beta distribution from smallest order statistics," Technometrics, vol. 9, pp. 607-620, 1967.
29. L. T. An and P. D. Tao, "Solving a class of linearly constrained indefinite quadratic problems by d. c. Algorithms," J. Global Optim. vol. 11, pp. 253-285, 1997.
30. R. Blanquero and E. Carrizosa, "On covering methods for d. c. optimization," J. Global Optim., vol. 18, pp. 256-274, 2000.
31. J. C. Platt, "Fast training of support vector machines using sequential minimal optimization," in Advances in Kernel Methods-Support Vector Learning, B. Schölkopf, C. J. Burges, and A. J. Smola, Eds. Cambridge, MA: MIT Press, 1999, pp. 185-208.
32. Y. Rong, A MATLAB Package for Classification Algorithms Mar. 2006 [Online]. Available: Http://www.informedia.cs.cmu.edu/yanrong/ MATLABArsenal/MATLABARsenal.htm
33. F. Provost and T. Fawcett, "Analysis and visualization of classifier performance comparison under imprecise class and cost distribution," in Proc. 3rd Int. Conf. Knowl. Disc. Data Mining, 1997, pp. 43-48.
34. F. Provost, T. Fawcett, and R. Kohavi, "The case accuracy estimation for comparing induction algorithms," in Proc. 15th Int. Conf. Mach. Learn., 1998, pp. 445-453.