Support vector regression of membership functions and belief functions - Application for pattern recognition

Information Fusion

Volumn 11, Issue 4, 2010, Pages 338-350

  Laanaya, Hicham ^a,b   Martin, Arnaud ^b   Aboutajdine, Driss ^a   Khenchaf, Ali ^b  

^a FACULTÉ DES SCIENCES   (Morocco)

^b ENSIETA   (France)

Author keywords

Belief functions; Membership functions; Regression; SVM; SVR

Indexed keywords

BELIEF FUNCTION; BELIEF FUNCTIONS; CLASSICAL APPROACH; CLASSIFICATION RESULTS; CLASSIFICATION TASKS; CONVEX PROBLEMS; FUZZY SVM; K-NEAREST NEIGHBORS; LEARNING DATA; STATISTICAL LEARNING THEORY; SUPPORT VECTOR REGRESSIONS; THEORY OF BELIEF FUNCTIONS; THEORY OF FUZZY SETS; UNCERTAIN DATAS;

CLASSIFIERS; FUZZY CONTROL; FUZZY SET THEORY; FUZZY SETS; PATTERN RECOGNITION; REGRESSION ANALYSIS; SUPPORT VECTOR MACHINES; UNCERTAINTY ANALYSIS;

MEMBERSHIP FUNCTIONS;

EID: 77953616673     PISSN: 15662535     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.inffus.2009.12.007     Document Type: Article

References (51)

1. Zadeh L. Fuzzy sets. Information Control 8 (1965) 338-353
2. Zadeh L. Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems 1 (1978) 3-28
3. Dubois D., and Prade H. Possibility Theory: An Approach to Computerized Processing of Uncertainty (1988), Plenum Press, New York
4. Dempster A. Upper and lower probabilities induced by a multivalued mapping. Annals of Mathematical Statistics 83 (1967) 325-339
5. Shafer G. A Mathematical Theory of Evidence (1976), Princeton University Press
6. Klir G., Clair U., and Yuan B. Fuzzy set theory: foundations and applications (1997), Prentice-Hall Inc., Upper Saddle River, NJ, USA
7. H. Zimmermann, Practical applications of fuzzy technologies, The Handbook of Fuzzy Sets Series, 1999.
8. P. Smets, Practical uses of belief functions, in: Fifteenth Conference on Uncertainty in Artificial Intelligence, Stockholm, Sweden, July 1999, pp. 612-621.
9. Dubois D., Grabisch M., Prade H., and Smets P. Using the transferable belief model and a qualitative possibility theory approach on an illustrative example: the assessment of the value of a candidate. International Journal of Intelligence Systems 16 (2001) 1245-1272
10. Vapnik V. The Nature of Statistical Learning Theory (1995), Springer, NY
11. Vapnik V. Statistical Learning Theory (1998), John Wesley and Sons
12. Tanaka H., Uejima A., and Asai K. Linear regression analysis with fuzzy model. IEEE Transactions on Systems, Man, and Cybernetics 12 6 (1982) 903-907
13. A. Miyazaki, K. Kwon, H. Ishibuchi, H. Tanaka, Fuzzy regression analysis by fuzzy neural networks and its application, in: Conference on Fuzzy Systems, Orlando, USA, vol.1, 1994, pp. 52-57.
14. Wu B., and Tseng N.-F. A new approach to fuzzy regression models with application to business cycle analysis. Fuzzy Sets and Systems 130 (2002) 33-42
15. Petit-Renaud S., and Denœux T. Nonparametric regression analysis of uncertain and imprecise data using belief functions. International Journal of Approximate Reasoning 35 (2004) 1-28
16. A. Smola, B. Schölkopf, A tutorial on support vector regression, NeuroCOLT2 Technical Report NC2-TR-1998-030, 1998.
17. S. Gunn, Support vector machines for classification and regression, ISIS Technical Report, University of Southampton, 1998.
18. Buckley J., and Hayashi Y. Fuzzy neural networks: a survey. Fuzzy Sets and Systems 66 1 (1994) 1-13
19. Jozwik A. A learning scheme for a fuzzy k-nn rule. Pattern Recognition Letters 1 (1983) 287-289
20. Keller J., Gray M., and Givens J. A fuzzy k-nn neighbor algorithm. IEEE Transactions on Systems, Man, and Cybernetics 15 (1985) 580-585
21. Denœux T. A neural network classifier based on Dempster-Shafer theory. IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans 30 2 (2000) 131-150
22. Denœux T. A k-nearest neighbor classification rule based on Dempster-Shafer theory. IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans 25 5 (1995) 804-813
23. T. Denœux, M.S. Bjanger, Induction of decision trees from partially classified data using belief function, in: Proceedings of SMC'2000, Nashville, USA, 2000, pp. 2923-2928.
24. P. Vannoorenberghe, T. Denœux, Handling uncertain labels in multiclass problems using belief decision trees, in: IPMU'2002, Annecy, France, vol. 3, 2002, pp. 1919-1926.
25. A. Martin, C. Osswald, Experts fusion and multilayer perceptron based on belief learning for sonar images classification, in: ICTTA, Damascus, Syria, 2008, pp. 7-11.
26. Han-Pang H., and Yi-Hung L. Fuzzy support vector machines for pattern recognition and data mining. International Journal of Fuzzy Systems 14 3 (2002) 25-28
27. T.Inoue, S.Abe, Fuzzy support vector machines for pattern classification, in: IJCNN'01. International Joint Conference on Neural Networks, vol. 2, 2001, pp. 1449-1454.
28. S. Abe, T. Inoue, Fuzzy support vector machines for multiclass problems, in: European Symposium on Artificial Neural Networks, 2002, pp. 113-118.
29. Tsujinishi D., and Abe S. Fuzzy least squares support vector machines for multiclass problems. Neural Networks 16 (2003) 785-792
30. Hong D., and Hwang C. Support vector fuzzy regression machines. Fuzzy Sets and Systems 138 (2003) 271-281
31. Quost B., Denœux T., and Masson M. Pairwise classifier combination using belief functions. Pattern Recognition Letters 28 (2007) 644-653
32. A. Aregui, T. Denœux, Fusion of one-class classifier in the belief function framework, in: International Conference on Information Fusion, Québec, Canada, July 2007.
33. A. Martin, I. Quidu, Decision support with belief functions theory for seabed characterization, in: International Conference on Information Fusion, Cologne, Germany, July 2008.
34. Zouhal L., and Denoeux T. An evidence-theoric k-nn rule with parameter optimization. IEEE Transactions on Systems, Man, and Cybernetics - Part C: Applications and Reviews 28 2 (1998) 263-271
35. Medasani S., Kim J., and Krishnapuram R. An overview of membership function generation techniques for pattern recognition. International Journal of Approximate Reasoning 19 (1998) 391-417
36. Smets P. Constructing the pignistic probability function in a context of uncertainty. Uncertainty in Artificial Intelligence 5 (1990) 29-39
37. Appriou A. Situation assessment based on spatially ambiguous multisensor measurements. International Journal of Intelligent Systems 16 10 (2001) 1135-1156
38. F. Pérez-Cruz, G. Camps, E. Soria, J. Pérez, A. Figueiras-Vidal, A. Artés-Rodriguez, Multi-dimensional function approximation and regression estimation, in: International Conference on Artificial Neural Networks, Madrid, Espagne.
39. Sanchez-Fernandez M., dePrado-Cumplido M., Arenas-Garcia J., and Pérez-Cruz F. SVM multiregression for non-linear channel estimation in multiple-input multiple-output systems. IEEE Transactions on Signal Processing 58 8 (2004) 2298-2307
40. B. Schölkopf, A.J. Smola, R. Williamson, Shrinking the tube: a new support vector regression algorithm, in: Proceedings of Conference on Advances in Neural Information Processing Systems, vol. II, 1999, pp. 330-336.
41. H. Laanaya, A. Martin, D. Aboutajdine, A. Khenchaf, Knowledge discovery on database for seabed characterization, in: MCSEAI 2006, Agadir, Morocco.
42. E. Osuna, R. Freund, F. Girosi, Improved training algorithm for support vector machines, in: NNSP'97, 1997, pp. 24-26.
43. J. Platt, Sequential minimal optimization: a fast algorithm for training support vector machines, Microsoft Research Technical Report MSR-TR-98-14, 1998.
44. Lin C.-J. On the convergence of the decomposition method for support vector machines. IEEE Transactions on Neural Networks 12 (2001) 1288-1298
45. Lin C.-J. Asymptotic convergence of an SMO algorithm without any assumptions. IEEE Transactions on Neural Networks 13 (2002) 248-250
46. C. Chang, C. Lin, LIBSVM: a library for support vector machines, .
47. A. Martin, Fusion for evaluation of image classification in uncertain environments, in: The 9th International Conference on Information Fusion.
48. Martin A., Laanaya H., and Arnold-Bos A. Evaluation for uncertain image classification and segmentation. Pattern Recognition 39 (2006) 1987-1995
49. A. Martin, G. Sévellec, I. Leblond, Characteristics vs decision fusion for sea-bottom characterization, Colloque Caractérisation in-situ des fonds marins, Brest, France.
50. R. Akbani, S. Kwek, N. Japkowicz, Applying support vector machines to imbalanced datasets, in: Proceedings of the 15th European Conference on Machine Learning (ECML), 2004, pp. 214-220.
51. S. Lessmann, Solving imbalanced classification problems with support vector machines, in: H. Arabnia (Ed.), Proceedings of the International Conference on Artificial Intelligence (IC-AI 04), Las Vegas, Nevada, USA, 2004, pp. 39-50.