Principal component analysis of fuzzy data using autoassociative neural networks

IEEE Transactions on Fuzzy Systems

Volumn 12, Issue 3, 2004, Pages 336-349

  Denoeux, Thierry ^a   Masson, Marie Hélène ^a  

^a UNIVERSITÉ DE TECHNOLOGIE DE COMPIÈGNE   (France)

Author keywords

Feature extraction; Fuzzy data analysis; Neural networks; Pattern recognition

Indexed keywords

CORRELATION METHODS; DATA REDUCTION; MEMBERSHIP FUNCTIONS; NEURAL NETWORKS; PATTERN RECOGNITION; PRINCIPAL COMPONENT ANALYSIS; PROBABILITY DISTRIBUTIONS;

AUTOASSOCIATIVE NEURAL NETWORKS; FUZZY DATA;

FUZZY SETS;

EID: 3042555475     PISSN: 10636706     EISSN: None     Source Type: Journal    
DOI: 10.1109/TFUZZ.2004.825990     Document Type: Article

References (37)

1. T. W. Anderson, An Introduction to Multivariate Statistical Analysis. New York: Wiley, 1984.
2. P. Baldi and K. Hornik, "Neural networks and principal component analysis: learning from examples without local minima," Neural Networks, vol. 2, pp. 53-58, 1989.
3. ____, "Learning in linear neural networks: a survey," IEEE Trans. Neural Networks, vol. 6, pp. 837-858, July 1995.
4. C. Bertoluzza, M. A. Gil, and D. A. Ralescu, Eds., Statistical Modeling, Analysis and Management of Fuzzy Data. Heidelberg, Germany: Physica Verlag, 2002.
5. J. C. Bezdek, J. Keller, R. Krishnapuram, and N. R. Pal, Fuzzy Models and Algorithms for Pattern Recognition and Image Processing. Boston, MA: Kluwer, 1999.
6. E. Bingham and H.Heikki Mannila, "Random projection in dimensionality reduction: applications to image and text data," in Proc. 7th ACM SIGKDD Int. Conf. Knowledge Discovery Data Mining (KDD 2001), F. Provost and R. Srikant, Eds., 2000, pp. 245-250.
7. H.-H. Bock and E. Diday, Eds., Analysis of Symbolic Data. Exploratory Methods for Extracting Statistical Information From Complex Data. Berlin, Germany: Springer Verlag, 2000.
8. H. Bourlard and Y. Kamp, "Auto-association by multilayer perceptrons and singular value decomposition," Biol. Cybern., vol. 59, pp. 291-294, 1988.
9. J. J. Buckley and Y. Hayashi, "Fuzzy neural networks: a survey," Fuzzy Sets Syst., vol. 66, pp. 1-13, 1994.
10. P. Cazes, A. Chouakria, E. Diday, and Y. Schektman, "Extension de l'analyze en composantes principales à des données de type infervalle," Revue de Statistique Appliquée, vol. 14, no. 3, pp. 5-24, 1997.
11. M. Delgado, M. A. Vila, and W. Voxman, "On a canonical representation of fuzzy numbers," Fuzzy Sets Syst., vol. 93, pp. 125-135, 1998.
12. T. Denoeligux and M. Masson, "Multidimensional scaling of interval-valued dissimilarity data," Pattern Recogn. Lett., vol. 21, pp. 83-92, 2000.
13. P. Diamond and H. Tanaka, "Fuzzy regression analysis," in Fuzzy Sets in Decision Analysis, Operations Research and Statistics, R. Slowinski, Ed. Boston, MA: Kluwer, 1998, pp. 349-387.
14. D. Dubois, E. Kerre, R. Mesiar, and H. Prade, "Fuzzy interval analysis," in Fundamentals of Fuzzy Sets, D. Dubois and H. Prade, Eds. Boston, MA: Kluwer, 2000, pp. 483-581.
15. D. Dubois, H. T. Nguyen, and H. Prade, "Possibility theory, probability and fuzzy sets: misunderstandings, bridges and gaps," in Fundamentals of Fuzzy Sets, D. Dubois and H. Prade, Eds. Boston, MA: Kluwer, 2000, pp. 343-438.
16. D. Dubois and H. Prade, Possibility Theory: An Approach to Computerized Processing of Uncertainty. New York: Plenum, 1988.
17. K. Fukunaga, Introduction to Statistical Pattern Recognition. New York: Academic, 1990.
18. J. Gebhardt, M. A. Gil, and R. Kruse, "Fuzzy set-theoretic methods in statistics," in Fuzzy Sets in Decision Analysis, Operations Research and Statistics, R. Slowinski, Ed. Boston, MA: Kluwer, 1998, pp. 311-347.
19. R. J. Hathaway, J. C. Bezdek, and W. Pedrycz, "A parametric model for fusing heterogeneous fuzzy data," IEEE Trans. Fuzzy Syst., vol. 4, pp. 270-281, June 1996.
20. Y. Hayashi, J. J. Buckley, and E. Czogala, "Fuzzy neural network with fuzzy signals and weights," Int. J. Intell. Syst., vol. 8, pp. 527-537, 1993.
21. S. Heilpern, "Representation and application of fuzzy numbers," Fuzzy Sets Syst., vol. 91, pp. 259-268, 1997.
22. H. Ishibuchi, R. Fujioka, and H. Tanaka, "An architecture of neural network for input vectors of fuzzy numbers," in Proc. FUZZ-IEEE'92, 1992, pp. 643-650.
23. H. Ishibuchi, K. Kwon, and H. Tanaka, "A learning algorithm of fuzzy neural networks with triangular fuzzy weights," Fuzzy Sets Syst., vol. 71, pp. 277-293, 1995.
24. H. Ishibuchi, L. Morioka, and I. B. Turksen, "Learning by fuzzified neural networks," Int. J. Approx. Reason., vol. 13, pp. 327-358, 1995.
25. J. E. Jackson, A User's Guide to Principal Components. New York: Wiley, 1991.
26. G. J. Klir and M. J. Wierman, Uncertainty-Based Information. Elements of Generalized Information Theory. New York: Springer-Verlag, 1998.
27. C. N. Lauro and F. Palumbo, "Principal component analysis of interval data: A symbolic data analysis approach," Comput. Stat., vol. 15, no.1, pp. 73-87, 2000.
28. Z. Li, V. Kecman, and A. Ichikawa, "Fuzzified neural network based on fuzzy number operations," Fuzzy Sets Syst., vol. 130, pp. 291-304, 2002.
29. S. T. Liu and C. Kao, "Fuzzy measures for correlation coefficient of fuzzy numbers," Fuzzy Sets Syst., vol. 128, pp. 267-275, 2002.
30. M.-H. Manson and T. Denoeligux, "Multidimensional scaling of fuzzy dissimilarity data," Fuzzy Sets Syst., vol. 128, no. 3, pp. 339-352, 2002.
31. W. Pedrycz, J. C. Bezdek, R. J. Hathaway, and G. W. Rogers, "Two non-parametric models for fusing heterogeneous fuzzy data," IEEE Trans. Fuzzy Syst., vol. 6, pp. 411-425, June 1998.
32. O. Rodriguez, E. Diday, and S. Winsberg, "Generalization of principal components analysis to histogram data," presented at the Workshop Symbolic Data Analysis, 4th Eur. Conf. Principles and Practice of Knowledge Discovery in Databases, Lyon, France, Sept. 2000.
33. S. Rowies, "EM algorithms for PCA and SPCA," Neural Inform. Processing Syst. 10, pp. 626-632, 1997.
34. D. E. Rumelhart, G. E. Hinton, and R. J. Williams, "Learning internal representations by error propagation," in Parallel Distributed Processing: Explorations in the Microstructure of Cognition, D. E. Rumelhart and J. L. McClelland, Eds. Cambridge, MA: MIT Press, 1988, vol. 1, pp. 318-362.
35. D. Valentin, H. Abdi, A. J. O'Toole, and G. W. Cottrell, "Connectionist models of face processing: A survey," Pattern Recogn., vol. 27, pp. 1209-1230, 1994.
36. R. Viertl, Statistical Methods for Non-Precise Data. Boca Raton, FL: CRC Press, 1996.
37. L. A. Zadeh, "Fuzzy sets as a basis for a theory of possibility," Fuzzy Sets Syst., vol. 1, pp. 3-28, 1978.