Self-Organizing Maps for imprecise data

Fuzzy Sets and Systems

Volumn 237, Issue , 2014, Pages 63-89

  D'Urso, Pierpaolo ^a   De Giovanni, Livia ^b   Massari, Riccardo ^a  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

^b LUISS UNIVERSITY   (Italy)

Author keywords

Distance measures for imprecise data; Fuzziness; Imprecise data; SOMs for imprecise data; Vector quantization for imprecise data

Indexed keywords

FUZZINESS; IMPRECISE DATA; INPUT SPACE; INPUT VECTOR; NEIGHBOURHOOD; SIMULATION STUDIES;

CONFORMAL MAPPING; NEURONS; VECTOR SPACES;

VECTOR QUANTIZATION;

EID: 84891859160     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fss.2013.09.011     Document Type: Article

References (42)

1. T. Kohonen Self-Organization and Associative Memory 3rd edition 1989 Springer-Verlag New York
2. T. Kohonen Self-Organizing Maps 1995 Springer-Verlag
3. H.H. Bock Clustering methods and Kohonen maps for symbolic data J. Jpn. Soc. Comput. Stat. 15 2 1999 217 229
4. H. Bock Visualizing symbolic data by Kohonen maps E. Diday, M. Noihome-Fraiture, Symbolic Data Analysis and the SODAS Software 2008 Wiley 205 234
5. D. Chen, W. Hung, and M. Yang et al. A batch version of the SOM for symbolic data 2010 Sixth International Conference on Natural Computation (ICNC) vol. 1 2010 IEEE 1 5
6. P. D'Urso, and L. De Giovanni Midpoint radius self-organizing maps for interval-valued data with telecommunications application Appl. Soft Comput. 11 5 2011 3877 3886
7. C. Hajjar, and H. Hamdan Self-organizing map based on city-block distance for interval-valued data M. Aiguier, F. Bretaudeau, D. Krob, Complex Systems Design & Management 2012 Springer 281 292
8. M. Yang, W. Hung, and D. Chen Self-organizing map for symbolic data Fuzzy Sets Syst. 203 2012 49 73
9. R. Coppi, P. D'Urso, and P. Giordani Fuzzy and possibilistic clustering for fuzzy data Comput. Stat. Data Anal. 56 4 2012 915 927
10. M. Yang, and C. Ko On a class of fuzzy c-numbers clustering procedures for fuzzy data Fuzzy Sets Syst. 84 1 1996 49 60 (Pubitemid 126682900)
11. R. Coppi Management of uncertainty in statistical reasoning: The case of regression analysis Int. J. Approx. Reason. 47 3 2008 284 305
12. R. Coppi, P. Giordani, and P. D'Urso Component models for fuzzy data Psychometrika 71 4 2006 733 761
13. D. Dubois Prade, Possibility Theory 1988 Plenum Press New York
14. H. Zimmermann Fuzzy Set Theory and Its Applications 2001 Kluwer Boston
15. R. Coppi The fuzzy approach to multivariate statistical analysis Tech. Rep. 11 2003 Dipartimento di Statistica, Probabilità e Statistiche Applicate, Sapienza Università di Roma
16. P. D'Urso Clustering of fuzzy data J. de Oliveira, W. Pedrycz, Advances in Fuzzy Clustering and Its Applications 2007 J. Wiley and Sons 155 192
17. A. Celmiņš Multidimensional least-squares fitting of fuzzy models Math. Model. 9 9 1987 669 690
18. A. Celmiņš A practical approach to nonlinear fuzzy regression SIAM J. Sci. Stat. Comput. 12 3 1991 521 546
19. I. Bloch On fuzzy distances and their use in image processing under imprecision Pattern Recognit. 32 11 1999 1873 1895
20. R. Zwick, E. Carlstein, and D. Budescu Measures of similarity among fuzzy concepts: A comparative analysis Int. J. Approx. Reason. 1 2 1987 221 242
21. R. Lowen, and W. Peeters Distances between fuzzy sets representing grey level images Fuzzy Sets Syst. 99 2 1998 135 149 (Pubitemid 128654959)
22. C. Pappis, and N. Karacapilidis A comparative assessment of measures of similarity of fuzzy values Fuzzy Sets Syst. 56 2 1993 171 174
23. A. De Luca, and S. Termini A definition of non-probabilistic entropy in the setting of fuzzy set theory Inf. Control 20 1972 301 312
24. S. Chen, M. Yeh, and P. Hsiao A comparison of similarity measures of fuzzy values Fuzzy Sets Syst. 72 1 1995 79 89
25. W. Wang New similarity measures on fuzzy sets and on elements Fuzzy Sets Syst. 85 3 1997 305 309 (Pubitemid 127699051)
26. P. D'Urso, and P. Giordani A weighted fuzzy c-means clustering model for fuzzy data Comput. Stat. Data Anal. 50 6 2006 1496 1523 (Pubitemid 41617914)
27. M. Yang, P. Hwang, and D. Chen Fuzzy clustering algorithms for mixed feature variables Fuzzy Sets Syst. 141 2 2004 301 317
28. M. Yang, and H. Liu Fuzzy clustering procedures for conical fuzzy vector data Fuzzy Sets Syst. 106 2 1999 189 200 (Pubitemid 129524616)
29. H. Ritter, and K. Schulten Kohonen's self-organizing maps: Exploring their computational capabilities Proceedings of IEEE International Conference on Neural Networks 1988 IEEE 109 116
30. P. Conti, and L. De Giovanni On the mathematical treatment of self organization: extension of some classical results International Conference on Artificial Neural Networks 1991 1809 1812
31. H. Ritter, and K. Schulten Convergence properties of Kohonen's topology conserving maps: fluctuations, stability, and dimension selection Biol. Cybern. 60 1 1988 59 71
32. M. Budinich, and J. Taylor On the ordering conditions for self-organizing maps Neural Comput. 7 2 1995 284 289
33. H. Ritter Asymptotic level density for a class of vector quantization processes IEEE Trans. Neural Netw. 2 1 1991 173 175
34. T. Kohonen The self-organizing map Proc. IEEE 78 9 1990 1464 1480
35. H. Bauer, M. Herrmann, and T. Villmann Neural maps and topographic vector quantization Neural Netw. 12 4 1999 659 676 (Pubitemid 29348437)
36. L. Hubert, and P. Arabie Comparing partitions J. Classif. 2 1 1985 193 218
37. E. Erwin, K. Obermayer, and K. Shulten Convergence properties of self-organizing maps T. Kohonen, K. Mäkisara, O. Simula, J. Kangas, Artificial Neural Networks 1991 409 414
38. W. Hung, and M. Yang Fuzzy clustering on LR-type fuzzy numbers with an application in Taiwanese tea evaluation Fuzzy Sets Syst. 150 3 2005 561 577 (Pubitemid 40061318)
39. W. Hung, M. Yang, and E. Lee A robust clustering procedure for fuzzy data Comput. Math. Appl. 60 2010 151 165
40. E. Huskisson Visual analogue scale R. Melzack, Pain Measurement and Assessment 1983 Raven Press New York 33 37
41. D.S. Guru, B.B. Kiranagi, and P. Nagabhushan Multivalued type proximity measure and concept of mutual similarity value useful for clustering symbolic patterns Pattern Recognit. Lett. 25 10 2004 1203 1213 (Pubitemid 38763662)
42. B. Sinova, M. Ángeles Gil, A. Colubi, and S. Van Aelst The median of a random fuzzy number. The 1-norm distance approach Fuzzy Sets Syst. 200 2011 99 115