Parameter estimation from interval-valued data using the expectation-maximization algorithm

References

• Noirhomme-Fraiture M, Brito P. Far beyond the classical data models: symbolic data analysis. Stat Anal Data Min. 2011;4, 157–170. (doi: 10.1002/sam.10112)
   Google Scholar
• Hao PY. Interval regression analysis using support vector networks. Fuzzy Sets Syst. 2009;160, 2466–2485. (doi: 10.1016/j.fss.2008.10.012)
   Web of Science ®Google Scholar
• Hladik M, Cerny M. Interval regression by tolerance analysis approach. Fuzzy Sets Syst. 2012;193, 85–107. (doi: 10.1016/j.fss.2011.07.009)
   Web of Science ®Google Scholar
• Hu Y-C. Function-link nets with genetic algorithm based learning for robust nonlinear interval regression analysis. Neurocomputing. 2009;72, 7–91808–1816. (doi: 10.1016/j.neucom.2008.07.002)
   Web of Science ®Google Scholar
• Hwang C, Hong DH, Seok KH. Support vector interval regression machine for crisp input and output data. Fuzzy Sets Syst. 2006;157, 1114–1125. (doi: 10.1016/j.fss.2005.09.008)
   Web of Science ®Google Scholar
• Ishibuchi H, Tanaka H. Several formulations of interval regression analysis. Proceedings Sino-Japan Joint Meeting on Fuzzy Sets and Systems, Beijing; 1990. p. B2–2.
   Google Scholar
• Jeng J-S, Chuang C-C, Su S-F. Support vector interval regression networks for interval regression analysis. Fuzzy Sets Syst. 2003;138, 283–300. (doi: 10.1016/S0165-0114(02)00570-5)
   Web of Science ®Google Scholar
• Tanaka H. Fuzzy data analysis by possibilistic linear models. Fuzzy Sets Syst. 1987;24, 363–375. (doi: 10.1016/0165-0114(87)90033-9)
   Web of Science ®Google Scholar
• Denoeux T, Masson M. Multidimensional scaling of interval-valued dissimilarity data. Pattern Recognit Lett. 2000;21, 183–92. (doi: 10.1016/S0167-8655(99)00135-X)
   Web of Science ®Google Scholar
• Palumbo F, Lauro CN. A PCA for interval-valued data based on midpoints and radii. In: Yanai H, Okada A, Shigemasu K, Kano Y, Meulman J, editors. New developments in psychometrics, psychometric society. Tokyo: Springer; 2003. p. 641–648.
   Google Scholar
• Wang H, Guan R, Wu J. CIPCA: complete-information-based principal component analysis for interval-valued data. Neurocomputing. 2012;86, 158–169. (doi: 10.1016/j.neucom.2012.01.018)
   Web of Science ®Google Scholar
• Canvalho FAT, Tenono CP. Fuzzy K-means clustering algorithms for interval-valued data based on adaptive quadratic distances. Fuzzy Sets Syst. 2010;161, 232978–2999. (doi: 10.1016/j.fss.2010.08.003)
   Web of Science ®Google Scholar
• Masson M, Denoeux T. Clustering interval-valued proximity data using belief function. Pattern Recognit Lett. 2004;25, 2163–171. (doi: 10.1016/j.patrec.2003.09.008)
   Web of Science ®Google Scholar
• Sato-llic M. Symbolic clustering with interval-valued data. Procedia Comput Sci. 2011;6, 358–363. (doi: 10.1016/j.procs.2011.08.066)
   Google Scholar
• Denoeux T. Maximum likelihood from fuzzy data using the EM algorithm. Fuzzy Sets Syst. 2011;183, 72–91. (doi: 10.1016/j.fss.2011.05.022)
   Web of Science ®Google Scholar
• Denoeux T. Maximum likelihood from evidential data: an extension of the EM algorithm. In: Borgelt C, Gonzalez-Rodriguez G, Trutschnig W, Lubiano MA, Gil MA, Grzegorzewski P, Hryniewicz O, editors. Combining soft computing and statistical methods in data analysis. Proceedings of SMPS. Advances in intelligent and soft computing. Oviedeo, Spain: Springer; 2010. p. 181–188.
   Google Scholar
• Denoeux T. Maximum likelihood estimation from uncertain data in the belief function framework. IEEE Trans Knowl Data Eng. 2013;25, 1119–130. (doi: 10.1109/TKDE.2011.201)
   Web of Science ®Google Scholar
• Su ZG, Wang PH, Wang YF. Interval-valued EM algorithm with application to estimating parameters. Proceedings of the World Congress on Engineering and Computer Science, Vol. 1; 2012; San Francisco. p. 551–556.
   Google Scholar
• Quost B, Denoeux T. Clustering fuzzy data using the fuzzy EM algorithm. The 4th International Conference on Scalable Uncertainty Management; 2010; Toulouse, France. p. 333–346.
   Google Scholar
• Su ZG, Wang PH, Song ZL. Kernel based nonlinear fuzzy regression model. Eng Appl Artif Intell. 2013;26, 2724–738. (doi: 10.1016/j.engappai.2012.05.009)
   Web of Science ®Google Scholar
• Dempster AP, Laird NM, Rubin DB. Maximum likelihood from incomplete data via the EM algorithm. J R Stat Soc B. 1977;39, 1–38.
   Google Scholar
• Algahtani OJ. An interval Kalman filter, interval EM algorithm with application to weather prediction [PhD thesis]. Dhahran, Saudi Arabia: King Fahd University of Petroleum and Minerals; 2011.
   Google Scholar
• Hamdan H, Govaert G. Mixture model clustering of uncertain data. The 14th IEEE International Conference on Fuzzy Systems; 2005; Reno, Nevada. p. 879–884.
   Google Scholar
• John ST, Nello C Kernel methods for pattern analysis, Cambridge: Cambridge University Press; 2004.
   Google Scholar
• Gil MA, González-Rodríguez G, Colubi A, Montenegro M. Testing linear independence in linear models with interval-valued data. Comput Stat Data Anal. 2007;51, 3002–3015. (doi: 10.1016/j.csda.2006.01.015)
   Web of Science ®Google Scholar
• Neto EAL, Cordeiro GM, de Carvalho FAT. Bivariate symbolic regression models for interval-valued variables. J Stat Comput Simul. 2011;81, 111727–1744. (doi: 10.1080/00949655.2010.500470)
   Web of Science ®Google Scholar