메뉴 건너뛰기




Volumn 25, Issue 1, 2013, Pages 119-130

Maximum likelihood estimation from uncertain data in the belief function framework

Author keywords

clustering; Dempster Shafer theory; EM algorithm; Evidence theory; mixture models; Uncertain data mining

Indexed keywords

CLUSTERING; DEMPSTER-SHAFER THEORY; EM ALGORITHMS; EVIDENCE THEORIES; MIXTURE MODEL; UNCERTAIN DATAS;

EID: 84870426604     PISSN: 10414347     EISSN: None     Source Type: Journal    
DOI: 10.1109/TKDE.2011.201     Document Type: Article
Times cited : (209)

References (67)
  • 1
    • 63449133366 scopus 로고    scopus 로고
    • A survey of uncertain data algorithms and applications
    • May
    • C.C. Aggarwal and P.S. Yu, "A Survey of Uncertain Data Algorithms and Applications," IEEE Trans. Knowledge and Data Eng., vol. 21, no. 5, pp. 609-623, May 2009.
    • (2009) IEEE Trans. Knowledge and Data Eng. , vol.21 , Issue.5 , pp. 609-623
    • Aggarwal, C.C.1    Yu, P.S.2
  • 3
    • 77955146963 scopus 로고    scopus 로고
    • Guest editors' introduction: Special section on mining large uncertain and probabilistic databases
    • Sept.
    • R. Cheng, M. Chau, M. Garofalakis, and J.X. Yu, "Guest Editors' Introduction: Special Section on Mining Large Uncertain and Probabilistic Databases," IEEE Trans. Knowledge and Data Eng., vol. 22, no. 9, pp. 1201-1202, Sept. 2010.
    • (2010) IEEE Trans. Knowledge and Data Eng. , vol.22 , Issue.9 , pp. 1201-1202
    • Cheng, R.1    Chau, M.2    Garofalakis, M.3    Yu, J.X.4
  • 4
    • 77649253432 scopus 로고    scopus 로고
    • Probabilistic reverse nearest neighbor queries on uncertain data
    • Apr.
    • M.A. Cheema, X. Lin, W. Wang, W. Zhang, and J. Pei, "Probabilistic Reverse Nearest Neighbor Queries on Uncertain Data," IEEE Trans. Knowledge and Data Eng., vol. 22, no. 4, pp. 550- 564, Apr. 2010.
    • (2010) IEEE Trans. Knowledge and Data Eng. , vol.22 , Issue.4 , pp. 550-564
    • Cheema, M.A.1    Lin, X.2    Wang, W.3    Zhang, W.4    Pei, J.5
  • 8
    • 77955150205 scopus 로고    scopus 로고
    • Clustering uncertain data using voronoi diagrams and r-tree index
    • Sept.
    • B. Kao, S.D. Lee, F. Lee, D. Cheung, and W.-S. Ho, "Clustering Uncertain Data Using Voronoi Diagrams and R-Tree Index," IEEE Trans. Knowledge and Data Eng., vol. 22, no. 9, pp. 1219-1233, Sept. 2010.
    • (2010) IEEE Trans. Knowledge and Data Eng. , vol.22 , Issue.9 , pp. 1219-1233
    • Kao, B.1    Lee, S.D.2    Lee, F.3    Cheung, D.4    Ho, W.-S.5
  • 10
    • 34548736497 scopus 로고    scopus 로고
    • On density based transforms for uncertain data mining
    • DOI 10.1109/ICDE.2007.367932, 4221735, 23rd International Conference on Data Engineering, ICDE 2007
    • C.C. Aggarwal, "On Density Based Transforms for Uncertain Data Mining," Proc. IEEE 23rd Int'l Conf. Data Eng. (ICDE '07), pp. 866- 875, 2007. (Pubitemid 47422090)
    • (2007) Proceedings - International Conference on Data Engineering , pp. 866-875
    • Aggarwal, C.C.1
  • 12
    • 84898996224 scopus 로고    scopus 로고
    • Support vector classification with input data uncertainty
    • L.K. Saul, Y. Weiss, and L. Bottou, eds.
    • J. Bi and T. Zhang, "Support Vector Classification with Input Data Uncertainty," Proc. Advances in Neural Information Processing Systems 17, L.K. Saul, Y. Weiss, and L. Bottou, eds., pp. 161-168, 2005.
    • (2005) Proc. Advances in Neural Information Processing Systems , vol.17 , pp. 161-168
    • Bi, J.1    Zhang, T.2
  • 14
    • 49349133217 scopus 로고
    • Fuzzy sets as a basis for a theory of possibility
    • L.A. Zadeh, "Fuzzy Sets as a Basis for a Theory of Possibility," Fuzzy Sets and Systems, vol. 1, pp. 3-28, 1978.
    • (1978) Fuzzy Sets and Systems , vol.1 , pp. 3-28
    • Zadeh, L.A.1
  • 16
    • 0039957466 scopus 로고    scopus 로고
    • Extension de l'analyse en composantes principales à des données de type intervalle
    • P. Cazes, A. Chouakria, E. Diday, and Y. Schektman, "Extension de l'analyse en Composantes Principales à Des Données de type Intervalle," Revue de Statistique Appliquée, vol. 14, no. 3, pp. 5-24, 1997.
    • (1997) Revue de Statistique Appliquée , vol.14 , Issue.3 , pp. 5-24
    • Cazes, P.1    Chouakria, A.2    Diday, E.3    Schektman, Y.4
  • 17
    • 3042555475 scopus 로고    scopus 로고
    • Principal component analysis of fuzzy data using autoassociative neural networks
    • June
    • T. Denoeux and M.-H. Masson, "Principal Component Analysis of Fuzzy Data Using Autoassociative Neural Networks," IEEE Trans. Fuzzy Systems, vol. 12, no. 3, pp. 336-349, June 2004.
    • (2004) IEEE Trans. Fuzzy Systems , vol.12 , Issue.3 , pp. 336-349
    • Denoeux, T.1    Masson, M.-H.2
  • 18
    • 33750347543 scopus 로고    scopus 로고
    • A comparison of three methods for principal component analysis of fuzzy interval data
    • DOI 10.1016/j.csda.2006.02.019, PII S0167947306000648
    • P. Giordani and H.A.L. Kiers, "A Comparison of Three Methods for Principal Component Analysis of Fuzzy Interval Data," Computational Statistics and Data Analysis, vol. 51, no. 1, pp. 379- 397, 2006. (Pubitemid 44634790)
    • (2006) Computational Statistics and Data Analysis , vol.51 , Issue.1 , pp. 379-397
    • Giordani, P.1    Kiers, H.A.L.2
  • 19
    • 0026831106 scopus 로고
    • Symbolic clustering using a new similarity measure
    • Mar./Apr.
    • K.C. Gowda and E. Diday, "Symbolic Clustering Using a New Similarity Measure," IEEE Trans. Systems, Man and Cybernetics, vol. 22, no. 2, pp. 368-378, Mar./Apr. 1992.
    • (1992) IEEE Trans. Systems, Man and Cybernetics , vol.22 , Issue.2 , pp. 368-378
    • Gowda, K.C.1    Diday, E.2
  • 20
    • 27744444692 scopus 로고    scopus 로고
    • A weighted fuzzy c-means clustering model for fuzzy data
    • DOI 10.1016/j.csda.2004.12.002, PII S0167947304003949
    • P. D'Urso and P. Giordani, "A Weighted Fuzzy C-Means Clustering Model for Fuzzy Data," Computational Statistics and Data Analysis, vol. 50, no. 6, pp. 1496-1523, 2006. (Pubitemid 41617914)
    • (2006) Computational Statistics and Data Analysis , vol.50 , Issue.6 , pp. 1496-1523
    • D'Urso, P.1    Giordani, P.2
  • 21
    • 62349117695 scopus 로고    scopus 로고
    • Partitional clustering algorithms for symbolic interval data based on single adaptive distances
    • F.D.T.D. Carvalho and Y. Lechevallier, "Partitional Clustering Algorithms for Symbolic Interval Data Based on Single Adaptive Distances," Pattern Recognition, vol. 42, no. 7, pp. 1223-1236, 2009.
    • (2009) Pattern Recognition , vol.42 , Issue.7 , pp. 1223-1236
    • Carvalho, F.D.T.D.1    Lechevallier, Y.2
  • 22
    • 38249035267 scopus 로고
    • Fuzzy data analysis by possibilistic linear models
    • H. Tanaka, "Fuzzy Data Analysis by Possibilistic Linear Models," Fuzzy Sets and Systems, vol. 24, pp. 363-375, 1987.
    • (1987) Fuzzy Sets and Systems , vol.24 , pp. 363-375
    • Tanaka, H.1
  • 23
    • 38349025453 scopus 로고    scopus 로고
    • Management of uncertainty in statistical reasoning: The case of regression
    • R. Coppi, "Management of Uncertainty in Statistical Reasoning: The Case of Regression," Int'l J. Approximate Reasoning, vol. 47, no. 3, pp. 284-305, 2008.
    • (2008) Int'l J. Approximate Reasoning , vol.47 , Issue.3 , pp. 284-305
    • Coppi, R.1
  • 25
    • 0033898684 scopus 로고    scopus 로고
    • Multidimensional scaling of interval-valued dissimilarity data
    • DOI 10.1016/S0167-8655(99)00135-X
    • T. Denoeux and M.-H. Masson, "Multidimensional Scaling of Interval-Valued Dissimilarity Data," Pattern Recognition Letters, vol. 21, pp. 83-92, 2000. (Pubitemid 30534051)
    • (2000) Pattern Recognition Letters , vol.21 , Issue.1 , pp. 83-92
    • Denoeux, T.1    Masson, M.2
  • 26
    • 0037118549 scopus 로고    scopus 로고
    • Multidimensional scaling of fuzzy dissimilarity data
    • DOI 10.1016/S0165-0114(01)00162-2, PII S0165011401001622
    • M.-H. Masson and T. Denoeux, "Multidimensional Scaling of Fuzzy Dissimilarity Data," Fuzzy Sets and Systems, vol. 128, no. 3, pp. 339-352, 2002. (Pubitemid 34531610)
    • (2002) Fuzzy Sets and Systems , vol.128 , Issue.3 , pp. 339-352
    • Masson, M.1    Denoeux, T.2
  • 27
  • 28
    • 0000516376 scopus 로고
    • Upper and lower probabilities induced by a multivalued mapping
    • A.P. Dempster, "Upper and Lower Probabilities Induced by a Multivalued Mapping," Annals of Math. Statistics, vol. 38, pp. 325- 339, 1967.
    • (1967) Annals of Math. Statistics , vol.38 , pp. 325-339
    • Dempster, A.P.1
  • 29
    • 0000582933 scopus 로고
    • Upper and lower probabilities generated by a random closed interval
    • A.P. Dempster, "Upper and Lower Probabilities Generated by a Random Closed Interval," Annals of Math. Statistics, vol. 39, no. 3, pp. 957-966, 1968.
    • (1968) Annals of Math. Statistics , vol.39 , Issue.3 , pp. 957-966
    • Dempster, A.P.1
  • 31
    • 0025434991 scopus 로고
    • Combination of evidence in the transferable belief model
    • DOI 10.1109/34.55104
    • P. Smets, "The Combination of Evidence in the Transferable Belief Model," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 12, no. 5, pp. 447-458, May 1990. (Pubitemid 20702887)
    • (1990) IEEE Transactions on Pattern Analysis and Machine Intelligence , vol.12 , Issue.5 , pp. 447-458
    • Smets Philippe1
  • 32
    • 0028406490 scopus 로고
    • The transferable belief model
    • P. Smets and R. Kennes, "The Transferable Belief Model," Artificial Intelligence, vol. 66, pp. 191-243, 1994.
    • (1994) Artificial Intelligence , vol.66 , pp. 191-243
    • Smets, P.1    Kennes, R.2
  • 33
    • 0029307876 scopus 로고
    • A k-nearest neighbor classification rule based on dempster-shafer theory
    • May
    • T. Denoeux, "A k-Nearest Neighbor Classification Rule Based on Dempster-Shafer Theory," IEEE Trans. Systems, Man and Cybernetics, vol. 25, no. 5, pp. 804-813, May 1995.
    • (1995) IEEE Trans. Systems, Man and Cybernetics , vol.25 , Issue.5 , pp. 804-813
    • Denoeux, T.1
  • 34
    • 0035899792 scopus 로고    scopus 로고
    • Handling possibilistic labels in pattern classification using evidential reasoning
    • T. Denoeux and L.M. Zouhal, "Handling Possibilistic Labels in Pattern Classification Using Evidential Reasoning," Fuzzy Sets and Systems, vol. 122, no. 3, pp. 47-62, 2001.
    • (2001) Fuzzy Sets and Systems , vol.122 , Issue.3 , pp. 47-62
    • Denoeux, T.1    Zouhal, L.M.2
  • 35
    • 33947108026 scopus 로고    scopus 로고
    • Classification using belief functions: The relationship between the case-based and model-based approaches
    • Dec.
    • T. Denoeux and P. Smets, "Classification Using Belief Functions: the Relationship between the Case-Based and Model-Based Approaches," IEEE Trans. Systems, Man and Cybernetics B, vol. 36, no. 6, pp. 1395-1406, Dec. 2006.
    • (2006) IEEE Trans. Systems, Man and Cybernetics B , vol.36 , Issue.6 , pp. 1395-1406
    • Denoeux, T.1    Smets, P.2
  • 36
    • 0242490050 scopus 로고    scopus 로고
    • Nonparametric regression analysis of uncertain and imprecise data using belief functions
    • S. Petit-Renaud and T. Denoeux, "Nonparametric Regression Analysis of Uncertain and Imprecise Data Using Belief Functions," Int'l J. Approximate Reasoning, vol. 35, no. 1, pp. 1-28, 2004.
    • (2004) Int'l J. Approximate Reasoning , vol.35 , Issue.1 , pp. 1-28
    • Petit-Renaud, S.1    Denoeux, T.2
  • 38
    • 0035501830 scopus 로고    scopus 로고
    • Belief decision trees: Theoretical foundations
    • DOI 10.1016/S0888-613X(01)00045-7, PII S0888613X01000457
    • Z. Elouedi, K. Mellouli, and P. Smets, "Belief Decision Trees: Theoretical Foundations," Int'l J. Approximate Reasoning, vol. 28, pp. 91-124, 2001. (Pubitemid 32833458)
    • (2001) International Journal of Approximate Reasoning , vol.28 , Issue.2-3 , pp. 91-124
    • Elouedi, Z.1    Mellouli, K.2    Smets, P.3
  • 39
    • 36148967330 scopus 로고    scopus 로고
    • Pruning belief decision tree methods in averaging and conjunctive approaches
    • DOI 10.1016/j.ijar.2007.02.004, PII S0888613X07000199
    • S. Trabelsi, Z. Elouedi, and K. Mellouli, "Pruning Belief Decision tree Methods in Averaging and Conjunctive Approaches," Int'l J. Approximate Reasoning, vol. 46, no. 3, pp. 568-595, 2007. (Pubitemid 350103813)
    • (2007) International Journal of Approximate Reasoning , vol.46 , Issue.3 , pp. 568-595
    • Trabelsi, S.1    Elouedi, Z.2    Mellouli, K.3
  • 43
    • 54549108812 scopus 로고    scopus 로고
    • Learning from partially supervised data using mixture models and belief functions
    • E. Côme, L. Oukhellou, T. Denoeux, and P. Aknin, "Learning from Partially Supervised Data Using Mixture Models and Belief Functions," Pattern Recognition, vol. 42, no. 3, pp. 334- 348, 2009.
    • (2009) Pattern Recognition , vol.42 , Issue.3 , pp. 334-348
    • Côme, E.1    Oukhellou, L.2    Denoeux, T.3    Aknin, P.4
  • 44
    • 0002629270 scopus 로고
    • Maximum likelihood from incomplete data via the em algorithm
    • A.P. Dempster, N.M. Laird, and D.B. Rubin, "Maximum Likelihood From Incomplete Data via the EM Algorithm," J. the Royal Statistical Soc., vol. B 39, pp. 1-38, 1977.
    • (1977) J. The Royal Statistical Soc. , vol.B 39 , pp. 1-38
    • Dempster, A.P.1    Laird, N.M.2    Rubin, D.B.3
  • 46
    • 80052273061 scopus 로고    scopus 로고
    • Maximum likelihood from evidential data: An extension of the em algorithm
    • C. Borgelt et al., ed.
    • T. Denoeux, "Maximum Likelihood from Evidential Data: an Extension of the EM Algorithm," Proc. Int'l Conf. Soft Methods in Probability and Statistics (SMPS '10), C. Borgelt et al., ed., pp. 181- 188, 2010.
    • (2010) Proc. Int'l Conf. Soft Methods in Probability and Statistics (SMPS '10) , pp. 181-188
    • Denoeux, T.1
  • 48
    • 27744441822 scopus 로고    scopus 로고
    • Belief functions on real numbers
    • DOI 10.1016/j.ijar.2005.04.001, PII S0888613X0500023X
    • P. Smets, "Belief Functions on Real Numbers," Int'l J. Approximate Reasoning, vol. 40, no. 3, pp. 181-223, 2005. (Pubitemid 41625553)
    • (2005) International Journal of Approximate Reasoning , vol.40 , Issue.3 , pp. 181-223
    • Smets, P.1
  • 49
    • 60349128618 scopus 로고    scopus 로고
    • Extending stochastic ordering to belief functions on the real line
    • T. Denoeux, "Extending Stochastic Ordering to Belief Functions on the Real Line," Information Sciences, vol. 179, pp. 1362-1376, 2009.
    • (2009) Information Sciences , vol.179 , pp. 1362-1376
    • Denoeux, T.1
  • 50
    • 18844390885 scopus 로고    scopus 로고
    • Accessed Online Book, W3K Pub., Feb.
    • J.O. Smith, Spectral Audio Signal Processing, https://ccrma.stanford.edu/ ~jos/sasp/, Accessed Online Book, W3K Pub., Feb. 2011.
    • (2011) Spectral Audio Signal Processing
    • Smith, J.O.1
  • 51
    • 84947749482 scopus 로고    scopus 로고
    • Focusing vs. Belief Revision: A Fundamental Distinction When Dealing with Generic Knowledge
    • Qualitative and Quantitative Practical Reasoning
    • D. Dubois and H. Prade, "Focusing vs. Belief Revision: A Fundamental Distinction when Dealing with Generic Knowledge," Proc. Fifth Int'l Joint Conf. Qualitative and Quantitative Practical Reasoning, pp. 96-107, 1997. (Pubitemid 127083993)
    • (1997) Lecture notes in computer science , Issue.1244 , pp. 96-107
    • Dubois, D.1    Prade, H.2
  • 54
    • 33748062355 scopus 로고    scopus 로고
    • Overview on the development of fuzzy random variables
    • DOI 10.1016/j.fss.2006.05.002, PII S016501140600203X, Fuzzy Sets and Probability/Statistics Theory
    • M.A. Gil, M. López-Díaz, and D.A. Ralescu, "Overview on the Development of Fuzzy Random Variables," Fuzzy Sets and Systems, vol. 157, no. 19, pp. 2546-2557, 2006. (Pubitemid 44301496)
    • (2006) Fuzzy Sets and Systems , vol.157 , Issue.19 , pp. 2546-2557
    • Gil, M.A.1    Lopez-Diaz, M.2    Ralescu, D.A.3
  • 57
    • 49949126152 scopus 로고
    • Probability measures of fuzzy events
    • L.A. Zadeh, "Probability Measures of Fuzzy Events," J. Math. Analysis and Applications, vol. 10, pp. 421-427, 1968.
    • (1968) J. Math. Analysis and Applications , vol.10 , pp. 421-427
    • Zadeh, L.A.1
  • 58
    • 80052261743 scopus 로고    scopus 로고
    • Maximum likelihood estimation from fuzzy data using the fuzzy em algorithm
    • T. Denoeux, "Maximum Likelihood Estimation from Fuzzy Data Using the Fuzzy EM Algorithm," Fuzzy Sets and Systems, vol. 183, no. 1, pp. 72-91, 2011.
    • (2011) Fuzzy Sets and Systems , vol.183 , Issue.1 , pp. 72-91
    • Denoeux, T.1
  • 61
    • 33644864393 scopus 로고    scopus 로고
    • On the plausibility transformation method for translating belief function models to probability models
    • DOI 10.1016/j.ijar.2005.06.008, PII S0888613X05000472
    • B.R. Cobb and P.P. Shenoy, "On the Plausibility Transformation Method for Translating Belief Function Models to Probability Models," Int'l J. Approximate Reasoning, vol. 41, no. 3, pp. 314-330, 2006. (Pubitemid 43374978)
    • (2006) International Journal of Approximate Reasoning , vol.41 , Issue.3 , pp. 314-330
    • Cobb, B.R.1    Shenoy, P.P.2
  • 62
    • 0007125205 scopus 로고
    • Constructive probability
    • G. Shafer, "Constructive Probability," Synthese, vol. 48, no. 1, pp. 1-60, 1981.
    • (1981) Synthese , vol.48 , Issue.1 , pp. 1-60
    • Shafer, G.1
  • 63
    • 85041975304 scopus 로고
    • Exploratory latent structure analysis using both identifiable and unidentifiable models
    • L.A. Goodman, "Exploratory Latent Structure Analysis Using Both Identifiable and Unidentifiable Models," Biometrika, vol. 61, no. 2, pp. 215-231, 1974.
    • (1974) Biometrika , vol.61 , Issue.2 , pp. 215-231
    • Goodman, L.A.1
  • 64
    • 0000306608 scopus 로고
    • Clustering criteria for discrete data and latent class models
    • G. Celeux and G. Govaert, "Clustering Criteria for Discrete Data and Latent Class Models," J. Classification, vol. 8, pp. 157-176, 1991.
    • (1991) J. Classification , vol.8 , pp. 157-176
    • Celeux, G.1    Govaert, G.2
  • 65
    • 0000008146 scopus 로고
    • Comparing partitions
    • L. Hubert and P. Arabie, "Comparing Partitions," J. Classification, vol. 2, no. 1, pp. 193-218, 1985.
    • (1985) J. Classification , vol.2 , Issue.1 , pp. 193-218
    • Hubert, L.1    Arabie, P.2
  • 66
    • 0027453616 scopus 로고
    • Model-based Gaussian and non-Gaussian clustering
    • J.D. Banfield and A.E. Raftery, "Model-Based Gaussian and Non- Gaussian Clustering," Biometrics, vol. 49, pp. 803-821, 1993. (Pubitemid 23298358)
    • (1993) Biometrics , vol.49 , Issue.3 , pp. 803-821
    • Banfield, J.D.1    Raftery, A.E.2
  • 67
    • 0029305528 scopus 로고
    • Gaussian parsimonious clustering models
    • G. Celeux and G. Govaert, "Gaussian Parsimonious Clustering Models," Pattern Recognition, vol. 28, no. 5, pp. 781-793, 1995.
    • (1995) Pattern Recognition , vol.28 , Issue.5 , pp. 781-793
    • Celeux, G.1    Govaert, G.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.