The belief K-modes method (BKM) approach is a new
clustering technique handling uncertainty in the attribute values of
objects in both the cluster construction task and the classification one.
Like the standard version of this method, the BKM results depend on
the chosen initial modes. So, one selection method of initial modes
is developed, in this paper, aiming at improving the performances of
the BKM approach. Experiments with several sets of real data show
that by considered the developed selection initial modes method, the
clustering algorithm produces more accurate results.
[1] J.A. Barnett, Calculating Dempster-Shafer plausibility, IEEE Transactions
on Pattern Analysis and Machine Intelligence, 13 (6), 1991, pp.599-602.
[2] M. Bauer, Approximation algorithms and decision making in
the Dempster-Shafer theory of evidence - an empirical study,
Int.J.Approx.Reason. 17 (2-3), 1997, pp.217.
[3] S. Ben Hariz, Z. Elouedi, and K. Mellouli, Clustering Approach using
Belief Function Theory, Proceeding of the Twelfth International Conference
on Artificial Intelligence: Methodology, Systems, Applications
(AIMSA2006), 2006, pp.162-171.
[4] E. Bosse, D. Grenier and A.L. Jousselme, A new distance between two
bodies of evidence, In Information Fusion 2, 2001, pp.91-101.
[5] P.S. Bradley, U.M. Fayyad, Refining Initial Points for K-Means Clustering,
Proceedings of the 15th International Conference on Machine
Learning (ICML98), San Francisco, Morgan Kaufmann, 1998.
[6] T. Denoeux, A k-nearest neighbor classification rule based on Dempster-
Shafer theory, IEEE Transactions on Systems, Man and Cybernetics, 25
(5), 1995, pp.804-813.
[7] T. Denoeux and M. Skarstein-Bjanger, Induction of decision trees from
partially classified data, Proceedings of SMC-2000,, Nashville, TN., 2000,
pp.2923-2928.
[8] T. Denoeux and M. Masson, Clustering of proximity data using belief
functions, Proceedings of IPMU-2002, Annecy, France., Vol I, 2002,
pp.609-616.
[9] T. Denoeux andM. Masson, EVCLUS: Evidential Clustering of Proximity
Data, IEEE Transactions on Systems, Man and Cybernetics, 34 (1), 2003,
pp.95-109.
[10] T. Denoeux andM.Masson, Clustering Interval-valued Data using Belief
Functions, Pattern Recognition Letters, 25 (2), 2004, pp.163-171.
[11] Z. Elouedi, K. Mellouli and P. Smets, Belief Decision trees: Theoretical
foundations, International Journal of Approximat Reasoning, 28 (2-3),
2001, pp.91-124.
[12] Z. Elouedi, K. Mellouli and P. Smets, Assessing sensor reliability
for multisensor data fusion within the transferable belief model, IEEE
Trans.Syst.Man Cybern, 34 (1), 2004, pp.782-787.
[13] D. Fixen and R.P.S. Mahler, The modified Dempster-Shafer approach to
classification, IEEE Trans.Syst.Man Cybern, 27 (1), 1997, pp.96-104.
[14] Z. Huang, Extensions to the k-means algorithm for clustering large data
sets with categorical values, Data Mining Knowl.Discov., 2 (2), 1998,
pp.283-304.
[15] Z. Huang and M.K. Ng, A fuzzy K-modes algorithm for clustering
categorical data. IEEE Transaction on Fuzzy Systems,7(4), 1999, pp.446-
452.
[16] A.K. Jain and R.C. Dubes, Algorithms for clustering data, Prentice-Hall,
Englewood cliffs, NJ, 1988, pp.197-198.
[17] D-W. Kim and K.H. Lee, Fuzzy clustering of categorical data using
fuzzy centroids. Pattern Recognition Letters, 25, 2004 , pp.1263-1271.
[18] S.S. Khan, A. Ahmad, Cluster center initialization algorithm for Kmeans
clustering. Pattern Recognition Letters, 25 (11), 2004, 1293-1302.
[19] S.S. Khan, Dr.S. Kant, Computation of Initial Modes for K-modes
Clustering Algorithm using Evidence Accumulation. IJCAI-07, 2007,
2784-2789.
[20] MP. Murphy and D.W. Aha, Uci repository
databases.http://www.ics.uci.edu/mlearn, 1996.
[21] J. MacQueen, Some methods for classification and analysis of multivariate
observations, Proceeding of the Fifth Berkeley Symposium on Math,
Stat and Prob., 1, 1967, pp.281-296.
[22] J. Schubert, Clustering belief functions based on attracting and conflicting
metalevel evidence, Intelligent Systems for Information Processing:
From Representation to Applications, 2003.
[23] G. Shafer, A mathematical theory of evidence, Princeton Univ. Press.
Princeton, NJ.30, 1976.
[24] P. Smets and R. Kennes, The transferable belief model, Artificial
Intelligence, 66, 1994, pp.191-234.
[25] P. Smets, The combination of evidence in the transferable belief model,
IEEE-Pattern analysis and Machine Intelligence, 12, 1990, pp.447-458.
[26] P. Smets, Belief functions: The disjunctive rule of combination and
the generalized bayesian theorem, International Journal of Approximate
Reasoning, 9, 1993, pp.1-35.
[27] P. Smets, The transferable belief model for quantified belief representation,
In D.M. Gabbay and P. Smets (Eds.), Handbook of defeasible
reasoning and uncertainty management systems, 1, 1998, pp.267-301.
[28] Y. Sun, Q. Zhu, Z. Chen: An Iterative initial points refinement algorithm
for categorical data clustering, Pattern Recognition Letters, 23, 875-884,
2002.
[29] B. Tessem, Approximations for efficient computation in the theory of
evidence, Artif.Intell, 61 (2), 1993, pp.315-329.
[30] L.M. Zouhal and T. Doeneux, An evidence-theory k-NN rule with
parameter optimization, IEEE Trans.Syst.Man Cybern. 28 (2), 1998,
pp.263-271.
[1] J.A. Barnett, Calculating Dempster-Shafer plausibility, IEEE Transactions
on Pattern Analysis and Machine Intelligence, 13 (6), 1991, pp.599-602.
[2] M. Bauer, Approximation algorithms and decision making in
the Dempster-Shafer theory of evidence - an empirical study,
Int.J.Approx.Reason. 17 (2-3), 1997, pp.217.
[3] S. Ben Hariz, Z. Elouedi, and K. Mellouli, Clustering Approach using
Belief Function Theory, Proceeding of the Twelfth International Conference
on Artificial Intelligence: Methodology, Systems, Applications
(AIMSA2006), 2006, pp.162-171.
[4] E. Bosse, D. Grenier and A.L. Jousselme, A new distance between two
bodies of evidence, In Information Fusion 2, 2001, pp.91-101.
[5] P.S. Bradley, U.M. Fayyad, Refining Initial Points for K-Means Clustering,
Proceedings of the 15th International Conference on Machine
Learning (ICML98), San Francisco, Morgan Kaufmann, 1998.
[6] T. Denoeux, A k-nearest neighbor classification rule based on Dempster-
Shafer theory, IEEE Transactions on Systems, Man and Cybernetics, 25
(5), 1995, pp.804-813.
[7] T. Denoeux and M. Skarstein-Bjanger, Induction of decision trees from
partially classified data, Proceedings of SMC-2000,, Nashville, TN., 2000,
pp.2923-2928.
[8] T. Denoeux and M. Masson, Clustering of proximity data using belief
functions, Proceedings of IPMU-2002, Annecy, France., Vol I, 2002,
pp.609-616.
[9] T. Denoeux andM. Masson, EVCLUS: Evidential Clustering of Proximity
Data, IEEE Transactions on Systems, Man and Cybernetics, 34 (1), 2003,
pp.95-109.
[10] T. Denoeux andM.Masson, Clustering Interval-valued Data using Belief
Functions, Pattern Recognition Letters, 25 (2), 2004, pp.163-171.
[11] Z. Elouedi, K. Mellouli and P. Smets, Belief Decision trees: Theoretical
foundations, International Journal of Approximat Reasoning, 28 (2-3),
2001, pp.91-124.
[12] Z. Elouedi, K. Mellouli and P. Smets, Assessing sensor reliability
for multisensor data fusion within the transferable belief model, IEEE
Trans.Syst.Man Cybern, 34 (1), 2004, pp.782-787.
[13] D. Fixen and R.P.S. Mahler, The modified Dempster-Shafer approach to
classification, IEEE Trans.Syst.Man Cybern, 27 (1), 1997, pp.96-104.
[14] Z. Huang, Extensions to the k-means algorithm for clustering large data
sets with categorical values, Data Mining Knowl.Discov., 2 (2), 1998,
pp.283-304.
[15] Z. Huang and M.K. Ng, A fuzzy K-modes algorithm for clustering
categorical data. IEEE Transaction on Fuzzy Systems,7(4), 1999, pp.446-
452.
[16] A.K. Jain and R.C. Dubes, Algorithms for clustering data, Prentice-Hall,
Englewood cliffs, NJ, 1988, pp.197-198.
[17] D-W. Kim and K.H. Lee, Fuzzy clustering of categorical data using
fuzzy centroids. Pattern Recognition Letters, 25, 2004 , pp.1263-1271.
[18] S.S. Khan, A. Ahmad, Cluster center initialization algorithm for Kmeans
clustering. Pattern Recognition Letters, 25 (11), 2004, 1293-1302.
[19] S.S. Khan, Dr.S. Kant, Computation of Initial Modes for K-modes
Clustering Algorithm using Evidence Accumulation. IJCAI-07, 2007,
2784-2789.
[20] MP. Murphy and D.W. Aha, Uci repository
databases.http://www.ics.uci.edu/mlearn, 1996.
[21] J. MacQueen, Some methods for classification and analysis of multivariate
observations, Proceeding of the Fifth Berkeley Symposium on Math,
Stat and Prob., 1, 1967, pp.281-296.
[22] J. Schubert, Clustering belief functions based on attracting and conflicting
metalevel evidence, Intelligent Systems for Information Processing:
From Representation to Applications, 2003.
[23] G. Shafer, A mathematical theory of evidence, Princeton Univ. Press.
Princeton, NJ.30, 1976.
[24] P. Smets and R. Kennes, The transferable belief model, Artificial
Intelligence, 66, 1994, pp.191-234.
[25] P. Smets, The combination of evidence in the transferable belief model,
IEEE-Pattern analysis and Machine Intelligence, 12, 1990, pp.447-458.
[26] P. Smets, Belief functions: The disjunctive rule of combination and
the generalized bayesian theorem, International Journal of Approximate
Reasoning, 9, 1993, pp.1-35.
[27] P. Smets, The transferable belief model for quantified belief representation,
In D.M. Gabbay and P. Smets (Eds.), Handbook of defeasible
reasoning and uncertainty management systems, 1, 1998, pp.267-301.
[28] Y. Sun, Q. Zhu, Z. Chen: An Iterative initial points refinement algorithm
for categorical data clustering, Pattern Recognition Letters, 23, 875-884,
2002.
[29] B. Tessem, Approximations for efficient computation in the theory of
evidence, Artif.Intell, 61 (2), 1993, pp.315-329.
[30] L.M. Zouhal and T. Doeneux, An evidence-theory k-NN rule with
parameter optimization, IEEE Trans.Syst.Man Cybern. 28 (2), 1998,
pp.263-271.
@article{"International Journal of Information, Control and Computer Sciences:49741", author = "Sarra Ben Hariz and Zied Elouedi and Khaled Mellouli", title = "Selection Initial modes for Belief K-modes Method", abstract = "The belief K-modes method (BKM) approach is a new
clustering technique handling uncertainty in the attribute values of
objects in both the cluster construction task and the classification one.
Like the standard version of this method, the BKM results depend on
the chosen initial modes. So, one selection method of initial modes
is developed, in this paper, aiming at improving the performances of
the BKM approach. Experiments with several sets of real data show
that by considered the developed selection initial modes method, the
clustering algorithm produces more accurate results.", keywords = "Clustering, Uncertainty, Belief function theory, Belief
K-modes Method, Initial modes selection.", volume = "1", number = "6", pages = "1521-10", }
