Abstract
Evidence theory is widely used in data mining, machine learning, clustering and database systems. In these applications, often combination of mass functions is performed without checking the degree of consistency between the mass functions, which may lead to counterintuitive results. In this paper, we aim to measure the divergences among mass functions which can hence prevent highly inconsistent mass functions from been combined. To this end, we propose a divergence measure between two mass functions. In addition, incompleteness measures and similarity measures are also provided based on divergence measures.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Anand, S., Bell, D., Hughes, J.: Edm: A general framework for data mining based on evidence theory. Data & Knowledge Engineering 18(3), 189–223 (1996)
Aslandogan, Y., Mahajani, G., Taylor, S.: Inter. Conf. on Information Technology: Coding and Computing. Chapter Evidence Combination in Medical Data Mining, vol. 2 (2004)
Bi, Y., Guan, J., Bell, D.: The combination of multiple classifiers using an evidential reasoning approach. Artif. Intell. 172(15), 1731–1751 (2008)
Daniel, M.: Belief functions: a revision of plausibility conflict and pignistic conflict. In: Subrahmanian, V.S., Liu, W., Wijsen, J. (eds.) SUM 2013. LNCS(LNCS), vol. 8078, pp. 190–203. Springer, Heidelberg (2013)
Daniel, M.: Properties of plausibility conflict of belief functions. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2013, Part I. LNCS(LNAI), vol. 7894, pp. 235–246. Springer, Heidelberg (2013)
Daniel, M., Ma, J.: Conflicts of belief functions: continuity and frame resizement. In: Calì, A., Straccia, U. (eds.) SUM 2014. LNCS, vol. 8720, pp. 106–119. Springer, Heidelberg (2014)
Dempster, A.P.: Upper and lower probabilities induced by a multivalued mapping. The Annals of Statistics 28, 325–339 (1967)
Diaz, J., Rifqi, M., Bouchon-Meunier, B.: A similarity measure between basic belief assignments. In: Proceedings of the 9th International Conference on Information Fusion, pp. 1–6, July 2006
Dubois, D., Prade, H.: Representation and combination of uncertainty with belief functions and possibility measures. Comput. Intel. 4, 244–264 (1988)
He, D., Göker, A., Harper, D.: Combining evidence for automatic web session identification. Information Processing & Management 38(5), 727–742 (2002)
Hegarat-Mascle, S., Bloch, I., Vidal-Madjar, D.: Application of dempster-shafer evidence theory to unsupervised classification in multisource remote sensing. IEEE transactions on geoscience and remote sensing 35(4), 795–979 (1997)
Josang, A.: The consensus operator for combining beliefs. Artificial Intelligence 141(1–2), 157–170 (2002)
Jousselme, A., Grenier, D., Bosse, E.: A new distance between two bodies of evidence. Information Fusion 2(2), 91–101 (2001)
Jousselme, A., Maupin, P.: Distances in evidence theory: Comprehensive survey and generalizations. International Journal of Approximate Reasoning 53(2), 118–145 (2012)
Liu, W.: Analyzing the degree of conflict among belief functions. Artificial Intelligence 170, 909–924 (2006)
Ma, J., Liu, W., Dubois, D., Prade, H.: Bridging jeffery’s rule, agm revision, and dempster conditioning in the theory of evidence. International Journal of Artificial Intelligence Tools 20(4), 691–720 (2011)
Ma, J., Liu, W., Miller, P.: Event modelling and reasoning with uncertain information for distributed sensor networks. In: Deshpande, A., Hunter, A. (eds.) SUM 2010. LNCS, vol. 6379, pp. 236–249. Springer, Heidelberg (2010)
Ma, J., Liu, W., Miller, P.: Evidential fusion for gender profiling. In: Link, S., Fober, T., Seeger, B., Hüllermeier, E. (eds.) SUM 2012. LNCS, vol. 7520, pp. 514–524. Springer, Heidelberg (2012)
Ma, J., Liu, W., Miller, P.: An evidential improvement for gender profiling. In: Denoeux, T., Masson, M.-H. (eds.) Belief Functions: Theory and Applications. AISC, pp. 29–36. Springer, Heidelberg (2012)
Ma, J., Liu, W., Miller, P., Yan, W.: Event composition with imperfect information for bus surveillance. In: Proc. of AVSS 2009, pp. 382–387 (2009)
Ma, W., Liu, W., Ma, J., Miller, P.: An extended event reasoning framework for decision support under uncertainty. In: Bouchon-Meunier, B., Yager, R.R., Laurent, A., Strauss, O. (eds.) IPMU 2014, Part III. CCIS, vol. 444, pp. 335–344. Springer, Heidelberg (2014)
McClean, S., Scotney, B.: Using evidence theory for the integration of distributed databases. International Journal of Intelligent Systems 12(10), 763–776 (1998)
Daniel, M.: Conflict between belief functions: a new measure based on their non-conflicting parts. In: Cuzzolin, F. (ed.) BELIEF 2014. LNCS(LNAI), vol. 8764, pp. 321–330. Springer, Heidelberg (2014)
Perry, W., Stephanou, H.: Proc. of IEEE Inter. Symp. on Intelligent Control. Chapter Belief Function Divergence as a Classifier, pp. 280–285 (1991)
Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press (1976)
Smarandache, F., Dezert, J.: An introduction to the dsm theory for the combination of paradoxical, uncertain, and imprecise sources of information. http://arxiv.org/abs/cs/0608002
Smets, P.: Data fusion in the transferable belief model. In: Proceedings of International Conference on Information Fusion, Paris, July 2000
Smets, P., Kennes, R.: The transferable belief model. Artificial Intelligence 66(2), 191–234 (1994)
Xie, Y., Phoha, V.: Procs. of 1st inter. conf. on knowledge capture, K-cap 2001, pp. 202–208. ACM (2001)
Yager, R.: On the relationships of methods of aggregation of evidence in expert systems. Cybernetics and Systems 16, 1–21 (1985)
Yager, R.: On the dempster-shafer framework and new combination rules. Inform. Sci. 41, 93–138 (1987)
Zadeh, L.: A simple view of the dempster-shafer theory of evidence and its implication for the rule of combination. AI Magazine 7, 85–90 (1986)
Zeng, D., Xu, J., Xu, G.: Data fusion for traffic incident detection using d-s evidence theory with probabilistic svms. Journal of Computers 3(10), 36–43 (2008)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Ma, J. (2015). A Divergence Measure Between Mass Functions. In: Zhang, S., Wirsing, M., Zhang, Z. (eds) Knowledge Science, Engineering and Management. KSEM 2015. Lecture Notes in Computer Science(), vol 9403. Springer, Cham. https://doi.org/10.1007/978-3-319-25159-2_5
Download citation
DOI: https://doi.org/10.1007/978-3-319-25159-2_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-25158-5
Online ISBN: 978-3-319-25159-2
eBook Packages: Computer ScienceComputer Science (R0)