Abstract
This paper proposes a new discretization algorithm for uncertain data. Uncertainty is widely spread in real-world data. Numerous factors lead to data uncertainty including data acquisition device error, approximate measurement, sampling fault, transmission latency, data integration error and so on. In many cases, estimating and modeling the uncertainty for underlying data is available and many classical data mining algorithms have been redesigned or extended to process uncertain data. It is extremely important to consider data uncertainty in the discretization methods as well. In this paper, we propose a new discretization algorithm called UCAIM (Uncertain Class-Attribute Interdependency Maximization). Uncertainty can be modeled as either a formula based or sample based probability distribution function (pdf). We use probability cardinality to build the quanta matrix of these uncertain attributes, which is then used to evaluate class-attribute interdependency by adopting the redesigned ucaim criterion. The algorithm selects the optimal discretization scheme with the highest ucaim value. Experiments show that the usage of uncertain information helps UCAIM perform well on uncertain data. It significantly outperforms the traditional CAIM algorithm, especially when the uncertainty is high.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Kaufman, K.A., Michalski, R.S.: Learning from inconsistent and noisy data: the AQ18 approach. In: Proceeding of 11th International Symposium on Methodologies for Intelligent Systems (1999)
Cios, K.J., et al.: Hybrid inductive machine learning: an overview of clip algorithm. In: Jain, L.C., Kacprzyk, J. (eds.) New Learning Paradigms in Soft Computing, pp. 276–322. Springer, Heidelberg (2001)
Clark, P., Niblett, T.: The CN2 Algorithm. Machine Learning 3(4), 261–283 (1989)
Catlett, J.: On Changing Continues Attributes into Ordered Discrete Attributes. In: Kodratoff, Y. (ed.) EWSL 1991. LNCS, vol. 482, pp. 164–178. Springer, Heidelberg (1991)
Liu, H., Hussain, F., Tan, C.L., Dash, M.: Discretization: An Enable Technique. Data Mining and Knowledge Discovery 6, 393–423 (2002)
Fayyad, U.M., Irani, K.B.: Multi-Interval Discretization of Continues- Valued Attributes for Classification Learning. In: Proceedings of the 13th Joint Conference on Artificial Intelligence, pp. 1022–1029 (1993)
Hanse, M.H., Yu, B.: Model Selection and the Principle of Minimum Description Length. Journal of the American Statistical Association (2001)
Kurgan, L.A.: CAIM Discretization Algorithm. In: IEEE Transactions on Knowledge and Data Engineering, p. 145 (2004)
Aggarwal, C.C., Yu, P.: A framework for clustering uncertain data streams. In: IEEE International Conference on Data Engineering, ICDE (2008)
Cormode, G., McGregor, A.: Approximation algorithms for clustering uncertain data. In: Principle of Data base System, PODS (2008)
Kriegel, H., Pfeifle, M.: Density-based clustering of uncertain data. In: ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD), pp. 672–677 (2005)
Singh, S., Mayfield, C., Prabhakar, S., Shah, R., Hambrusch, S.: Indexing categorical data with uncertainty. In: IEEE International Conference on Data Engineering (ICDE), pp. 616–625 (2007)
Kriegel, H., Pfeifle, M.: Hierarchical density-based clustering of uncertain data. In: IEEE International Conference on Data Mining (ICDM), pp. 689–692 (2005)
Aggarwal, C.C.: On Density Based Transforms for uncertain Data Mining. In: IEEE International Conference on Data Engineering, ICDE (2007)
Aggarwal, C.C.: A Survey of Uncertain Data Algorithms and Applications. IEEE Transactions on Knowledge and Data Engineering 21(5) (2009)
Ren, J., et al.: Naïve Bayes Classification of Uncertain Data. In: IEEE International Conference on Data Mining (2009)
Dougherty, J., Kohavi, R., Sahavi, M.: Supervised and Unsupervised Discretization of Continues Attributes. In: Proceedings of the 12th International Conference on Machine Learning, pp. 194–202 (1995)
Linde, Y., Buzo, A., Gray, R.M.: An Algorithm for Vector Quantizer Design. IEEE Transactions on Communications 28, 84–95 (1980)
Wong, A.K.C., Chiu, D.K.Y.: Synthesizing Statistical Knowledge from Incomplete Mixed-Mode Data. IEEE Transactions on Pattern Analysis and Machine Intelligence 9, 796–805 (1987)
Kurgan, L., Cios, K.J.: Fast Class-Attribute Interdependence Maximization (CAIM) Discretization Algorithm. In: Proceeding of International Conference on Machine Learning and Applications, pp. 30–36 (2003)
Kerber, R.: ChiMerge: discretization of numeric attributes. In: Proceeding of 9th International Conference on Artificial Intelligence, pp. 123–128 (1992)
Liu, H., Setiono, R.: Feature Selection via discretization. IEEE Transactions on knowledge and Data Engineering 9(4), 642–645 (1997)
Tray, F., Shen, L.: A modified Chi2 algorithm for discretization. IEEE Transactions on Knowledge and Data Engineering 14(3), 666–670 (2002)
Su, C.T., Hsu, J.H.: An extended Chi2 algorithm for discretization of real value attributes. IEEE Transactions on Knowledge and Data Engineering 17(3), 437–441 (2005)
Jing, R., Breitbart, Y.: Data Discretization Unification. In: IEEE International Conference on Data Mining, p. 183 (2007)
Berzal, F., et al.: Building Multi-way decision Trees with Numerical Attributes. Information Sciences 165, 73–90 (2004)
Bi, J., Zhang, T.: Support Vector Machines with Input Data Uncertainty. In: Proc. Advances in Neural Information Processing Systems (2004)
Qin, B., Xia, Y., Li, F.: DTU: A Decision Tree for Classifying Uncertain Data. In: Theeramunkong, T., Kijsirikul, B., Cercone, N., Ho, T.-B. (eds.) PAKDD 2009. LNCS, vol. 5476, pp. 4–15. Springer, Heidelberg (2009)
Cheng, R., Kalashnikov, D., Prabhakar, S.: Evaluating Probabilistic Queries over Imprecise Data. In: Proceedings of the ACM SIGMOD, pp. 551–562 (2003)
Asuncion, A., Newman, D.: UCI machine learning repository (2007), http://www.ics.uci.edu/mlearn/MLRepository.html
Aggarwal, C.C., Yu, P.S.: Outlier Detection with Uncertain Data. In: SIAM International Conference on Data Mining (2009)
Han, J., Kamber, M.: Data Mining: Concepts and Techniques, 2nd edn. Morgan Kaufmann, San Francisco (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ge, J., Xia, Y., Tu, Y. (2010). A Discretization Algorithm for Uncertain Data. In: Bringas, P.G., Hameurlain, A., Quirchmayr, G. (eds) Database and Expert Systems Applications. DEXA 2010. Lecture Notes in Computer Science, vol 6262. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15251-1_38
Download citation
DOI: https://doi.org/10.1007/978-3-642-15251-1_38
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15250-4
Online ISBN: 978-3-642-15251-1
eBook Packages: Computer ScienceComputer Science (R0)