Abstract
Discretization of the value range of a numerical feature is a common task in data mining and machine learning. Optimal multivariate discretization is in general computationally intractable. We have proposed approximation algorithms with performance guarantees for training error minimization by axis-parallel hyperplanes. This work studies their efficiency and practicability. We give efficient implementations to both greedy set covering and linear programming approximation of optimal multivariate discretization. We also contrast the algorithms empirically to an efficient heuristic discretization method.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bay, S.D.: Multivariate discretization of continuous variables for set mining. In: Proc. 6th ACM SIGKDD, pp. 315–319. ACM Press, New York (2000)
Călinescu, G., Dumitrescu, A., Wan, P.-J.: Separating points by axis-parallel lines. In: Proc. 16th Canadian Conference on Computational Geometry, pp. 7–10 (2004)
Chlebus, B.S., Nguyen, S.H.: On finding optimal discretizations for two attributes. In: Polkowski, L., Skowron, A. (eds.) RSCTC 1998. LNCS (LNAI), vol. 1424, pp. 537–544. Springer, Heidelberg (1998)
Chmielewski, M.R., Grzymala-Busse, J.W.: Global discretization of continuous attributes as preprocessing for machine learning. Int. J. Approximate Reasoning 15, 319–331 (1996)
Dougherty, J., Kohavi, R., Sahami, M.: Supervised and unsupervised discretization of continuous features. In: Proc. 12th ICML, pp. 194–202. Morgan Kaufmann, San Francisco (1995)
Elomaa, T., Kujala, J., Rousu, J.: Approximation algorithms for minimizing empirical error by axis-parallel hyperplanes. In: Gama, J., Camacho, R., Brazdil, P.B., Jorge, A.M., Torgo, L. (eds.) ECML 2005. LNCS (LNAI), vol. 3720, pp. 547–555. Springer, Heidelberg (2005)
Elomaa, T., Rousu, J.: On decision boundaries of Naïve Bayes in continuous domains. In: Lavrač, N., Gamberger, D., Todorovski, L., Blockeel, H. (eds.) PKDD 2003. LNCS (LNAI), vol. 2838, pp. 144–155. Springer, Heidelberg (2003)
Elomaa, T., Rousu, J.: Efficient multisplitting revisited: Optima-preserving elimination of partition candidates. Data Mining and Knowl. Discovery 8, 97–126 (2004)
Fayyad, U.M., Irani, K.B.: On the handling of continuous-valued attributes in decision tree generation. Machine Learn. 8, 87–102 (1992)
Fayyad, U.M., Irani, K.B.: Multi-interval discretization of continuous-valued attributes for classification learning. In: Proc. 13th IJCAI, pp. 1022–1027. Morgan Kaufmann, San Francisco (1993)
Friedman, N., Goldszmidt, M.: Discretizing continuous attributes while learning Bayesian networks. In: Proc. 13th ICML, pp. 157–165. Morgan Kaufmann, San Francisco (1996)
Miller, R.J., Yang, Y.: Association rules over interval data. In: Proc. 1997 ACM SIGMOD, pp. 452–461. ACM Press, New York (1997)
Monti, S., Cooper, G.F.: A multivariate discretization method for learning Bayesian networks from mixed data. In: Proc. 14th UAI, pp. 404–413. Morgan Kaufmann, San Francisco (2002)
Muhlenbach, F., Rakotomalala, R.: Multivariate supervised discretization, a neighborhood graph approach. In: Proc. 2002 ICDM, pp. 314–321. IEEE CS Press, Los Alamitos (2002)
Srikant, R., Agrawal, R.: Mining quantitative association rules in large relational tables. In: Proc. 1996 ACM SIGMOD, pp. 1–12. ACM Press, New York (1996)
Vazirani, V.V.: Approximation Algorithms. Springer, Heidelberg (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Elomaa, T., Kujala, J., Rousu, J. (2006). Practical Approximation of Optimal Multivariate Discretization. In: Esposito, F., Raś, Z.W., Malerba, D., Semeraro, G. (eds) Foundations of Intelligent Systems. ISMIS 2006. Lecture Notes in Computer Science(), vol 4203. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11875604_68
Download citation
DOI: https://doi.org/10.1007/11875604_68
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-45764-0
Online ISBN: 978-3-540-45766-4
eBook Packages: Computer ScienceComputer Science (R0)