Abstract
This paper presents a generalized theory for capturing and manipulating classification information. We define decision algebra which models decision-based classifiers as higher order decision functions abstracting from implementations using decision trees (or similar), decision rules, and decision tables. As a proof of the decision algebra concept we compare decision trees with decision graphs, yet another instantiation of the proposed theoretical framework, which implement the decision algebra operations efficiently and capture classification information in a non-redundant way. Compared to classical decision tree implementations, decision graphs gain learning and classification speed up to 20% without accuracy loss and reduce memory consumption by 44%. This is confirmed by experiments.
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References
King, P.: Decision tables. The Computer Journal 10(2), 135–142 (1967)
Tan, M.S.P.-N., Kumar, V.: Introduction to Data Mining. Addison-Wesley, Reading (2005)
Rokach, L., Maimon, O.: Data Mining with Decision Trees: Theory and Applications. World Scientific, Singapore (2008)
Bryant, R.E.: Graph-based algorithms for boolean function manipulation. IEEE Transactions on Computers 35, 677–691 (1986)
Frank, A., Asuncion, A.: UCI machine learning repository. University of California, Irvine, School of Information and Computer Sciences (2010), http://archive.ics.uci.edu/ml
Bryant, R.E.: Symbolic boolean manipulation with ordered binary-decision diagrams. ACM Computing Surveys 24, 293–318 (1992)
Trapp, M.: Optimierung objektorientierter programme. Ph.D. dissertation. Universität Karlsruhe, Karlsruhe (December 1999)
Ping He, L.C., Xu, X.-H.: Fast C4.5. In: Proc. Int. Conf. Machine Learning Cybernetics, ICMLC 2007, Hong Kong, China, vol. 5, pp. 2841–2846 (August 2007)
Ruggieri, S.: Efficient c4.5. IEEE Transactions on Knowledge and Data Engineering 14, 438–444 (2002)
Quinlan, J.R.: Simplifying decision trees. Int. J. Man-Mach. Stud. 27(3), 221–234 (1987)
Nilsson, N.J.: Introduction to machine learning: An early draft of proposed text book. Stanford University, Stanford (1996), http://ai.stanford.edu/~nilsson/mlbook.html
Lam, K.-W., Lee, V.C.S.: Building decision trees using functional dependencies. In: ITCC 2004: Proc. of the Int. Conf. on Inf. Technology: Coding and Computing (ITCC 2004), vol. 2, p. 470. IEEE Computer Society, Washington, DC, USA (2004)
Pagallo, G., Haussler, D.: Boolean feature discovery in empirical learning. Mach. Learn. 5(1), 71–99 (1990)
John, G.H.: Robust linear discriminant trees. In: AI & Statistics 1995, pp. 285–291. Springer, Heidelberg (1994)
Vilalta, R., Blix, G., Rendell, L.: Global data analysis and the fragmentation problem in decision tree induction. In: van Someren, M., Widmer, G. (eds.) ECML 1997. LNCS, vol. 1224, pp. 312–326. Springer, Heidelberg (1997)
Friedman, J.H., Kohavi, R., Yun, Y.: Lazy decision trees (1996)
Oliver, J.J.: Decision graphs - an extension of decision trees (1993)
Quinlan, J.R.: Generating production rules from decision trees. In: IJCAI 1987: Proceedings of the 10th International Joint Conference on Artificial Intelligence, pp. 304–307. Morgan Kaufmann Publishers Inc., San Francisco (1987)
Kargupta, H., Dutta, H.: Orthogonal decision trees. In: Proceedings of The Fourth IEEE International Conference on Data Mining (ICDM 2004), pp. 1028–1042 (2004)
Hafez, A., Deogun, J., Raghavan, V.V.: The item-set tree: A data structure for data mining. In: Mohania, M., Tjoa, A.M. (eds.) DaWaK 1999. LNCS, vol. 1676, pp. 183–192. Springer, Heidelberg (1999)
Tang, Y., Meersman, R.: On Constructing Semantic Decision Tables. In: Wagner, R., Revell, N., Pernul, G. (eds.) DEXA 2007. LNCS, vol. 4653, pp. 34–44. Springer, Heidelberg (2007)
Fernandez del Pozo, C.B.J.A., Gomez, M.: A list-based compact representation for large decision tables management. European Journal of Operational Research 160(3), 638–662 (2005)
Murphy, O.J., McCraw, R.L.: Designing storage efficient decision trees. IEEE Trans. Comput. 40(3), 315–320 (1991)
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Danylenko, A., Lundberg, J., Löwe, W. (2011). Decisions: Algebra and Implementation. In: Perner, P. (eds) Machine Learning and Data Mining in Pattern Recognition. MLDM 2011. Lecture Notes in Computer Science(), vol 6871. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23199-5_3
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DOI: https://doi.org/10.1007/978-3-642-23199-5_3
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