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Part of the book series: Massive Computing ((MACO,volume 6))

Abstract

Among the numerous learning tasks that fall within the field of knowledge discovery in databases, classification may be the most common. Furthermore, top-down induction of decision trees is one of the most popular techniques for inducing such classification models. Most of the research in decision tree induction has focused on single attribute trees, but in this chapter we review multi-attribute decision trees induction and discuss how such methods can improve both the accuracy and simplicity of the decision trees. As an example of this approach we consider the recently proposed second order decision tree induction (SODI) algorithm, which uses conjunctive and disjunctive combinations of two attributes for improved decision tree induction in nominal databases. We show via numerical examples that in many cases this generates more accurate classification models and easier to interpret decision trees and rules.

Triantaphyllou, E. and G. Felici (Eds.), Data Mining and Knowledge Discovery Approaches Based on Rule Induction Techniques, Massive Computing Series, Springer, Heidelberg, Germany, pp. 327–358, 2006.

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References

  • M. Ali and M. Pazzani, “HYDRA: A nose-tolerant relational concept learning algorithm,” International Joint Conference on Artificial Intelligence, Chambery, France, 1995.

    Google Scholar 

  • M. Ali and M. Pazzani, “Reducing the small disjuncts problems by learning probabilistic concept descriptions,” Computational Learning Theory and Natural Learning Systems, Vol. 3, pp. 183–199, 1995.

    Google Scholar 

  • E. Baker and A. K. Jain, “On feature ordering in practice and some finite sample effects,” Proceedings of the 3 rd International Joint Conference on Pattern Recognition, pp. 45–49, San Diego, CA, USA, 1976.

    Google Scholar 

  • M. Ben-Bassat, “Use of distance measures, information measures and error bounds on feature evaluation,” Classification, Pattern Recognition and Reduction of Dimensionality, In K. P. R. Krishnaiah and L. N. Kanal, editors, Vol. 2 of Handbook of Statistics, North-Holland Publishing Company, Amsterdam, The Netherlands, pp. 773–791, 1987.

    Google Scholar 

  • M. Ben-Bassat, “Myopic policies in sequential classification,” IEEE Transactions on Computing, Vol. 27, No, 2, pp. 170–174, 1978.

    MathSciNet  Google Scholar 

  • K. P. Bennett and O. L. Mangasarian, “Multicategory Discrimination via Linear Programming,” Optimization Methods and Software, Vol. 3, pp. 29–39, 1994.

    Google Scholar 

  • J. C. Bioch, O. Van der Meer, and R. Potharst, “Bivariate Decision Trees”, in J. Komorowski, J. Zytkow, eds. Principles of Data Mining and Knowledge Discovery, Lecture Notes in Artificial Intelligence 1263, Springer Verlag, 1997, New York, NY, USA, pp. 232–243.

    Google Scholar 

  • H. Blocked and L. De Raedt, “Top-down induction of first order logical decision trees,” Artificial Intelligence, Vol. 101, pp.285–297, 1998.

    Article  MathSciNet  Google Scholar 

  • L. Breiman, J. H. Friedman, R. A. Olshen, C. J. Stone, Classification and regression trees, Wadsworh International Group, Belmont, CA, USA, 1984.

    MATH  Google Scholar 

  • C. E. Brodley and P. E. Utgoff, “Multivariate Decision Trees,” Machine Learning, Vol. 19, pp. 45–77, 1995.

    MATH  Google Scholar 

  • W. Buntine, “Learning classification trees,” Statistics and Computing, Vol. 2, pp. 63–73, 1992.

    Article  Google Scholar 

  • R. G. Casey and G. Nagy, “Decision tree design using a probabilistic model,” IEEE Transactions on Information Theory, IT-30, No. 1, pp. 93–99, 1984.

    Article  Google Scholar 

  • T. G. Dietterich and E. B. Kong, “Machine learning bias, statistical bias and statistical variance of decision tree algorithms,” Machine Learning: Proceedings of the 12 th International Conference, Tahoe City, CA, USA, 1995.

    Google Scholar 

  • L. De Màntaras, “Technical note: A distance-based attribute selection measure for decision tree induction,” Machine Learning, Vol. 6, No. 1, pp.81–92, 1991.

    Google Scholar 

  • U. M. Fayyad, G. Piatetsky-Shapiro, P. Smyth, and R. Uthurusamy. Advances in Knowledge Discovery and Data Mining, MIT Press, Cambridge, MA, USA, 1996.

    Google Scholar 

  • U. M. Fayyad, J. E. Laird, K. B. Irani, The Fifth International Conference on Machine Learning, AI Magazine Vol. 10, No. 2, pp. 79–84, 1989.

    Google Scholar 

  • E. Frank and I. H. Witten, “Generating accurate rule sets without global optimization,” Machine Learning: Proceedings of the 15 th International Conference edited by J. Shavlik, Morgan Kaufmann, San Francisco, CA, USA, 1998.

    Google Scholar 

  • S. B. Gelfand, C. S. Ravishankar, and E. J. Delp, “An iterative growing and pruning algorithm for classification tree design,” IEEE Transaction on Pattern Analysis and Machine Intelligence, Vol. 13, No. 2, pp. 163–174, 1991.

    Article  Google Scholar 

  • M. Golea and M. Marchand, “A growth algorithm for neural network decision trees,” EuroPhysics Letters, Vol. 12, No. 3, pp.205–210, 1990.

    Google Scholar 

  • D. Heath, S. Kasif, and S. Salzberg, “Learning oblique decision trees,” IJCAI-93: Proceedings of the 13 th International Joint Conference On Artificial Intelligence, Vol. II, Chambery, France, 1993, Morgan Kaufmann, Vol. 160, pp. 1002–1007.

    Google Scholar 

  • D. Heath, S. Kasif, and S. Salzberg, “k-DT: A multi-tree learning method,” Proceedings of the 2 nd International Workshop on Multistrategy Learning, Harpers Ferry, WV, 1993. George Mason University, pp. 138–149.

    Google Scholar 

  • G. Kalkanis, “The application of confidence interval error analysis to the design of decision tree classifiers,” Pattern Recognition Letters, Vol. 14, No. 5, pp. 355–361, 1993.

    Article  Google Scholar 

  • I. Kononenko, “On biases in estimating multi-valued attributes,” in C. Mellishpages, ed, IJCAI-95: Proceedings of the 14 th International Joint Conference on Artificial Intelligence, Montreal, Canada, August 1995, Morgan Kaufmann, San Francisco, CA, USA, pp. 1034–1040.

    Google Scholar 

  • S. W. Kwok, and C. Carter, “Multiple decision trees,” Uncertainty in Artificial Intelligence, Elsevier Science, Amsterdam, Vol. 4, pp. 327–335, 1990.

    Google Scholar 

  • J. Lee, S. Olafsson, “SODI: A new approach of second order decision tree induction,” Working Paper, Department of Industrial and Manufacturing Systems Engineering, Iowa State University, Ames, IA, USA, 2002.

    Google Scholar 

  • J. K. Martin, “An exact probability metric for decision tree splitting and stopping,” AI&Stats-95: the 5 th International Workshop on Artificial Intelligence and Statistics, Ft. Lauderdale, FL, 1995. Society for AI and Statistics, pp. 379–385.

    Google Scholar 

  • J. Mingers, “Expert systems: rule induction with statistical data,” Journal of the Operational Research Society, Vol. 38, No. 1, pp. 39–47, 1987.

    Article  Google Scholar 

  • M. Miyakawa, “Criteria for selecting a variable in the construction of efficient decision trees,” IEEE Transactions on Computers, Vol. 38, No. 1, pp. 130–141, 1989.

    Article  MATH  MathSciNet  Google Scholar 

  • P. M. Murphy and M. Pazzani, “ID2-of-3: Constructive induction of M-of-N concepts for discriminators in decision trees,” Proceedings of the 8 th International Workshop of Machine Learning, 1991.

    Google Scholar 

  • P. M. Murphy and M. Pazzani, “Exploring the decision forest: An empirical investigation of Occam’s Razor in decision tree induction,” Journal of Artificial Intelligence Research, Vol. 1., pp.257–275, 1994.

    MATH  Google Scholar 

  • S. K. Murthy, S. Kasif, and S. Salzberg, “A system for induction of oblique decision trees’” Journal of Artificial Intelligence Research, Vol. 2, pp. 1–33, 1994.

    Article  MATH  Google Scholar 

  • A. L. Oliveria and A. S. Vincentelli, “Learning complex Boolean functions: Algorithms and applications,” Advances in Neural Information Processing Systems 6, Morgan Kaufmann, San Francisco, CA, USA, 1993

    Google Scholar 

  • K. R. Pattipati and M. G. Alexandridis, “Application of heuristic search and information theory to sequential fault diagnosis,” IEEE Transactions on Systems, Man and Cybernetics, Vol. 20, No. 4, pp. 872–887, 1990.

    Article  MATH  Google Scholar 

  • M. Pazzani, P. Murphy, K. Ali, and D. Schulenburg, “Trading off coverage for accuracy in forecasts: Applications to clinical data analysis,” AAAI Symposium on AI in Medicine, Stanford, CA, USA, pp. 106–110, 1994.

    Google Scholar 

  • J. R. Quinlan, “Induction of decision trees,” Machine Learning, Vol. 1, pp. 81–106, 1986.

    Google Scholar 

  • J. R. Quinlan, C4.5: Programs for machine learning, Vol. 29, pp. 5–44, Morgan Kaufmann, 1993.

    Google Scholar 

  • J. R. Quinlan and R. L. Rivest, “Inferring decision trees using the minimum description length principle. Information and Computation,” Vol. 80, No. 3, pp. 227–248, 1989.

    MATH  MathSciNet  Google Scholar 

  • J. Risannen, Stochastic Complexity in Statistica Enquiry, World Scientific, Teaneck, N.J, USA, 1989.

    Google Scholar 

  • I. K. Sethi and G. P. R. Sarvarayudu, “Hierarchical classifier design using mutual information,” IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-4, No. 4, pp. 441–445, 1982.

    Article  Google Scholar 

  • C.E. Shannon, “A Mathematical Theory of Communication”, Bell System Technical Journal, Vol. 27, pp. 379–423, pp. 623–656, 1948.

    MathSciNet  MATH  Google Scholar 

  • S. Shlien, “Multiple binary decision tree classifiers,” Pattern Recognition, Vol. 23, No. 7, pp.757–763, 1990.

    Article  Google Scholar 

  • S. Shlien, “Nonparametric classification using matched binary decision trees,” Pattern Recognition Letters, Vol. 13, No. 2, pp. 83–88, 1992.

    Article  Google Scholar 

  • J. L. Talmon, “A multiclass nonparametric partitioning algorithm,” Pattern Recognition Letters, Vol. 4, pp. 31–38, 1986.

    Article  Google Scholar 

  • P. C. Taylor and B. W. Silverman, “Block diagrams and splitting criteria for classification trees,” Statistics and Computing, Vol. 3, No. 4, pp. 147–161, 1993.

    Article  Google Scholar 

  • T. Van De Merckt, “Decision trees in numerical attribute spaces,” In IJCAI-93: Proceedings of the 13th International Joint Conference on Artificial Intelligence, Vol. 2, Chambery, France, September 1993, Morgan Kaufmann, pp. 1016–1021.

    Google Scholar 

  • P. K. Varshney, C. R. P. Hartmann, and J. M. De Faria Jr., “Applications of information theory to sequential fault diagnosis,” IEEE Transactions on Computers, Vol. 31, No. 2, pp. 164–170, 1982.

    MATH  Google Scholar 

  • P. White and W. Z. Liu, “Technical note: Bias in information-based measures in decision tree induction,” Machine Learning, Vol. 15, No. 3, pp. 321–329, 1994.

    MATH  Google Scholar 

  • H. Witten and E. Frank, Data mining: practical machine learning tools and techniques with Java implementations. Morgan Kaufmann, San Francisco, CA, USA, 1999.

    Google Scholar 

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Lee, JY., Olafsson, S. (2006). Multi-Attribute Decision Trees and Decision Rules. In: Triantaphyllou, E., Felici, G. (eds) Data Mining and Knowledge Discovery Approaches Based on Rule Induction Techniques. Massive Computing, vol 6. Springer, Boston, MA . https://doi.org/10.1007/0-387-34296-6_10

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  • DOI: https://doi.org/10.1007/0-387-34296-6_10

  • Publisher Name: Springer, Boston, MA

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