Abstract
Many classifier induction systems express the induced classifier in terms of a disjunctive description. Small disjuncts are those that classify few training examples. These disjuncts are interesting because they are known to have a much higher error rate than large disjuncts and are responsible for many, if not most, of all classification errors. Previous research has investigated this phenomenon by performing ad hoc analyses of a small number of data sets. In this chapter we provide a much more systematic study of small disjuncts and analyze how they affect classifiers induced from 30 real-world data sets. A new metric, error concentration, is used to show that for these 30 data sets classification errors are often heavily concentrated toward the smaller disjuncts. Various factors, including pruning, training set size, noise, and class imbalance are then analyzed to determine how they affect small disjuncts and the distribution of errors across disjuncts. This analysis provides many insights into why some data sets are difficult to learn from and also provides a better understanding of classifier learning in general.We believe that such an understanding is critical to the development of improved classifier induction algorithms.
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References
Ali, K.M., Pazzani, M.J.: Reducing the small disjuncts problem by learning probabilistic concept Descriptions. In: Petsche, T. (ed.) Computational Learning Theory and Natural Learning Systems, Volume 3, MIT Press, Cambridge, MA (1992)
Asuncion, A., Newman, D.J.: UCI Machine Learning Repository. University of California, Irvine, School of Information and Computer Science. http://www.ics.uci.edu/mlearn/MLRepository.html. Cited Sept 2008
Carvalho D.R., Freitas A.A.: A hybrid decision tree/genetic algorithm for coping with the problem of small disjuncts in data mining. In: Proceedings of the 2000 Genetic and Evolutionary Computation Conference, pp. 1061–1068 (2000)
Chawla N.V., Bowyer K.W., Hall L.O., Kegelmeyer W.P.: SMOTE: Synthetic minority over-sampling technique. Journal of Artificial Intelligence Research, 16, 321–357 (2002)
Chawla N.V., Cieslak D.A., Hall L.O., Joshi A.: Automatically countering imbalance and its empirical relationship to cost. Data Mining and Knowledge Discovery, 17(2), 225–252 (2008)
Cohen W.: Fast effective rule induction. In: Proceedings of the Twelfth International Conference on Machine Learning, pp. 115–123 (1995)
Cohen W., Singer Y.: A simple, fast, and effective rule learner. In: Proceedings of the Sixteenth National Conference on Artificial Intelligence, pp. 335–342 (1999)
Danyluk A.P., Provost F.J.: Small disjuncts in action: learning to diagnose errors in the local loop of the telephone network. In: Proceedings of the Tenth International Conference on Machine Learning, pp. 81–88 (1993)
Holte R.C., Acker L.E., Porter B.W.: Concept learning and the problem of small disjuncts. In: Proceedings of the Eleventh International Joint Conference on Artificial Intelligence, pp. 813–818 (1989)
Japkowicz N., Stephen S.: The class imbalance problem: a systematic study. Intelligent Data Analysis 6(5), 429–450 (2002)
Jo T., Japkowicz, N. Class imbalances versus small disjuncts. SIGKDD Explorations 6(1), 40–49 (2004)
Quinlan J.R.: The effect of noise on concept learning. In: Michalski R.S., Carbonell J.G., Mitchell T.M. (eds.), Machine Learning, an Artificial Intelligence Approach, Volume II, Morgan Kaufmann, San Francisco, CA (1986)
Quinlan J.R.: Technical note: improved estimates for the accuracy of small disjuncts. Machine Learning, 6(1) (1991)
Quinlan J.R.: C4.5: Programs for Machine Learning. Morgan Kaufmann, San Mateo, CA (1993)
Ting K.M.: The problem of small disjuncts: its remedy in decision trees. In: Proceedings of the Tenth Canadian Conference on Artificial Intelligence, pp. 91–97 (1994)
Van den Bosch A., Weijters A., Van den Herik H.J., Daelemans W.: When small disjuncts abound, try lazy learning: A case study. In: Proceedings of the Seventh Belgian-Dutch Conference on Machine Learning, pp. 109–118 (1997)
Weiss G.M.: Learning with rare cases and small disjuncts. In: Proceedings of the Twelfth International Conference on Machine Learning, pp. 558–565 (1995)
Weiss G.M.: Mining with rarity: A unifying framework, SIGKDD Explorations 6(1), 7–19 (2004)
Weiss G.M., Hirsh H.: The problem with noise and small disjuncts. In: Proceedings of the Fifteenth International Conference on Machine Learning, pp. 574–578 (1998)
Weiss G.M., Hirsh H.: A quantitative study of small disjuncts. In: Proceedings of the Seventeenth National Conference on Artificial Intelligence, Austin, Texas, pp. 665–670 (2000)
Weiss G.M., McCarthy K., Zabar B.: Cost-Sensitive Learning vs. Sampling: Which is best for handling unbalanced classes with unequal error costs? In: Proceedings of the 2007 International Conference on Data Mining, pp. 35–41 (2007)
Weiss G.M., Provost F.: Learning when training data are costly: the effect of class distribution on tree induction. Journal of AI Research 19, 315–354 (2003)
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Weiss, G.M. (2010). The Impact of Small Disjuncts on Classifier Learning. In: Stahlbock, R., Crone, S., Lessmann, S. (eds) Data Mining. Annals of Information Systems, vol 8. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-1280-0_9
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