Abstract
In order to acquire knowledge from databases, there have been proposed several methods of inductive learning, such as ID3 family and AQ family. These methods are applied to discover meaningful knowledge from large databases, and their usefulness is ensured. However, since there has been no formal approach proposed to treat these methods, efficiency of each method is only compared empirically. In this paper, we introduce matroid theory and rough sets to construct a common framework for empirical machine learning methods which induce the combination of attribute-value pairs from databases. Combination of the concepts of rough sets and matroid theory gives us an excellent framework and enables us to understand the differences and the similarities between these methods clearly. In this paper, we compare three classical methods, AQ, Pawlak's Consistent Rules and ID3. The results show that there exists the differences in algebraic structure between the former two and the latter and that this causes the differences between AQ and ID3.
Preview
Unable to display preview. Download preview PDF.
References
Bergadano, F., Matwin, S., Michalski, R.S. and Zhang, J. Learning Two-Tiered Descriptions of Flexible Concepts: The POSEIDON System, Machine Learning, 8, 5–43, 1992.
Breiman, L., Freidman, J., Olshen, R. and Stone, C. Classification And Regression Trees. Belmont, CA: Wadsworth International Group, 1984.
Hunter, L.(eds). Proceedings of AAAI-94 Spring Workshop on Goal-Driven Learning, AAAI Press, 1994.
Michalski, R.S. A Theory and Methodology of Machine Learning. Michalski, R.S., Carbonell, J.G. and Mitchell, T.M., Machine Learning — An Artificial Intelligence Approach, 83–134, Morgan Kaufmann, CA, 1983.
Michalski, R.S., et al. The Multi-Purpose Incremental Learning System AQ15 and its Testing Application to Three Medical Domains, Proc. of AAAI-86, 1041–1045, Morgan Kaufmann, CA, 1986.
Michalski, R.S., and Tecuci, G.(eds) Machine Learning vol.4 — A Multistrategy Approach-, Morgan Kaufmann, CA, 1994.
Mingers, J. An Empirical Comparison of Selection Measures for Decision Tree Induction. Machine Learning, 3, 319–342, 1989.
Mingers, J. An Empirical Comparison of Pruning Methods for Decision Tree Induction. Machine Learning, 4, 227–243, 1989.
Nakakuki, Y., Koseki, Y., and Tanaka, M. Inductive Learning in Probabilistic Domain in Proc. of AAAI-90, 809–814, 1990.
Pawlak, Z. Rough Sets, Kluwer Academic Publishers, Dordrecht, 1991.
Pendnault, E.P.D. Some Experiments in Applying Inductive Inference Principles to Surface Reconstruction, Proceedings of IJCAI-89, 1603–1609, 1989.
Pendnault, E.P.D. Inferring probabilistic theories from data, Proceedings of AAAI-88, 1988.
Quinlan, J.R. Induction of decision trees, Machine Learning, 1, 81–106, 1986.
Quinlan, J.R. Simplifying Decision Trees. International Journal of Man-Machine Studies, 27, 221–234, 1987.
Quinlan, J.R. and Rivest, R.L. Inferring Decision Trees Using the Minimum Description Length Principle, Information and Computation, 80, 227–248, 1989.
Rissanen, J. Stochastic complexity and modeling, Ann. of Statist., 14, 1080–1100, 1986.
Rissanen, J. Universal Coding, Information, Prediction, and Estimation, IEEE. Trans. Inform. Theory, IT-30, 629–636, 1984.
Schaffer, C. Overfitting Avoidance as Bias. Machine Learning, 10, 153–178, 1993.
Tsumoto, S. and Tanaka, H. PRIMEROSE: Probabilistic Rule Induction Method based on Rough Sets. in: Ziarko, W.(eds) Rough Sets, Fuzzy Sets, and Knowledge Discovery, Springer, London, 1994.
Welsh, D.J.A. Matroid Theory, Academic Press, London, 1976.
White, N.(ed.) Matroid Applications, Cambridge University Press, 1991.
Whitney, H. On the abstract properties of linear dependence, Am. J. Math., 57, 509–533, 1935.
Ziarko, W. The Discovery, Analysis, and Representation of Data Dependencies in Databases, in: Knowledge Discovery in Database, Morgan Kaufmann, 1991.
Ziarko, W. Variable Precision Rough Set Model, Journal of Computer and System Sciences, 46, 39–59, 1993.
Ziarko, W. Analysis of Uncertain Information in the Framework of Variable Precision Rough Sets, Foundation of Computing and Decision Science, 18, 381–396, 1993.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Tsumoto, S., Tanaka, H. (1995). Algebraic specification of empirical inductive learning methods based on rough sets and matroid theory. In: Calmet, J., Campbell, J.A. (eds) Integrating Symbolic Mathematical Computation and Artificial Intelligence. AISMC 1994. Lecture Notes in Computer Science, vol 958. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60156-2_16
Download citation
DOI: https://doi.org/10.1007/3-540-60156-2_16
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-60156-2
Online ISBN: 978-3-540-49533-8
eBook Packages: Springer Book Archive