Abstract
In this paper we propose a new approach to data mining and knowledge discovery based on information flow distribution in a flow graph. Flow graphs introduced in this paper are different from those proposed by Ford and Fulkerson for optimal flow analysis and they model flow distribution in a network rather than the optimal flow which is used for information flow examination in decision algorithms. It is revealed that flow in a flow graph is governed by Bayes’ rule, but the rule has an entirely deterministic interpretation without referring to its probabilistic roots. Besides, a decision algorithm induced by a flow graph and dependency between conditions and decisions of decision rules is introduced and studied, which is used next to simplify decision algorithms.
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Bernardo, J.M., Smith, A.F.M.: Bayesian Theory. Wiley series in probability and mathematical statistics. John Wiley & Sons, Chichester (1994)
Berthold, M., Hand, D.J.: Intelligent Data Analysis - An Introduction. Springer, Heidelberg (1999)
Box, G.E.P., Tiao, G.C.: Bayesian Inference in Statistical Analysis. John Wiley and Sons, Inc., Chichester (1992)
Ford, L.R., Fulkerson, D.R.: Flows in Networks. Princeton University Press, Princeton (1962)
Grinstead, C.M., Snell, J.L.: Introduction to Probability: Second Revised Edition American Mathematical Society (1997)
Greco, S., Pawlak, Z., Słowiński, R.: Generalized decision algorithms, rough inference rules and flow graphs. In: Alpigini, J.J., Peters, J.F., Skowron, A., Zhong, N. (eds.) RSCTC 2002. LNCS (LNAI), vol. 2475, pp. 93–104. Springer, Heidelberg (2002)
Greco, S., Pawlak, Z., Słowiński, R.: Bayesion confirmation measures within rough set approach. In: Tsumoto, S., S_lowiński, R., Komorowski, J., Grzyma_la-Busse, J. (eds.) RSCTC 2004. LNCS (LNAI), vol. 3066, pp. 261–270. Springer, Heidelberg (2004)
Łukasiewicz, J.: Die logishen Grundlagen der Wahrscheinilchkeitsrechnung. Kraków (1913). In: Borkowski, L. (ed.) Jan Łukasiewicz - Selected Works, pp. 16–63. North Holland Publishing Company, Amsterdam, Polish Scientific Publishers, Warsaw (1970)
Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning about Data. Kluwer, Dordrecht (1991)
Pawlak, Z.: Rough sets, decision algorithms and Bayes theorem. European Journal of Operational Research 136, 181–189 (2002)
Pawlak, Z.: Flow graphs. their fusion and data analysis (2003) (to appear)
Skowron, A., Stepaniuk, J.: Tolerance approximation spaces. Fundamenta Informaticae 27(2-3), 245–253 (1996)
Swinburne, R.: Bayes’ Theorem. Oxford University Press, Oxford (2002)
Tsumoto, S., Tanaka, H.: Discovery of Functional Components of Proteins Based on PRIMEROSE and Domain Knowledge Hierarchy. In: Lin, T.Y., Wildberger, A.M. (eds.) Proceedings of the Workshop on Rough Sets and Soft Computing (RSSC 1994), Soft Computing, SCS, pp. 280–285 (1995)
Wong, S.K.M., Ziarko, W.: Algorithm for inductive learning. Bull. Polish Academy of Sciences 34(5-6), 271–276 (1986)
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Pawlak, Z. (2005). Flow Graphs and Data Mining. In: Peters, J.F., Skowron, A. (eds) Transactions on Rough Sets III. Lecture Notes in Computer Science, vol 3400. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11427834_1
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DOI: https://doi.org/10.1007/11427834_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-25998-5
Online ISBN: 978-3-540-31850-7
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