Abstract.
We consider the relation of a learning model described in terms of Formal Concept Analysis in [3] with a standard model of Machine Learning called version spaces. A version space consists of all possible functions compatible with training data. The overlap and distinctions of these two models are discussed. We give an algorithm how to generate a version space for which the classifiers are closed under conjunction.
As an application we discuss an example from predicitive toxicology. The classifiers here are chemical compounds and their substructures. The example also indicates how the methodology can be applied to Conceptual Graphs.
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References
Blinova, V.G., Dobrynin, D.A., Finn, V.K., Kuznetsov, S.O., Pankratova, E.S.: Toxicology Analysis by Means of the JSM-Method. Bioinformatics (2003)
Finn, V.K.: Plausible Reasoning in Systems of JSM Type. Itogi Nauki i Tekhniki, Seriya Informatika 15, 54–101 (1991)
Ganter, B., Kuznetsov, S.: Formalizing Hypotheses with Concepts. In: Ganter, B., Mineau, G.W. (eds.) ICCS 2000. LNCS (LNAI), vol. 1867, pp. 342–356. Springer, Heidelberg (2000)
Ganter, B., Kuznetsov, S.O.: Pattern Structures and Their Projections. In: Delugach, H.S., Stumme, G. (eds.) ICCS 2001. LNCS (LNAI), vol. 2120, pp. 129–142. Springer, Heidelberg (2001)
Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundations. Springer, Heidelberg (1999)
Gunter, C.A., Ngair, T.-H., Subramanian, D.: The Common Order-Theoretic Structure of Version Spaces and ATMSs. Artificial Intelligence 95, 357–407 (1997)
Hirsh, H.: Generalizing Version Spaces. Machine Learning 17, 5–46 (1994)
Hirsh, H., Mishra, N., Pitt, L.: Version Spaces Without Boundary Sets. In: Proc. of the 14th National Conference on Artificial Intelligence (AAAI 1997). AAAI Press/MIT Press (1997)
Kuznetsov, S.O.: JSM-method as a machine learning method. Itogi Nauki i Tekhniki, ser. Informatika 15, 17–50 (1991)
Kuznetsov, S.O.: Learning of Simple Conceptual Graphs from Positive and Negative Examples. In: Żytkow, J.M., Rauch, J. (eds.) PKDD 1999. LNCS (LNAI), vol. 1704, pp. 384–392. Springer, Heidelberg (1999)
Kuznetsov, S.O., Finn, V.K.: On a model of learning and classification based on similarity operation. Obozrenie Prikladnoi i Promyshlennoi Matematiki 3(1), 66–90 (1996) [in Russian]
Mitchell, T.: Version Space: An Approach to Concept Learning, PhD thesis, Stanford University (1978)
Mitchell, T.: Generalization as Search. Artificial Intelligence 18(2) (1982)
Mitchell, T.: Machine Learning. The McGraw-Hill Companies, New York (1997)
Mugnier, M.-L., Chein, M.: Représenter des connaissances et raisonner avec des graphes. Revue d’Intelligence Artificielle 10(1), 7–56 (1996)
Mugnier, M.-L.: Knowledge Representation and Reasonings Based on Graph Homomorphisms. In: Ganter, B., Mineau, G.W. (eds.) ICCS 2000. LNCS (LNAI), vol. 1867, pp. 172–192. Springer, Heidelberg (2000)
Nienhuys-Cheng, S.-H., de Wolf, R.: Foundations of Inductive Logic Programming. LNCS (LNAI), vol. 1228. Springer, Heidelberg (1997)
Sebag, M.: Using Constraints to Building Version Spaces. In: Bergadano, F., De Raedt, L. (eds.) ECML 1994. LNCS, vol. 784, pp. 257–271. Springer, Heidelberg (1994)
Sebag, M.: Delaying the Choice of Bias: A Disjunctive Version Space Approach. In: Saitta, L. (ed.) Proc. of the 13th International Conference on Machine Learning, pp. 444–452. Morgan Kaufmann, San Francisco (1996)
Smirnov, E.N., Braspenning, P.J.: Version Space Learning with Instance-Based Boundary Sets. In: Prade, H. (ed.) Proceedings of the 13th European Conference on Artificial Intelligence, pp. 460–464. J. Wiley, Chichester (1998)
The web-site on Predictive Toxicology, http://www.predictive-toxicology.org/ptc/
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Ganter, B., Kuznetsov, S.O. (2003). Hypotheses and Version Spaces. In: Ganter, B., de Moor, A., Lex, W. (eds) Conceptual Structures for Knowledge Creation and Communication. ICCS 2003. Lecture Notes in Computer Science(), vol 2746. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45091-7_6
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DOI: https://doi.org/10.1007/978-3-540-45091-7_6
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