Learning of Finite Unions of Tree Patterns with Repeated Internal Structured Variables from Queries
In the field of Web mining, a Web page can be represented by a rooted tree T such that every internal vertex of T has ordered children and string data such as tags or texts are assigned to edges of T. A term tree is an ordered tree pattern, which has ordered tree structures and variables, and is suited for a representation of a tree structured pattern in Web pages. A term tree t is allowed to have a repeated variable which occurs in t more than once. In this paper, we consider the learnability of finite unions of term trees with repeated variables in the query learning model of Angluin (1988). We present polynomial time learning algorithms for finite unions of term trees with repeated variables by using superset and restricted equivalence queries. Moreover we show that there exists no polynomial time learning algorithm for finite unions of term trees by using restricted equivalence, membership and subset queries. This result indicates the hardness of learning finite unions of term trees in the query learning model.
KeywordsAlgorithm Learn Polynomial Time Term Tree Tree Pattern Internal Vertex
Unable to display preview. Download preview PDF.
- 1.Abiteboul, S., Buneman, P., Suciu, D.: Data on the Web: From Relations to Semistructured Data and XML. Morgan Kaufmann, San Francisco (2000)Google Scholar
- 5.Angluin, D.: Queries and concept learning. Machine Learning 2, 319–342 (1988)Google Scholar
- 9.Lovász, L.: Two classical enumeration problems in graph theory. In: Lovász, L. (ed.) Combinatorial Problems and Exercises, North-Holland Publishing Company, Amsterdam (1979)Google Scholar
- 11.Matsumoto, S., Shoudai, T., Miyahara, T., Uchida, T.: Learning unions of term tree languages using queries. In: Proceedings of LA Summer Symposium, July 2002, pp. 21–10 (2002)Google Scholar
- 13.Suzuki, Y., Akanuma, R., Shoudai, T., Miyahara, T., Uchida, T.: Polynomial time inductive inference of ordered tree patterns with internal structured variables from positive data. In: Kivinen, J., Sloan, R.H. (eds.) COLT 2002. LNCS (LNAI), vol. 2375, pp. 169–184. Springer, Heidelberg (2002)CrossRefGoogle Scholar