Abstract
We study the problem of mining closed patterns in multi-relational databases. Garriga et al. (IJCAI’07) proposed an algorithm RelLCM2 for mining closed patterns (i.e., conjunctions of literals) in multi-relational data, which is an extension of LCM, an efficient enumeration algorithm for frequent closed itemsets mining proposed in the seminal paper by Uno et al. (DS’04). We assume that a database considered contains a special predicate called key (or target), which determines the entities of interest and what is to be counted. We introduce a notion of closed patterns with key (key-closedness for short), where variables in a pattern other than the one in a key predicate are considered to be existentially quantified, and they are linked to a given target object. We then define a closure operation (key-closure) for computing key-closed patterns, and show that the difference between the semantics of key-closed patterns and that of the closed patterns in RelLCM2 implies different properties of the closure operations; in particular, the uniqueness of closure does not hold for key-closure. Nevertheless, we show that we can enumerate key-closed patterns using the technique of ppc-extensions à la LCM, thereby making the enumeration possible without storage space for previously generated patterns. We also propose a literal order designed for mining key-closed patterns, which will require less search space. The correctness of our algorithm is shown, and its computational complexity is discussed. Some preliminary experimental results are also given.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Agrawal, R., Srikant, R.: Fast Algorithms for Mining Association Rules. In: VLDB, pp. 487–499 (1994)
Appice, A., Ceci, M., Turi, A., Malerba, D.: A Parallel Distributed Algorithm for Relational Frequent Pattern Discovery from Very Large Data Sets. Intell. Data Anal. (2009) (to appear)
Arimura, H., Uno, T.: Polynomial-Delay and Polynomial-Space Algorithms for Mining Closed Sequences, Graphs, and Pictures in Accessible Set Systems. In: SIAM Int’l. Conf. on Data Mining, pp. 1087–1098 (2009)
Blockeel, H., Sebag, M.: Scalability and efficiency in multi-relational data mining. SIGKDD Explorations Newsletter 2003 4(2), 1–14 (2003)
Dehaspe, L.: Frequent pattern discovery in first-order logic, PhD thesis, Dept. Computer Science, Katholieke Universiteit Leuven (1998)
De Raedt, L., Ramon, J.: Condensed representations for Inductive Logic Programming. In: Proc. KR 2004, pp. 438–446 (2004)
Dzeroski, S.: Multi-Relational Data Mining: An Introduction. SIGKDD Explorations Newsletter 5(1), 1–16 (2003)
Dzeroski, S., Lavrač, N. (eds.): Relational Data Mining. Springer, Heidelberg (2001)
Garcia-Molina, H., Widom, J., Ullman, J.D.: Database System Implementation. Prentice-Hall, Inc., Englewood Cliffs (1999)
Garriga, G.C., Khardon, R., De Raedt, L.: On Mining Closed Sets in Multi-Relational Data. In: IJCAI 2007, pp.804–809 (2007)
Han, J., Kamber, M.: Data Mining: Concepts and Techniques, 2nd edn. Morgan Kaufmann Publishers Inc., San Francisco (2005)
Helft, N.: Induction as nonmonotonic inference. In: Proc. KR 1989, pp. 149–156 (1989)
Lavrač, N., Flach, P.A.: An Extended Transformation Approach to Inductive Logic Programming. ACM Trans. Computational Logic 2(4), 458–494 (2001)
Lloyd, J.W.: Foundations of Logic Programming, 2nd edn. Springer, Heidelberg (1987)
Motoyama, J., Urazawa, S., Nakano, T., Inuzuka, N.: A Mining Algorithm using Property Items Extracted from Sampled Examples. In: Muggleton, S.H., Otero, R., Tamaddoni-Nezhad, A. (eds.) ILP 2006. LNCS (LNAI), vol. 4455, pp. 335–350. Springer, Heidelberg (2007)
Nagano, S., Honda, Y., Seki, H.: On Enumerating Frequent Closed Patterns in Multi-Relational Data Mining. In: Proc. WiNF 2009, pp. 89–94 (2009) (in Japanese)
Pasquier, N., Bastide, Y., Taouil, R., Lakhal, L.: Discovering Frequent Closed Itemsets for Association Rules. In: Beeri, C., Bruneman, P. (eds.) ICDT 1999. LNCS, vol. 1540, pp. 398–416. Springer, Heidelberg (1998)
Uno, T., Asai, T., Uchida, Y., Arimura, H.: An Efficient Algorithm for Enumerating Closed Patterns in Transaction Databases. In: Suzuki, E., Arikawa, S. (eds.) DS 2004. LNCS (LNAI), vol. 3245, pp. 16–31. Springer, Heidelberg (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Seki, H., Honda, Y., Nagano, S. (2010). On Enumerating Frequent Closed Patterns with Key in Multi-relational Data. In: Pfahringer, B., Holmes, G., Hoffmann, A. (eds) Discovery Science. DS 2010. Lecture Notes in Computer Science(), vol 6332. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16184-1_6
Download citation
DOI: https://doi.org/10.1007/978-3-642-16184-1_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-16183-4
Online ISBN: 978-3-642-16184-1
eBook Packages: Computer ScienceComputer Science (R0)