Abstract
In standard frequent item set mining one tries to find item sets the support of which exceeds a user-specified threshold (minimum support) in a database of transactions. We, instead, strive to find item sets for which the similarity of the covers of the items (that is, the sets of transactions containing the items) exceeds a user-defined threshold. This approach yields a much better assessment of the association strength of the items, because it takes additional information about their occurrences into account. Starting from the generalized Jaccard index we extend our approach to a total of twelve specific similarity measures and a generalized form. In addition, standard frequent item set mining turns out to be a special case of this flexible framework. We present an efficient mining algorithm that is inspired by the well-known Eclat algorithm and its improvements. By reporting experiments on several benchmark data sets we demonstrate that the runtime penalty incurred by the more complex (but also more informative) item set assessment is bearable and that the approach yields high quality and more useful item sets.
Chapter PDF
Similar content being viewed by others
References
Agrawal, R., Srikant, R.: Fast Algorithms for Mining Association Rules. In: Proc. 20th Int. Conf. on Very Large Databases, VLDB 1994, Santiago de Chile, pp. 487–499. Morgan Kaufmann, San Mateo (1994)
Agrawal, R., Mannila, H., Srikant, R., Toivonen, H., Verkamo, A.: Fast Discovery of Association Rules. In: [13], pp. 307–328
Asuncion, A., Newman, D.J.: UCI Machine Learning Repository. School of Information and Computer Science, University of California at Irvine, CA, USA (2007), http://www.ics.uci.edu/~mlearn/MLRepository.html
Baroni-Urbani, C., Buser, M.W.: Similarity of Binary Data. Systematic Zoology 25(3), 251–259 (1976)
Bayardo, R., Goethals, B., Zaki, M.J. (eds.): Proc. Workshop Frequent Item Set Mining Implementations, FIMI 2004, Brighton, UK, Aachen, Germany. CEUR Workshop Proceedings, vol. 126 (2004), http://www.ceur-ws.org/Vol-126/
Borgelt, C., Wang, X.: SaM: A Split and Merge Algorithm for Fuzzy Frequent Item Set Mining. In: Proc.13th Int. Fuzzy Systems Association World Congress and 6th Conf. of the European Society for Fuzzy Logic and Technology, IFSA/EUSFLAT 2009. IFSA/EUSFLAT Organization Committee, Lisbon (2009)
Cha, S.-H., Tappert, C.C., Yoon, S.: Enhancing Binary Feature Vector Similarity Measures. J. Pattern Recognition Research 1, 63–77 (2006)
Choi, S.-S., Cha, S.-H., Tappert, C.C.: A Survey of Binary Similarity and Distance Measures. Journal of Systemics, Cybernetics and Informatics 8(1), 43–48 (2010); Int. Inst. of Informatics and Systemics, Caracas, Venezuela (2010)
Czekanowski, J.: Zarys metod statystycznych w zastosowaniu do antropologii (An Outline of Statistical Methods Applied in Anthropology). Towarzystwo Naukowe Warszawskie, Warsaw, Poland (1913)
Dice, L.R.: Measures of the Amount of Ecologic Association between Species. Ecology 26, 297–302 (1945)
Dunn, G., Everitt, B.S.: An Introduction to Mathematical Taxonomy. Cambridge University Press, Cambirdge (1982)
Faith, D.P.: Asymmetric Binary Similarity Measures. Oecologia 57(3), 287–290 (1983)
Fayyad, U.M., Piatetsky-Shapiro, G., Smyth, P., Uthurusamy, R. (eds.): Advances in Knowledge Discovery and Data Mining. AAAI Press / MIT Press, Cambridge (1996)
Goethals, B. (ed.): Frequent Item Set Mining Dataset Repository. University of Helsinki, Finland (2004), http://fimi.cs.helsinki.fi/data/
Goethals, B., Zaki, M.J. (eds.): Proc. Workshop Frequent Item Set Mining Implementations, FIMI 2003, Melbourne, FL, USA. CEUR Workshop Proceedings 90, Aachen, Germany (2003), http://www.ceur-ws.org/Vol-90/
Grahne, G., Zhu, J.: Efficiently Using Prefix-trees in Mining Frequent Itemsets. In: Proc. Workshop Frequent Item Set Mining Implementations, FIMI, Melbourne, FL [15] (2003)
Grahne, G., Zhu, J.: Reducing the Main Memory Consumptions of FPmax* and FPclose. In: Proc. Workshop Frequent Item Set Mining Implementations, FIMI, Brighton, UK [5] (2004)
Gower, J.C., Legendre, P.: Metric and Euclidean Properties of Dissimilarity Coefficients. Journal of Classification 3, 5–48 (1986)
Han, J., Pei, H., Yin, Y.: Mining Frequent Patterns without Candidate Generation. In: Proc. Conf. on the Management of Data, SIGMOD 2000, Dallas, TX, pp. 1–12. ACM Press, New York (2000)
Hamann, V.: Merkmalbestand und Verwandtschaftsbeziehungen der Farinosae. Ein Beitrag zum System der Monokotyledonen. Willdenowia 2, 639–768 (1961)
Hamming, R.V.: Error Detecting and Error Correcting Codes. Bell Systems Tech. Journal 29, 147–160 (1950)
Jaccard, P.: Étude comparative de la distribution florale dans une portion des Alpes et des Jura. Bulletin de la Société Vaudoise des Sciences Naturelles 37, 547–579 (1901)
Kohavi, R., Bradley, C.E., Frasca, B., Mason, L., Zheng, Z.: KDD-Cup 2000 Organizers’ Report: Peeling the Onion. SIGKDD Exploration 2(2), 86–93 (2000)
Kötter, T., Berthold, M.R.: Concept Detection. In: Proc. 8th Conf. on Computing and Philosophy, ECAP 2010. University of Munich, Munich (2010)
Kulczynski, S.: Classe des Sciences Mathématiques et Naturelles. Bulletin Int. de l’Acadamie Polonaise des Sciences et des Lettres Série B (Sciences Naturelles) (Supp. II), 57–203 (1927)
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)
Rogers, D.J., Tanimoto, T.T.: A Computer Program for Classifying Plants. Science 132, 1115–1118 (1960)
Russel, P.F., Rao, T.R.: On Habitat and Association of Species of Anopheline Larvae in South-eastern Madras. J. Malaria Institute 3, 153–178 (1940)
Sneath, P.H.A., Sokal, R.R.: Numerical Taxonomy. Freeman Books, San Francisco (1973)
Sokal, R.R., Michener, C.D.: A Statistical Method for Evaluating Systematic Relationships. University of Kansas Scientific Bulletin 38, 1409–1438 (1958)
Sokal, R.R., Sneath, P.H.A.: Principles of Numerical Taxonomy. Freeman Books, San Francisco (1963)
Sørensen, T.: A Method of Establishing Groups of Equal Amplitude in Plant Sociology based on Similarity of Species and its Application to Analyses of the Vegetation on Danish Commons. Biologiske Skrifter / Kongelige Danske Videnskabernes Selskab 5(4), 1–34 (1948)
Tanimoto, T.T.: IBM Internal Report, November 17 (1957)
Uno, T., Kiyomi, M., Arimura, H.: LCM ver. 2: Efficient Mining Algorithms for Frequent/Closed/Maximal Itemsets. Proc. Workshop Frequent Item Set Mining Implementations, FIMI 2004, Brighton, UK. CEUR Workshop Proceedings 126, Aachen, Germany (2004)
Uno, T., Kiyomi, M., Arimura, H.: LCM ver. 3: Collaboration of Array, Bitmap and Prefix Tree for Frequent Itemset Mining. Proc. 1st Open Source Data Mining on Frequent Pattern Mining Implementations, OSDM 2005, Chicago, IL, pp. 77–86. ACM Press, New York (2005)
Webb, G.I., Zhang, S.: k-Optimal-Rule-Discovery. Data Mining and Knowledge Discovery 10(1), 39–79 (2005)
Webb, G.I.: Discovering Significant Patterns. Machine Learning 68(1), 1–33 (2007)
Zaki, M.J., Parthasarathy, S., Ogihara, M., Li, W.: New Algorithms for Fast Discovery of Association Rules. In: Proc. 3rd ACM SIGKDD Int. Conf. on Knowledge Discovery and Data Mining, KDD 1997, Newport Beach, CA, pp. 283–296. AAAI Press, Menlo Park (1997)
Zaki, M.J., Gouda, K.: Fast Vertical Mining Using Diffsets. In: Proc. 9th ACM SIGKDD Int. Conf. on Knowledge Discovery and Data Mining, KDD 2003, Washington, DC, pp. 326–335. ACM Press, New York (2003)
Zheng, Z., Kohavi, R., Mason, L.: Real World Performance of Association Rule Algorithms. In: Proc. 7th ACM SIGKDD Int. Conf. on Knowledge Discovery and Data Mining, KDD 2001, San Francisco, CA, ACM Press, New York (2001)
Synthetic Data Generation Code for Associations and Sequential Patterns. Intelligent Information Systems, IBM Almaden Research Center, http://www.almaden.ibm.com/software/quest/Resources/index.shtml
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 2.5 International License (http://creativecommons.org/licenses/by-nc/2.5/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.
The images or other third party material in this chapter are included in the chapter’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
Copyright information
© 2012 The Author(s)
About this chapter
Cite this chapter
Segond, M., Borgelt, C. (2012). Cover Similarity Based Item Set Mining. In: Berthold, M.R. (eds) Bisociative Knowledge Discovery. Lecture Notes in Computer Science(), vol 7250. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31830-6_8
Download citation
DOI: https://doi.org/10.1007/978-3-642-31830-6_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31829-0
Online ISBN: 978-3-642-31830-6
eBook Packages: Computer ScienceComputer Science (R0)