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Interesting pattern mining in multi-relational data

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Abstract

Mining patterns from multi-relational data is a problem attracting increasing interest within the data mining community. Traditional data mining approaches are typically developed for single-table databases, and are not directly applicable to multi-relational data. Nevertheless, multi-relational data is a more truthful and therefore often also a more powerful representation of reality. Mining patterns of a suitably expressive syntax directly from this representation, is thus a research problem of great importance. In this paper we introduce a novel approach to mining patterns in multi-relational data. We propose a new syntax for multi-relational patterns as complete connected subsets of database entities. We show how this pattern syntax is generally applicable to multi-relational data, while it reduces to well-known tiles “ Geerts et al. (Proceedings of Discovery Science, pp 278–289, 2004)” when the data is a simple binary or attribute-value table. We propose RMiner, a simple yet practically efficient divide and conquer algorithm to mine such patterns which is an instantiation of an algorithmic framework for efficiently enumerating all fixed points of a suitable closure operator “Boley et al. (Theor Comput Sci 411(3):691–700, 2010)”. We show how the interestingness of patterns of the proposed syntax can conveniently be quantified using a general framework for quantifying subjective interestingness of patterns “De Bie (Data Min Knowl Discov 23(3):407–446, 2011b)”. Finally, we illustrate the usefulness and the general applicability of our approach by discussing results on real-world and synthetic databases.

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Notes

  1. In contrast to some traditional fixpoint enumeration algorithms, as they are for instance used in the context of formal concept analysis, this divide and conquer approach does neither assume an underlying complete lattice nor that the fixpoint set is closed under intersection. This is important because the set system of CCSs is not necessarily closed under intersection (due to connectivity) and two MCCSs cannot be joined to a common supremum (due to completeness).

  2. Strongly accessible set systems generalize greedoids such as, e.g., poset ideals [see Boley (2011, Sect. 3.5.2) and Korte and Lovász (1985)].

  3. Please note that by entities and entity types here, we actually refer to our notion of the terms. The same notions are defined as objects and entities respectively in Nijssen et al. (2011).

  4. Note that practically, the quadratic space complexity of RMiner results from multiplying a linear space complexity with the maximal search tree depth, which, as we will show in Sect. 7.3, is practically a small constant. Also, as we discussed in Sect. 3.5, the practical time delay of RMiner depends on the density of the data set and can be optimised in practice by taking particular implementation choices. Thus, even though the theoretical complexities of Makino and Uno (2004) and RMiner are comparable, RMiner probably scales better in practice.

  5. See http://www.imdb.com/

  6. See http://www.informatik.uni-trier.de/~ley/db/

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Acknowledgments

We are grateful to Michael Mampaey for providing the Smurfig code and data and for his support in using Smurfig, Siegfried Nijssen for his assistance in using Farmer and Thomas Gärtner for discussions on this work. This work was partially funded by PASCAL 2 Network of Excellence. Eirini Spyropoulou and Tijl De Bie are supported by EPSRC Grant EP/G056447/1. Mario Boley is partially funded by DFG (German National Research Foundation) under GA 1615/2-1.

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Authors and Affiliations

  1. Intelligent Systems Laboratory, University of Bristol, Woodland Road, Bristol, UK

    Eirini Spyropoulou & Tijl De Bie

  2. Fraunhofer IAIS, Schloss Birlinghoven, 53754 , Sankt Augustin, Germany

    Mario Boley

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  1. Eirini Spyropoulou
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  2. Tijl De Bie
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  3. Mario Boley
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Correspondence to Eirini Spyropoulou.

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Responsible editor: M.J. Zaki.

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Spyropoulou, E., De Bie, T. & Boley, M. Interesting pattern mining in multi-relational data. Data Min Knowl Disc 28, 808–849 (2014). https://doi.org/10.1007/s10618-013-0319-9

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