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Counting frequent patterns in large labeled graphs: a hypergraph-based approach

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Abstract

In recent years, the popularity of graph databases has grown rapidly. This paper focuses on single-graph as an effective model to represent information and its related graph mining techniques. In frequent pattern mining in a single-graph setting, there are two main problems: support measure and search scheme. In this paper, we propose a novel framework for designing support measures that brings together existing minimum-image-based and overlap-graph-based support measures. Our framework is built on the concept of occurrence/instance hypergraphs. Based on such, we are able to design a series of new support measures: minimum instance (MI) measure, and minimum vertex cover (MVC) measure, that combine the advantages of existing measures. More importantly, we show that the existing minimum-image-based support measure is an upper bound of the MI measure, which is also linear-time computable and results in counts that are close to number of instances of a pattern. We show that not only most major existing support measures and new measures proposed in this paper can be mapped into the new framework, but also they occupy different locations of the frequency spectrum. By taking advantage of the new framework, we discover that MVC can be approximated to a constant factor (in terms of number of pattern nodes) in polynomial time. In contrast to common belief, we demonstrate that the state-of-the-art overlap-graph-based maximum independent set (MIS) measure also has constant approximation algorithms. We further show that using standard linear programming and semidefinite programming techniques, polynomial-time relaxations for both MVC and MIS measures can be developed and their counts stand between MVC and MIS. In addition, we point out that MVC, MIS, and their relaxations are bounded within constant factor. In summary, all major support measures are unified in the new hypergraph-based framework which helps reveal their bounding relations and hardness properties.

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Notes

  1. For that, we use the words frequency and support interchangeably in this paper. We also use the word support and the phrase support measure in the same way.

  2. In this paper, following conventions of this field, computing time of support measures does not include that for constructing the framework (e.g., overlap graph in the MIS case).

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Acknowledgements

This work is supported by a grant (IIS-1253980) from the National Science Foundation (NSF) of U.S.A. Jinghan Meng was partially supported by an award (R01GM086707) from US National Institutes of Health (NIH).

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  1. University of South Florida, 4202 E Fowler Ave, Tampa, FL, 33620, USA

    Jinghan Meng, Napath Pitaksirianan & Yi-Cheng Tu

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  1. Jinghan Meng
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  2. Napath Pitaksirianan
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  3. Yi-Cheng Tu
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Correspondence to Yi-Cheng Tu.

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Meng, J., Pitaksirianan, N. & Tu, YC. Counting frequent patterns in large labeled graphs: a hypergraph-based approach. Data Min Knowl Disc 34, 980–1021 (2020). https://doi.org/10.1007/s10618-020-00686-9

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