Abstract
This paper presents a collection of similarity measures based on refinement operators for directed labeled graphs (DLGs). We build upon previous work on refinement operators for other representation formalisms such as feature terms and description logics. Specifically, we present refinement operators for DLGs, which enable the adaptation of three similarity measures to DLGs: the anti-unification-based, \(S_{\lambda }\), the property-based, \(S_{\pi }\), and the weighted property-based, \(S_{w\pi }\), similarities. We evaluate the resulting measures empirically comparing them to existing similarity measures for structured data.
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Notes
- 1.
A Refinement-Operator Library for Directed Labeled Graphs: https://github.com/santiontanon/RHOG.
- 2.
A graph trivially subsumes itself with the mapping \(m(v) = v\).
- 3.
If a graph \(g_1\) subsumes \(g_2\) through a mapping \(m_1\), and \(g_2\) subsumes \(g_3\) through a mapping \(m_2\), then we know \(g_1\) subsumes \(g_3\) via the mapping \(m(v) = m_2(m_1(v))\).
- 4.
Notice that it is possible to compute the remainder without the need to actually perform any type of unification operation, which can be computationally expensive.
- 5.
Datasets can be downloaded in dot, GML and GraphML format from https://github.com/santiontanon/RHOG.
- 6.
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This research was supported by grant IIS-1551338 from the National Science Foundation (NSF).
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Ontañón, S., Shokoufandeh, A. (2016). Refinement-Based Similarity Measures for Directed Labeled Graphs. In: Goel, A., Díaz-Agudo, M., Roth-Berghofer, T. (eds) Case-Based Reasoning Research and Development. ICCBR 2016. Lecture Notes in Computer Science(), vol 9969. Springer, Cham. https://doi.org/10.1007/978-3-319-47096-2_21
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