Abstract
We propose a fast algorithm for approximating graph similarities. For its advantageous semantic and algorithmic properties, we define the similarity between two graphs by the Jaccard-similarity of their images in a binary feature space spanned by the set of frequent subtrees generated for some training dataset. Since the feature space embedding is computationally intractable, we use a probabilistic subtree isomorphism operator based on a small sample of random spanning trees and approximate the Jaccard-similarity by min-hash sketches. The partial order on the feature set defined by subgraph isomorphism allows for a fast calculation of the min-hash sketch, without explicitly performing the feature space embedding. Experimental results on real-world graph datasets show that our technique results in a fast algorithm. Furthermore, the approximated similarities are well-suited for classification and retrieval tasks in large graph datasets.
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Notes
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In practice, we do not store the patterns in \({\textsc {Sketch}}_{\pi _1,\ldots ,\pi _K}(G)\) explicitly. Instead, we define some arbitrary total order on \(\mathcal {F}\) and represent each pattern by its position according to this order.
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Welke, P., Horváth, T., Wrobel, S. (2016). Min-Hashing for Probabilistic Frequent Subtree Feature Spaces. In: Calders, T., Ceci, M., Malerba, D. (eds) Discovery Science. DS 2016. Lecture Notes in Computer Science(), vol 9956. Springer, Cham. https://doi.org/10.1007/978-3-319-46307-0_5
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DOI: https://doi.org/10.1007/978-3-319-46307-0_5
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