Abstract
We address the problem of finding local patterns and related local knowledge, represented as implication rules, in an attributed graph. Our approach consists in extending frequent closed pattern mining to the case in which the set of objects is the set of vertices of a graph, typically representing a social network. We recall the definition of abstract closed patterns, obtained by restricting the support set of an attribute pattern to vertices satisfying some connectivity constraint, and propose a specificity measure of abstract closed patterns together with an informativity measure of the associated abstract implication rules. We define in the same way local closed patterns, i.e. maximal attribute patterns each associated to a connected component of the subgraph induced by the support set of some pattern, and also define specificity of local closed patterns together with informativity of associated local implication rules. We also show how, by considering a derived graph, we may apply the same ideas to the discovery of local patterns and local implication rules in non disjoint parts of a subgraph as k-cliques communities.
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Notes
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defined by (i) \(T \subseteq \mathrm {UnionClosure}(T)\) and (ii) if q and w belong to \(\mathrm {UnionClosure}(T)\) then \(q \cup w\) belongs to \(\mathrm {UnionClosure}(T)\). By considering any subset \(T\subseteq 2^O\) and closing it under union we obtain an abstraction of \(2^O\) [10].
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Soldano, H., Santini, G., Bouthinon, D. (2015). Abstract and Local Rule Learning in Attributed Networks. In: Esposito, F., Pivert, O., Hacid, MS., Rás, Z., Ferilli, S. (eds) Foundations of Intelligent Systems. ISMIS 2015. Lecture Notes in Computer Science(), vol 9384. Springer, Cham. https://doi.org/10.1007/978-3-319-25252-0_34
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