Probabilistic and exact frequent subtree mining in graphs beyond forests

Motivated by the impressive predictive power of simple patterns, we consider the problem of mining frequent subtrees in arbitrary graphs. Although the restriction of the pattern language to trees does not resolve the computational complexity of frequent subgraph mining, in a recent work we have show...

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Veröffentlicht in:Machine learning Jg. 108; H. 7; S. 1137 - 1164
Hauptverfasser: Welke, Pascal, Horváth, Tamás, Wrobel, Stefan
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.07.2019
Springer Nature B.V
Schlagworte:
Algorithms
Artificial Intelligence
Clustering
Complexity
Computer Science
Control
Delay
Graph theory
Graphs
Mechatronics
Natural Language Processing (NLP)
Polynomials
Robotics
Set theory
Simulation and Modeling
Special Issue of the Inductive Logic Programming (ILP) 2017-2018
Trees (mathematics)
Probabilistic patterns
Pattern mining
Frequent subtree mining
Frequent subgraph mining
ISSN:0885-6125, 1573-0565
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Zusammenfassung:Motivated by the impressive predictive power of simple patterns, we consider the problem of mining frequent subtrees in arbitrary graphs. Although the restriction of the pattern language to trees does not resolve the computational complexity of frequent subgraph mining, in a recent work we have shown that it gives rise to an algorithm generating probabilistic frequent subtrees, a random subset of all frequent subtrees, from arbitrary graphs with polynomial delay. It is based on replacing each transaction graph in the input database with a forest formed by a random subset of its spanning trees. This simple technique turned out to be quite powerful on molecule classification tasks. It has, however, the drawback that the number of sampled spanning trees must be bounded by a polynomial of the size of the transaction graphs, resulting in less impressive recall even for slightly more complex structures beyond molecular graphs. To overcome this limitation, in this work we propose an algorithm mining probabilistic frequent subtrees also with polynomial delay, but by replacing each graph with a forest formed by an exponentially large implicit subset of its spanning trees. We demonstrate the superiority of our algorithm over the simple one on threshold graphs used e.g. in spectral clustering. In addition, providing sufficient conditions for the completeness and efficiency of our algorithm, we obtain a positive complexity result on exact frequent subtree mining for a novel, practically and theoretically relevant graph class that is orthogonal to all graph classes defined by some constant bound on monotone graph properties.
Bibliographie:ObjectType-Article-1
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ISSN:0885-6125
1573-0565
DOI:10.1007/s10994-019-05779-1