Mining Tree Patterns with Partially Injective Homomorphisms

One of the main differences between ILP and graph mining is that while pattern matching in ILP is mainly defined by homomorphism (subsumption), it is the subgraph isomorphism in graph mining. Using that subgraph isomorphisms are injective homomorphisms, we bridge the gap between the two pattern matching operators with partially injective homomorphisms, which are homomorphisms requiring the injectivity constraint only for subsets of the vertex pairs in the pattern. Utilizing positive complexity results on the efficiency of homomorphisms from bounded tree-width graphs, we sketch the main ingredients of an algorithm mining frequent trees with respect to partially injective homomorphisms. Our experimental results on benchmark datasets show that the predictive performance of the patterns obtained is comparable to that of ordinary frequent patterns. Thus, our approach provides a trade-off between predictive power and tractability, while bridging the gap between ILP and graph mining.