Beyond Frequencies: Graph Paern Mining in Multi-weighted Graphs

Graph pattern mining aims at identifying structures that appear frequently in large graphs, under the assumption that frequency signi�es importance. Several measures of frequency have been proposed that respect the apriori property, essential for an e�cient search of the patterns. This property states that the number of appearances of a pattern in a graph cannot be larger than the frequency of any of its sub-patterns. In real life, there are many graphs with weights on nodes and/or edges. For these graphs, it is fair that the importance (score) of a pattern is determined not only by the number of its appearances, but also by the weights on the nodes/edges of those appearances. Scoring functions based on the weights do not generally satisfy the apriori property, thus forcing many approaches to employ other, less e�cient, pruning strategies to speed up the computation. The problem becomes even more challenging in the case of multiple weighting functions that assign di�erent weights to the same nodes/edges. In this work, we provide e�cient and e�ective techniques for mining patterns in multi-weight graphs. We devise both an exact and an approximate solution. The �rst is characterized by intelligent storage and computation of the pattern scores, while the second is based on the aggregation of similar weighting functions to allow scalability and avoid redundant computations. Both methods adopt a scoring function that respects the apriori property, and thus they can rely on e�ective pruning strategies. Extensive experiments under di�erent parameter settings prove that the presence of edge weights and the choice of scoring function a�ect the patterns mined, and hence the quality of the results returned to the user. Finally, experiments on datasets of di�erent sizes and increasing numbers of weighting functions show that, even when the performance of the exact algorithm degrades, the approximate algorithm performs well and with quite good quality.