An efficiently computable subgraph pattern support measure: counting independent observations
Graph support measures are functions measuring how frequently a given subgraph pattern occurs in a given database graph. An important class of support measures relies on overlap graphs. A major advantage of overlap-graph based approaches is that they combine anti-monotonicity with counting the occurrences of a subgraph pattern which are independent according to certain criteria. However, existing overlap-graph based support measures are expensive to compute. In this paper, we propose a new support measure which is based on a new notion of independence. We show that our measure is the solution to a sparse linear program, which can be computed efficiently using interior point methods. We study the anti-monotonicity and other properties of this new measure, and relate it to the statistical power of a sample of embeddings in a network. We show experimentally that, in contrast to earlier overlap-graph based proposals, our support measure makes it feasible to mine subgraph patterns in large networks.
overlap graph linear program graph mining frequency counting variance on sample estimates