Data mining-based analysis methods are increasingly being applied to data sets derived from science and engineering domains that model various physical phenomena and objects. In many of these data sets, a key requirement for their effective analysis is the ability to capture the relational and geometric characteristics of the underlying entities and objects. Geometric graphs, by modeling the various physical entities and their relationships with vertices and edges, provide a natural method to represent such data sets. In this paper we present gFSG, a computationally efficient algorithm for finding frequent patterns corresponding to geometric subgraphs in a large collection of geometric graphs. gFSG is able to discover geometric subgraphs that can be rotation, scaling, and translation invariant, and it can accommodate inherent errors on the coordinates of the vertices. We evaluated its performance using a large database of over 20,000 chemical structures, and our results show that it requires relatively little time, can accommodate low support values, and scales linearly with the number of transactions.
Bibliographical noteFunding Information:
This work was supported by NSF CCR-9972519, EIA-9986042, ACI-9982274, ACI-0133464 and ACI-0312828, by Army Research Office contract DA/DAAG55-98-1-0441, by the DOE ASCI program, by the Army High Performance Computing Research Center (AHPCRC) under the auspices of the Department of the Army, Army Research Laboratory (ARL) under Cooperative Agreement numbers DAAH04-95-C-0008 and DAAD19-01-2-0014, and by the Digital Technology Center at the University of Minnesota. The content of which does not necessarily reflect the position or the policy of the government, and no official endorsement should be inferred. Access to research and computing facilities was provided by the Digital Technology Center and the Minnesota Supercomputing Institute.
- Geometric subgraphs
- Graph mining
- Pattern discovery