Iterative active learning strategies for subgraph matching

The subgraph matching problem arises in a variety of domains including pattern recognition for segmented images, meshes of 3D objects, biochemical reactions, and security applications. Large and complex solution spaces are common for this graph-based problem, especially when the world graph contains many more nodes and edges in comparison to the template graph. Researchers have focused on the task of finding one match or many matches, however a real use-case scenario can necessitate identifying specific matches from a combinatorially complex solution space. Our work directly addresses this challenge. We propose to introduce additional queries to the subgraph that iteratively reduce the size of the solution space, and consider the optimal strategy for doing so. We formalize this problem and demonstrate that it is NP-complete. We compare different quantitative criteria for choosing nodes to query. We introduce a new method based on a spanning tree that outperforms other graph-based criteria for the multichannel datasets. Finally, we present numerical experiments for single channel and multichannel subgraph matching problems created from both synthetic and real world datasets.