This post will summarize the paper SimGNN which aims for fast graph similarity computation. Graphs are structures that are used to link different entities that we call nodes using relationships called edges. Graphs exist everywhere from bonds between the atoms to friends on Facebook, all these scenarios can be represented as a graph. One of the fundamental graph problems includes finding similarity between graphs. The similarity between graphs can be defined using these metrics :
- Graph Edit Distance
- Maximum Common Subgraph
However, currently available algorithms that are used to calculate these metrics have high complexities and it is not yet possible to compute exact GED using these for graphs having more than 16 nodes.
Some ways to compute these metrics are :
- Pruning verification Framework
- Approximating the GED in fast and heuristic ways
SimGNN follows another approach to tackle this problem i.e turning similarity computation problem into a learning problem.
Before getting into how SimGNN works, we must know the requirements to be satisfied by this model. It includes :
- Representation Invariant: Different representations of the same graph should give the same results.
- **Inductive: **Should be able to predict results for unseen graphs.
- Learnable: Must work on different similarity metrics like GED and MCS
**SimGNN Approach: **To achieve the above-stated requirements, SimGNN uses two strategies
- Design Learnable Embedding Function: This maps the graph into an embedding vector, which provides a global summary of a graph. Here, some nodes of importance are selected and used for embedding computation. (less time complexity)
- Pair-wise node comparison: The above embedding are too coarse, thus further compute the pairwise similarity scores between nodes from the two graphs, from which the histogram features are extracted and combined with the graph level information. (this is a time-consuming strategy)
#graph-edit-distance #machine-learning #graph-neural-networks #graph-convolution-network