SimGNN: A Neural Network Approach to Fast Graph Similarity Computation

HAO DING

Abstract:

Graph similarity search is among the most important graph-based
applications, e.g. finding the chemical compounds that are most
similar to a query compound. Graph similarity/distance computa-
tion, such as Graph Edit Distance (GED) and Maximum Common
Subgraph (MCS), is the core operation of graph similarity search
and many other applications, but very costly to compute in practice.
Inspired by the recent success of neural network approaches to
several graph applications, such as node or graph classification,
we propose a novel neural network based approach to address
this classic yet challenging graph problem, aiming to alleviate the
computational burden while preserving a good performance.
The proposed approach, called SimGNN, combines two strategies.
First, we design a learnable embedding function that maps every
graph into an embedding vector, which provides a global summary
of a graph. A novel attention mechanism is proposed to emphasize
the important nodes with respect to a specific similarity metric.
Second, we design a pairwise node comparison method to sup-
plement the graph-level embeddings with fine-grained node-level
information. Our model achieves better generalization on unseen
graphs, and in the worst case runs in quadratic time with respect to
the number of nodes in two graphs. Taking GED computation as an
example, experimental results on three real graph datasets demon-
strate the effectiveness and efficiency of our approach. Specifically,
our model achieves smaller error rate and great time reduction com-
pared against a series of baselines, including several approximation
algorithms on GED computation, and many existing graph neural
network based models. Our study suggests SimGNN provides a new
direction for future research on graph similarity computation and
graph similarity search