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Register a new userGraph Partitioning and Graph Neural Network based Hierarchical Graph Matching for Graph Similarity Computation
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Added by
Ziheng Duan
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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Graph similarity computation aims to predict a similarity score between one pair of graphs to facilitate downstream applications, such as finding the most similar chemical compounds similar to a query compound or Fewshot 3D Action Recognition. Recently, some graph similarity computation models based on neural networks have been proposed, which are either based on graph-level interaction or node-level comparison. However, when the number of nodes in the graph increases, it will inevitably bring about reduced representation ability or high computation cost. Motivated by this observation, we propose a graph partitioning and graph neural network-based model, called PSimGNN, to effectively resolve this issue. Specifically, each of the input graphs is partitioned into a set of subgraphs to extract the local structural features directly. Next, a novel graph neural network with an attention mechanism is designed to map each subgraph into an embedding vector. Some of these subgraph pairs are automatically selected for node-level comparison to supplement the subgraph-level embedding with fine-grained information. Finally, coarse-grained interaction information among subgraphs and fine-grained comparison information among nodes in different subgraphs are integrated to predict the final similarity score. Experimental results on graph datasets with different graph sizes demonstrate that PSimGNN outperforms state-of-the-art methods in graph similarity computation tasks using approximate Graph Edit Distance (GED) as the graph similarity metric.
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Graph edit distance / similarity is widely used in many tasks, such as graph similarity search, binary function analysis, and graph clustering. However, computing the exact graph edit distance (GED) or maximum common subgraph (MCS) between two graphs is known to be NP-hard. In this paper, we propose the hierarchical graph matching network (HGMN), which learns to compute graph similarity from data. HGMN is motivated by the observation that two similar graphs should also be similar when they are compressed into more compact graphs. HGMN utilizes multiple stages of hierarchical clustering to organize a graph into successively more compact graphs. At each stage, the earth mover distance (EMD) is adopted to obtain a one-to-one mapping between the nodes in two graphs (on which graph similarity is to be computed), and a correlation matrix is also derived from the embeddings of the nodes in the two graphs. The correlation matrices from all stages are used as input for a convolutional neural network (CNN), which is trained to predict graph similarity by minimizing the mean squared error (MSE). Experimental evaluation on 4 datasets in different domains and 4 performance metrics shows that HGMN consistently outperforms existing baselines in the accuracy of graph similarity approximation.
Graph representation learning has emerged as a powerful technique for addressing real-world problems. Various downstream graph learning tasks have benefited from its recent developments, such as node classification, similarity search, and graph classification. However, prior arts on graph representation learning focus on domain specific problems and train a dedicated model for each graph dataset, which is usually non-transferable to out-of-domain data. Inspired by the recent advances in pre-training from natural language processing and computer vision, we design Graph Contrastive Coding (GCC) -- a self-supervised graph neural network pre-training framework -- to capture the universal network topological properties across multiple networks. We design GCCs pre-training task as subgraph instance discrimination in and across networks and leverage contrastive learning to empower graph neural networks to learn the intrinsic and transferable structural representations. We conduct extensive experiments on three graph learning tasks and ten graph datasets. The results show that GCC pre-trained on a collection of diverse datasets can achieve competitive or better performance to its task-specific and trained-from-scratch counterparts. This suggests that the pre-training and fine-tuning paradigm presents great potential for graph representation learning.
The ability to compute similarity scores between graphs based on metrics such as Graph Edit Distance (GED) is important in many real-world applications, such as 3D action recognition and biological molecular identification. Computing exact GED values is typically an NP-hard problem and traditional algorithms usually achieve an unsatisfactory trade-off between accuracy and efficiency. Recently, Graph Neural Networks (GNNs) provide a data-driven solution for this task, which is more efficient while maintaining prediction accuracy in small graph (around 10 nodes per graph) similarity computation. Existing GNN-based methods, which either respectively embed two graphs (lack of low-level cross-graph interactions) or deploy cross-graph interactions for whole graph pairs (redundant and time-consuming), are still not able to achieve competitive results when the number of nodes in graphs increases. In this paper, we focus on similarity computation for large-scale graphs and propose the embedding-coarsening-matching framework, which first embeds and coarsens large graphs to coarsened graphs with denser local topology and then deploys fine-grained interactions on the coarsened graphs for the final similarity scores.
While the celebrated graph neural networks yield effective representations for individual nodes of a graph, there has been relatively less success in extending to the task of graph similarity learning. Recent work on graph similarity learning has considered either global-level graph-graph interactions or low-level node-node interactions, however ignoring the rich cross-level interactions (e.g., between each node of one graph and the other whole graph). In this paper, we propose a multi-level graph matching network (MGMN) framework for computing the graph similarity between any pair of graph-structured objects in an end-to-end fashion. In particular, the proposed MGMN consists of a node-graph matching network for effectively learning cross-level interactions between each node of one graph and the other whole graph, and a siamese graph neural network to learn global-level interactions between two input graphs. Furthermore, to compensate for the lack of standard benchmark datasets, we have created and collected a set of datasets for both the graph-graph classification and graph-graph regression tasks with different sizes in order to evaluate the effectiveness and robustness of our models. Comprehensive experiments demonstrate that MGMN consistently outperforms state-of-the-art baseline models on both the graph-graph classification and graph-graph regression tasks. Compared with previous work, MGMN also exhibits stronger robustness as the sizes of the two input graphs increase.
Graph Neural Networks (GNNs) draw their strength from explicitly modeling the topological information of structured data. However, existing GNNs suffer from limited capability in capturing the hierarchical graph representation which plays an important role in graph classification. In this paper, we innovatively propose hierarchical graph capsule network (HGCN) that can jointly learn node embeddings and extract graph hierarchies. Specifically, disentangled graph capsules are established by identifying heterogeneous factors underlying each node, such that their instantiation parameters represent different properties of the same entity. To learn the hierarchical representation, HGCN characterizes the part-whole relationship between lower-level capsules (part) and higher-level capsules (whole) by explicitly considering the structure information among the parts. Experimental studies demonstrate the effectiveness of HGCN and the contribution of each component.
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