Graph Partitioning and Graph Neural Network based Hierarchical Graph Matching for Graph Similarity Computation

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

Multivariate Time Series Classification with Hierarchical Variational Graph Pooling

With the advancement of sensing technology, multivariate time series classification (MTSC) has recently received considerable attention. Existing deep learning-based MTSC techniques, which mostly rely on convolutional or recurrent neural networks, are primarily concerned with the temporal dependency of single time series. As a result, they struggle to express pairwise dependencies among multivariate variables directly. Furthermore, current spatial-temporal modeling (e.g., graph classification) methodologies based on Graph Neural Networks (GNNs) are inherently flat and cannot aggregate hub data in a hierarchical manner. To address these limitations, we propose a novel graph pooling-based framework MTPool to obtain the expressive global representation of MTS. We first convert MTS slices to graphs by utilizing interactions of variables via graph structure learning module and attain the spatial-temporal graph node features via temporal convolutional module. To get global graph-level representation, we design an "encoder-decoder" based variational graph pooling module for creating adaptive centroids for cluster assignments. Then we combine GNNs and our proposed variational graph pooling layers for joint graph representation learning and graph coarsening, after which the graph is progressively coarsened to one node. At last, a differentiable classifier takes this coarsened representation to get the final predicted class. Experiments on ten benchmark datasets exhibit MTPool outperforms state-of-the-art strategies in the MTSC task