Deep Graph Similarity Learning for Brain Data Analysis

Abstract

In many domains where data are represented as graphs, learning a similarity metric among graphs is considered a key problem, which can further facilitate various learning tasks, such as classification, clustering, and similarity search. Recently, there has been an increasing interest in deep graph similarity learning, where the key idea is to learn a deep learning model that maps input graphs to a target space such that the distance in the target space approximates the structural distance in the input space. Here, we provide a comprehensive review of the existing literature of deep graph similarity learning. We propose a systematic taxonomy for the methods and applications. Finally, we discuss the challenges and future directions for this problem.

Deep graph similarity learning: a survey

“…During evaluation, most GSL methods take pairs or triplets of graphs as input during training with various objective functions used for various graph similarity tasks. The existing evaluation tasks mainly include pair classification (Xu et al 2017;Ktena et al 2018;Ma et al 2019;Li et al 2019;Fey et al 2019), graph classification (Tixier et al 2019;Nikolentzos et al 2017;Narayanan et al 2017;Atamna et al 2019;Wu et al 2018;Wang et al 2019a;Liu et al 2019b;Yanardag and Vishwanathan 2015;Al-Rfou et al 2019;Du et al 2019), graph clustering (Wang et al 2019a), graph distance prediction (Bai et al 2018(Bai et al , 2019aFey et al 2019), and graph similarity search (Wang et al 2019c). Classification AUC (i.e., Area Under the ROC Curve) or accuracy are used as the most popular metric for the evaluation of graph-pair classification or graph classification task (Ma et al 2019;Li et al 2019).…”

“…There are three main categories of deep graph similarity learning methods (see Fig. 1a): (1) graph embedding based methods, which apply graph embedding techniques to obtain node-level or graph-level representations and further use the representations for similarity learning (Tixier et al 2019;Nikolentzos et al 2017;Narayanan et al 2017;Atamna et al 2019;Wu et al 2018;Wang et al 2019a;Xu et al 2017;Liu et al 2019b); (2) graph neural network (GNN) based models, which are based on using GNNs for similarity learning, including GNN-CNNs (Bai et al 2018(Bai et al , 2019a, Siamese GNNs (Ktena et al 2018;Ma et al 2019;Liu et al 2019a;Wang et al 2019c;Chaudhuri et al 2019) and GNN-based graph matching networks (Li et al 2019;Ling et al 2019;Bai et al 2019b;Wang et al 2019b;Jiang et al 2019;Guo et al 2018); and (3) deep graph kernels that first map graphs into a new feature space, where kernel functions are defined for similarity learning on graph pairs, including sub-structure based deep kernels (Yanardag and Vishwanathan 2015) and deep neural Du et al 2019). In the meantime, different methods may use different types of features in the learning process.…”

“…Existing GSL approaches can be generally grouped into two categories (see Fig. 1b): (1) methods that uses single-graph features (Ktena et al 2018;Ma et al 2019;Liu et al 2019a;Wang et al 2019c;Chaudhuri et al 2019); (2) methods that uses crossgraph features for similarity learning (Li et al 2019;Ling et al 2019;Bai et al 2019b;Al-Rfou et al 2019;Wang et al 2019b;Bai et al 2019b). The main difference between these two categories of methods is that for methods using single-graph features, the representation of each graph is learned individually, while those methods that use cross-graph features allow graphs to learn and propagate features from each other and the cross-graph interaction is leveraged for pairs of graphs.…”

“…(2) Higher-order Siamese GCN. Higher-order Siamese GCN (HS-GCN) is proposed in Ma et al (2019), which incorporates higher-order node-level proximity into graph convolutional networks so as to perform higher-order convolutions on each of the input graphs for the graph similarity learning task. A Siamese framework is employed with the proposed higher-order GCN in each of the twin networks.…”

“…However, none of the traditional graph embedding methods are able to capture such special structure and jointly leverage the learned node representations for similarity learning on brain networks. In Ma et al (2019), a higher-order GNN model is developed to encode the community-structure of brain networks during the representation learning and leverage it for the similarity learning task on these brain networks. Some more examples from other domains include the GNN-based graph similarity predictive models introduced for chemical compound queries in computational chemistry (Bai et al 2019a), and the deep graph matching networks proposed for binary function similarity search and malware detection in computer security (Li et al 2019;Wang et al 2019c).…”