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1. Dynamic Graph Convolutional Networks Using the Tensor M-Product

   https://doi.org/10.1137/1.9781611976700  

   Malik, O. A.; Ubaru, S.; Horesh, L.; Kilmer, M. E.; Avron, H. (January 2021, Proceedings of the 2021 SIAM International Conference on Data Mining (SDM))

   Demeniconi, C.; Davidson, I (Ed.)

   Many irregular domains such as social networks, financial transactions, neuron connections, and natural language constructs are represented using graph structures. In recent years, a variety of graph neural networks (GNNs) have been successfully applied for representation learning and prediction on such graphs. In many of the real-world applications, the underlying graph changes over time, however, most of the existing GNNs are inadequate for handling such dynamic graphs. In this paper we propose a novel technique for learning embeddings of dynamic graphs using a tensor algebra framework. Our method extends the popular graph convolutional network (GCN) for learning representations of dynamic graphs using the recently proposed tensor M-product technique. Theoretical results presented establish a connection between the proposed tensor approach and spectral convolution of tensors. The proposed method TM-GCN is consistent with the Message Passing Neural Network (MPNN) framework, accounting for both spatial and temporal message passing. Numerical experiments on real-world datasets demonstrate the performance of the proposed method for edge classification and link prediction tasks on dynamic graphs. We also consider an application related to the COVID-19 pandemic, and show how our method can be used for early detection of infected individuals from contact tracing data. 

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2. Understanding the Representation Power of Graph Neural Networks in Learning Graph Topology

   Dehmamy, Nima; Barabasi, Albert-Laszlo; Yu, Rose (January 2019, Advances in Neural Information Processing Systems 32 (NIPS 2019))

   To deepen our understanding of graph neural networks, we investigate the representation power of Graph Convolutional Networks (GCN) through the looking glass of graph moments, a key property of graph topology encoding path of various lengths. We find that GCNs are rather restrictive in learning graph moments. Without careful design, GCNs can fail miserably even with multiple layers and nonlinear activation functions. We analyze theoretically the expressiveness of GCNs, arriving at a modular GCN design, using different propagation rules. Our modular design is capable of distinguishing graphs from different graph generation models for surprisingly small graphs, a notoriously difficult problem in network science. Our investigation suggests that, depth is much more influential than width and deeper GCNs are more capable of learning higher order graph moments. Additionally, combining GCN modules with different propagation rules is critical to the representation power of GCNs. 

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3. Feature-Attention Graph Convolutional Networks for Noise Resilient Learning

   https://doi.org/10.1109/TCYB.2022.3143798  

   Shi, Min; Tang, Yufei; Zhu, Xingquan; Zhuang, Yuan; Lin, Maohua; Liu, Jianxun (January 2022, IEEE Transactions on Cybernetics)

   Noise and inconsistency commonly exist in real-world information networks, due to the inherent error-prone nature of human or user privacy concerns. To date, tremendous efforts have been made to advance feature learning from networks, including the most recent graph convolutional networks (GCNs) or attention GCN, by integrating node content and topology structures. However, all existing methods consider networks as error-free sources and treat feature content in each node as independent and equally important to model node relations. Noisy node content, combined with sparse features, provides essential challenges for existing methods to be used in real-world noisy networks. In this article, we propose feature-based attention GCN (FA-GCN), a feature-attention graph convolution learning framework, to handle networks with noisy and sparse node content. To tackle noise and sparse content in each node, FA-GCN first employs a long short-term memory (LSTM) network to learn dense representation for each node feature. To model interactions between neighboring nodes, a feature-attention mechanism is introduced to allow neighboring nodes to learn and vary feature importance, with respect to their connections. By using a spectral-based graph convolution aggregation process, each node is allowed to concentrate more on the most determining neighborhood features aligned with the corresponding learning task. Experiments and validations, w.r.t. different noise levels, demonstrate that FA-GCN achieves better performance than the state-of-the-art methods in both noise-free and noisy network environments. 

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4. Multi-Class Imbalanced Graph Convolutional Network Learning

   https://doi.org/10.24963/ijcai.2020/398  

   Shi, Min; Tang, Yufei; Zhu, Xingquan; Wilson, David; Liu, Jianxun (July 2020, Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence (IJCAI))

   null (Ed.)

   Networked data often demonstrate the Pareto principle (i.e., 80/20 rule) with skewed class distributions, where most vertices belong to a few majority classes and minority classes only contain a handful of instances. When presented with imbalanced class distributions, existing graph embedding learning tends to bias to nodes from majority classes, leaving nodes from minority classes under-trained. In this paper, we propose Dual-Regularized Graph Convolutional Networks (DR-GCN) to handle multi-class imbalanced graphs, where two types of regularization are imposed to tackle class imbalanced representation learning. To ensure that all classes are equally represented, we propose a class-conditioned adversarial training process to facilitate the separation of labeled nodes. Meanwhile, to maintain training equilibrium (i.e., retaining quality of fit across all classes), we force unlabeled nodes to follow a similar latent distribution to the labeled nodes by minimizing their difference in the embedding space. Experiments on real-world imbalanced graphs demonstrate that DR-GCN outperforms the state-of-the-art methods in node classification, graph clustering, and visualization. 

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5. Learning Signed Network Embedding via Graph Attention

   https://doi.org/10.1609/aaai.v34i04.5911  

   Li, Yu; Tian, Yuan; Zhang, Jiawei; Chang, Yi (June 2020, Proceedings of the AAAI Conference on Artificial Intelligence)

   null (Ed.)

   Learning the low-dimensional representations of graphs (i.e., network embedding) plays a critical role in network analysis and facilitates many downstream tasks. Recently graph convolutional networks (GCNs) have revolutionized the field of network embedding, and led to state-of-the-art performance in network analysis tasks such as link prediction and node classification. Nevertheless, most of the existing GCN-based network embedding methods are proposed for unsigned networks. However, in the real world, some of the networks are signed, where the links are annotated with different polarities, e.g., positive vs. negative. Since negative links may have different properties from the positive ones and can also significantly affect the quality of network embedding. Thus in this paper, we propose a novel network embedding framework SNEA to learn Signed Network Embedding via graph Attention. In particular, we propose a masked self-attentional layer, which leverages self-attention mechanism to estimate the importance coefficient for pair of nodes connected by different type of links during the embedding aggregation process. Then SNEA utilizes the masked self-attentional layers to aggregate more important information from neighboring nodes to generate the node embeddings based on balance theory. Experimental results demonstrate the effectiveness of the proposed framework through signed link prediction task on several real-world signed network datasets. 

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