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Graph neural networks (GNNs) have been successfully employed in a myriad of applications involving graph-structured data. Theoretical findings establish that GNNs use nonlinear activation functions to create low-eigenvalue frequency content that can be processed in a stable manner by subsequent graph convolutional filters. However, the exact shape of the frequency content created by nonlinear functions is not known, and thus, it cannot be learned nor controlled. In this work, node-variant graph filters (NVGFs) are shown to be capable of creating frequency content and are thus used in lieu of nonlinear activation functions. This results in a novel GNN architecture that, although linear, is capable of creating frequency content as well. Furthermore, this new frequency content can be either designed or learned from data. In this way, the role of frequency creation is separated from the nonlinear nature of traditional GNNs. Extensive simulations are carried out to differentiate the contributions of frequency creation from those of the nonlinearity.
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Network data can be conveniently modeled as a graph signal, where data values are assigned to nodes of a graph that describes the underlying network topology. Successful learning from network data is built upon methods that effectively exploit this graph structure. In this work, we leverage graph signal processing to characterize the representation space of graph neural networks (GNNs). We discuss the role of graph convolutional filters in GNNs and show that any architecture built with such filters has the fundamental properties of permutation equivariance and stability to changes in the topology. These two properties offer insight about the workings of GNNs and help explain their scalability and transferability properties which, coupled with their local and distributed nature, make GNNs powerful tools for learning in physical networks. We also introduce GNN extensions using edge-varying and autoregressive moving average graph filters and discuss their properties. Finally, we study the use of GNNs in recommender systems and learning decentralized controllers for robot swarms.
Genetic mutations can cause disease by disrupting normal gene function. Identifying the disease-causing mutations from millions of genetic variants within an individual patient is a challenging problem. Computational methods which can prioritize disease-causing mutations have, therefore, enormous applications. It is well-known that genes function through a complex regulatory network. However, existing variant effect prediction models only consider a variant in isolation. In contrast, we propose VEGN, which models variant effect prediction using a graph neural network (GNN) that operates on a heterogeneous graph with genes and variants. The graph is created by assigning variants to genes and connecting genes with an gene-gene interaction network. In this context, we explore an approach where a gene-gene graph is given and another where VEGN learns the gene-gene graph and therefore operates both on given and learnt edges. The graph neural network is trained to aggregate information between genes, and between genes and variants. Variants can exchange information via the genes they connect to. This approach improves the performance of existing state-of-the-art models.
Graph representation learning has achieved great success in many areas, including e-commerce, chemistry, biology, etc. However, the fundamental problem of choosing the appropriate dimension of node embedding for a given graph still remains unsolved. The commonly used strategies for Node Embedding Dimension Selection (NEDS) based on grid search or empirical knowledge suffer from heavy computation and poor model performance. In this paper, we revisit NEDS from the perspective of minimum entropy principle. Subsequently, we propose a novel Minimum Graph Entropy (MinGE) algorithm for NEDS with graph data. To be specific, MinGE considers both feature entropy and structure entropy on graphs, which are carefully designed according to the characteristics of the rich information in them. The feature entropy, which assumes the embeddings of adjacent nodes to be more similar, connects node features and link topology on graphs. The structure entropy takes the normalized degree as basic unit to further measure the higher-order structure of graphs. Based on them, we design MinGE to directly calculate the ideal node embedding dimension for any graph. Finally, comprehensive experiments with popular Graph Neural Networks (GNNs) on benchmark datasets demonstrate the effectiveness and generalizability of our proposed MinGE.
Graph neural networks (GNNs) have shown broad applicability in a variety of domains. Some of these domains, such as social networks and product recommendations, are fertile ground for malicious users and behavior. In this paper, we show that GNNs are vulnerable to the extremely limited scenario of a single-node adversarial example, where the node cannot be picked by the attacker. That is, an attacker can force the GNN to classify any target node to a chosen label by only slightly perturbing another single arbitrary node in the graph, even when not being able to pick that specific attacker node. When the adversary is allowed to pick a specific attacker node, the attack is even more effective. We show that this attack is effective across various GNN types, such as GraphSAGE, GCN, GAT, and GIN, across a variety of real-world datasets, and as a targeted and a non-targeted attack. Our code is available at https://github.com/benfinkelshtein/SINGLE .
Node injection attack on Graph Neural Networks (GNNs) is an emerging and practical attack scenario that the attacker injects malicious nodes rather than modifying original nodes or edges to affect the performance of GNNs. However, existing node injection attacks ignore extremely limited scenarios, namely the injected nodes might be excessive such that they may be perceptible to the target GNN. In this paper, we focus on an extremely limited scenario of single node injection evasion attack, i.e., the attacker is only allowed to inject one single node during the test phase to hurt GNNs performance. The discreteness of network structure and the coupling effect between network structure and node features bring great challenges to this extremely limited scenario. We first propose an optimization-based method to explore the performance upper bound of single node injection evasion attack. Experimental results show that 100%, 98.60%, and 94.98% nodes on three public datasets are successfully attacked even when only injecting one node with one edge, confirming the feasibility of single node injection evasion attack. However, such an optimization-based method needs to be re-optimized for each attack, which is computationally unbearable. To solve the dilemma, we further propose a Generalizable Node Injection Attack model, namely G-NIA, to improve the attack efficiency while ensuring the attack performance. Experiments are conducted across three well-known GNNs. Our proposed G-NIA significantly outperforms state-of-the-art baselines and is 500 times faster than the optimization-based method when inferring.
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