Foundations and Modeling of Dynamic Networks Using Dynamic Graph Neural Networks: A Survey
TL;DR: This work establishes a foundation of dynamic networks with consistent, detailed terminology and notation and presents a comprehensive survey of dynamic graph neural network models using the proposed terminology.
Abstract: Dynamic networks are used in a wide range of fields, including social network analysis, recommender systems and epidemiology. Representing complex networks as structures changing over time allow network models to leverage not only structural but also temporal patterns. However, as dynamic network literature stems from diverse fields and makes use of inconsistent terminology, it is challenging to navigate. Meanwhile, graph neural networks (GNNs) have gained a lot of attention in recent years for their ability to perform well on a range of network science tasks, such as link prediction and node classification. Despite the popularity of graph neural networks and the proven benefits of dynamic network models, there has been little focus on graph neural networks for dynamic networks. To address the challenges resulting from the fact that this research crosses diverse fields as well as to survey dynamic graph neural networks, this work is split into two main parts. First, to address the ambiguity of the dynamic network terminology we establish a foundation of dynamic networks with consistent, detailed terminology and notation. Second, we present a comprehensive survey of dynamic graph neural network models using the proposed terminology.
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193 citations
TL;DR: In this article, the authors argue for using Graph Neural Networks as a method-of-choice, enabling information fusion for multi-modal causability (causability is the measurable extent to which an explanation to a human expert achieves a specified level of causal understanding).
182 citations
TL;DR: In this paper, the authors introduce Graph Recurrent Neural Networks (GRNNs) as a general learning framework that achieves this goal by leveraging the notion of a recurrent hidden state together with graph signal processing (GSP).
Abstract: Graph processes exhibit a temporal structure determined by the sequence index and and a spatial structure determined by the graph support. To learn from graph processes, an information processing architecture must then be able to exploit both underlying structures. We introduce Graph Recurrent Neural Networks (GRNNs) as a general learning framework that achieves this goal by leveraging the notion of a recurrent hidden state together with graph signal processing (GSP). In the GRNN, the number of learnable parameters is independent of the length of the sequence and of the size of the graph, guaranteeing scalability. We prove that GRNNs are permutation equivariant and that they are stable to perturbations of the underlying graph support. To address the problem of vanishing gradients, we also put forward gated GRNNs with three different gating mechanisms: time, node and edge gates. In numerical experiments involving both synthetic and real datasets, time-gated GRNNs are shown to improve upon GRNNs in problems with long term dependencies, while node and edge gates help encode long range dependencies present in the graph. The numerical results also show that GRNNs outperform GNNs and RNNs, highlighting the importance of taking both the temporal and graph structures of a graph process into account.
79 citations
TL;DR: Zhang et al. as discussed by the authors proposed a hyperbolic temporal graph network (HTGN) to capture the inherent complex and hierarchical properties in many real-world temporal networks, leading to sub-optimal embeddings.
Abstract: Representation learning over temporal networks has drawn considerable attention in recent years. Efforts are mainly focused on modeling structural dependencies and temporal evolving regularities in Euclidean space which, however, underestimates the inherent complex and hierarchical properties in many real-world temporal networks, leading to sub-optimal embeddings. To explore these properties of a complex temporal network, we propose a hyperbolic temporal graph network (HTGN) that fully takes advantage of the exponential capacity and hierarchical awareness of hyperbolic geometry. More specially, HTGN maps the temporal graph into hyperbolic space, and incorporates hyperbolic graph neural network and hyperbolic gated recurrent neural network, to capture the evolving behaviors and implicitly preserve hierarchical information simultaneously. Furthermore, in the hyperbolic space, we propose two important modules that enable HTGN to successfully model temporal networks: (1) hyperbolic temporal contextual self-attention (HTA) module to attend to historical states and (2) hyperbolic temporal consistency (HTC) module to ensure stability and generalization. Experimental results on multiple real-world datasets demonstrate the superiority of HTGN for temporal graph embedding, as it consistently outperforms competing methods by significant margins in various temporal link prediction tasks. Specifically, HTGN achieves AUC improvement up to 9.98% for link prediction and 11.4% for new link prediction. Moreover, the ablation study further validates the representational ability of hyperbolic geometry and the effectiveness of the proposed HTA and HTC modules.
44 citations
TL;DR: In this paper, the authors propose to embed static graphs in low-dimensional vector spaces, which plays a key role in network analytics and inference, supporting applications like node classification, link prediction, and graph visualization.
Abstract: Embedding static graphs in low-dimensional vector spaces plays a key role in network analytics and inference, supporting applications like node classification, link prediction, and graph visualizat...
37 citations
References
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TL;DR: A novel, efficient, gradient based method called long short-term memory (LSTM) is introduced, which can learn to bridge minimal time lags in excess of 1000 discrete-time steps by enforcing constant error flow through constant error carousels within special units.
Abstract: Learning to store information over extended time intervals by recurrent backpropagation takes a very long time, mostly because of insufficient, decaying error backflow. We briefly review Hochreiter's (1991) analysis of this problem, then address it by introducing a novel, efficient, gradient based method called long short-term memory (LSTM). Truncating the gradient where this does not do harm, LSTM can learn to bridge minimal time lags in excess of 1000 discrete-time steps by enforcing constant error flow through constant error carousels within special units. Multiplicative gate units learn to open and close access to the constant error flow. LSTM is local in space and time; its computational complexity per time step and weight is O. 1. Our experiments with artificial data involve local, distributed, real-valued, and noisy pattern representations. In comparisons with real-time recurrent learning, back propagation through time, recurrent cascade correlation, Elman nets, and neural sequence chunking, LSTM leads to many more successful runs, and learns much faster. LSTM also solves complex, artificial long-time-lag tasks that have never been solved by previous recurrent network algorithms.
72,897 citations
"Foundations and Modeling of Dynamic..." refers background in this paper
...where LSTM is a normal LSTM [87] and Vp ∈ Rn is defined as Vp = δpi where δ is the Kronecker delta....
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Proceedings Article•
12 Jun 2017TL;DR: This paper proposed a simple network architecture based solely on an attention mechanism, dispensing with recurrence and convolutions entirely and achieved state-of-the-art performance on English-to-French translation.
Abstract: The dominant sequence transduction models are based on complex recurrent orconvolutional neural networks in an encoder and decoder configuration. The best performing such models also connect the encoder and decoder through an attentionm echanisms. We propose a novel, simple network architecture based solely onan attention mechanism, dispensing with recurrence and convolutions entirely.Experiments on two machine translation tasks show these models to be superiorin quality while being more parallelizable and requiring significantly less timeto train. Our single model with 165 million parameters, achieves 27.5 BLEU onEnglish-to-German translation, improving over the existing best ensemble result by over 1 BLEU. On English-to-French translation, we outperform the previoussingle state-of-the-art with model by 0.7 BLEU, achieving a BLEU score of 41.1.
52,856 citations
08 Dec 2014
TL;DR: A new framework for estimating generative models via an adversarial process, in which two models are simultaneously train: a generative model G that captures the data distribution and a discriminative model D that estimates the probability that a sample came from the training data rather than G.
Abstract: We propose a new framework for estimating generative models via an adversarial process, in which we simultaneously train two models: a generative model G that captures the data distribution, and a discriminative model D that estimates the probability that a sample came from the training data rather than G. The training procedure for G is to maximize the probability of D making a mistake. This framework corresponds to a minimax two-player game. In the space of arbitrary functions G and D, a unique solution exists, with G recovering the training data distribution and D equal to ½ everywhere. In the case where G and D are defined by multilayer perceptrons, the entire system can be trained with backpropagation. There is no need for any Markov chains or unrolled approximate inference networks during either training or generation of samples. Experiments demonstrate the potential of the framework through qualitative and quantitative evaluation of the generated samples.
38,211 citations
"Foundations and Modeling of Dynamic..." refers background in this paper
...Available: http://arxiv.org/abs/1906.01529 [106] K. Lei, M. Qin, B. Bai, G. Zhang, and M. Yang, ‘‘GCN-GAN: A non-linear temporal link prediction model for weighted dynamic networks,’’ in Proc....
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...GCN-GAN [106] and DynGraphGAN [107] are two such models....
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...GCN-GAN use a stacked DGNN as a generator and a dense feed-forward networks as a discriminator [106] and DynGraphGAN use a shallow generator and a GCN [75] stacked with a CNN as a discriminator [107]....
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...These include: PATCHY-SAN, DyGGNN, RgGNN, StrGNN, EvolveGCN, JODIE, GC-LSTM, GCN-GAN, DynGraphGAN and DyREP. appearing and existing links disappearing....
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...Generative adversarial networks (GAN) [104] have proven to be very successful in the computer vision field [105]....
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TL;DR: A model based on these two ingredients reproduces the observed stationary scale-free distributions, which indicates that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems.
Abstract: Systems as diverse as genetic networks or the World Wide Web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a scale-free power-law distribution. This feature was found to be a consequence of two generic mechanisms: (i) networks expand continuously by the addition of new vertices, and (ii) new vertices attach preferentially to sites that are already well connected. A model based on these two ingredients reproduces the observed stationary scale-free distributions, which indicates that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems.
33,771 citations
"Foundations and Modeling of Dynamic..." refers background in this paper
...Many models define rules for how links are established [29], [30]....
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...models such as preferential attachment [29], forest fire [30] and GraphRNN [31]....
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Posted Content•
TL;DR: A scalable approach for semi-supervised learning on graph-structured data that is based on an efficient variant of convolutional neural networks which operate directly on graphs which outperforms related methods by a significant margin.
Abstract: We present a scalable approach for semi-supervised learning on graph-structured data that is based on an efficient variant of convolutional neural networks which operate directly on graphs. We motivate the choice of our convolutional architecture via a localized first-order approximation of spectral graph convolutions. Our model scales linearly in the number of graph edges and learns hidden layer representations that encode both local graph structure and features of nodes. In a number of experiments on citation networks and on a knowledge graph dataset we demonstrate that our approach outperforms related methods by a significant margin.
15,696 citations