图神经网络的全面调查

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"这篇资源是一份关于图神经网络（Graph Neural Networks, GNN）的全面调查报告，由Zonghan Wu、Shirui Pan、Fengwen Chen、Guodong Long、Chengqi Zhang和Philip S. Yu等人撰写，发表在2021年1月的IEEE Transactions on Neural Networks and Learning Systems期刊上。文章深入探讨了近年来GNN在非欧几里得领域数据处理中的应用，以及如何应对复杂关系和对象间相互依赖的挑战。" 在这篇文章中，作者首先强调了深度学习在诸如图像分类、视频处理、语音识别和自然语言理解等领域的巨大影响力。这些任务的数据通常以欧几里得空间的形式存在。然而，随着非欧几里得数据的增加，如图数据，其中包含了复杂的关系和对象间的相互依赖，现有的机器学习算法面临着显著的挑战。图神经网络作为解决这一问题的关键技术，已经引起了广泛的研究关注。GNNs能够有效地处理图结构数据，通过学习节点、边和整个图的特征来捕获复杂的拓扑信息。文章提出了一种新的分类方法，将当前最先进的GNN技术划分为不同的类别，这有助于读者理解和比较各种GNN模型。文章深入讨论了GNN的基本原理，包括消息传递框架，这是大多数GNN架构的核心。在这个框架下，节点特征通过图的结构进行传播和聚合，从而获得邻近节点的信息。此外，还介绍了层次化GNN、图卷积网络（GCN）、图注意力网络（GAT）等具体实现，并分析了它们的优缺点。文章进一步探讨了GNN在各个领域的应用，如社交网络分析、化学分子结构预测、推荐系统、异构信息网络处理等。同时，也提到了GNN在训练和推理效率、可解释性、图的动态性和无监督学习等方面面临的挑战。为了推动GNN的研究，作者还总结了现有的数据集和基准测试，这对于研究人员评估和比较不同GNN模型的性能至关重要。最后，文章对GNN的未来发展方向进行了展望，包括扩展到大规模图、改进模型的可解释性和适应性，以及探索更深层次的理论理解。这篇综合调查报告提供了对图神经网络的全面概述，是了解和研究GNN及其应用的重要参考资料，对于想要进入这个领域的研究人员和工程师来说具有很高的价值。

8 IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, VOL. 32, NO. 1, JANUARY 2021

Fig. 2. Different GNN models built with graph convolutional layers. The

term Gconv denotes a graph convolutional layer. The term MLP denotes a

multilayer perceptron. The term CNN denotes a standard convolutional layer .

(a) ConvGNN with multiple graph conv olutional layers. A graph convolu-

tional layer encapsulates each node’s hidden representation by aggregating

feature information from its neighbors. After feature aggregation, a nonlinear

transformation is applied to the resulted outputs. By stacking multiple layers,

the ﬁnal hidden representation of each node receives messages from a further

neighborhood. (b) ConvGNN with pooling and readout layers for graph

classiﬁcation [21]. A graph convolutional layer is followed by a pooling

layer to coarsen a graph into subgraphs so that node representations on

coarsened graphs represent higher graph-level representations. A readout

layer summarizes the ﬁnal graph representation by taking the sum/mean of

hidden representations of subgraphs. (c) GAE for network embedding [61].

The encoder uses graph convolutiona l layers to get a network embedding

for each node. The decoder computes the pairwise distance given network

embeddings. After applying a nonlinear activ ation function, the decoder

reconstructs the graph adjacency matrix. The network is trained by minimizing

the discrepancy between the real adjacency matrix and the reconstructed

adjacency matrix. (d) STGNN for spatial–temporal graph forecasting [74].

A graph convolutional layer is followed by a 1-D-CNN layer. The graph

convolutional layer operates on A and X

(t)

to capture the spatial dependence,

while the 1-D-CNN layer slides over X along the time axis to capture the

temporal dependence. The output layer is a linear transformation, generating

a prediction for each node, such as its future value at the next time step.

operation in each model. As methods in [19] and [20] require

eigenvalue decomposition, the time complexity is O(n

The time complexity of [46] is also O(n

) due to the

node pairwise shortest-path computation. Other methods incur

equivalent time complexity, which is O(m) if the graph

adjacency matrix is sparse and is O(n

) other w ise. This is

because, in these methods, the computation of each node

’s representation involves its d

neighbors, and the sum of

over all nodes exactly equals the number of edges. The

time complexity of several methods is missing in Table III.

These methods either lack a time complexity analysis in their

articles or report the time complexity of their overall m odels

or algorithms.

IV. R

ECURREN T GRAPH NEURAL NETWORKS

RecGNNs are mostly p io neer works of GNNs. Th ey app ly

the same set of parameters recurrently over nodes in a graph

to extract high-level node representations. Constrained by

computational power, earlier research is mainly focused on

directed acyclic graphs [13], [80].

GNN*

proposed by Scarselli et al. extends prior recurrent

models to handle g eneral types of graphs, e.g., acyclic, cyclic,

directed, and undirected graphs [15]. Based on an informa-

tion diffusion mechanism, GNN* updates nodes’ states by

exchanging neighborhood information recurrently until a sta-

ble equilibrium is reached. A node’s hidden state is recurrently

updated b y

(t)



u∈N (v)

f (x

, x

(v,u)

, x

, h

(t−1)

) (1)

where f (·) is a parametric function and h

(0)

is initialized

randomly. The sum operation enables GNN* to be applicable

to all nodes, even if the number of neighbors differs and

no neighborhood ordering is known. To ensure convergence,

the recurrent function f (·) must be a contraction mapping,

which shrinks the distance between two points after projecting

them into a latent space. In the case o f f (·) being a neural net-

work, a penalty term has to b e imposed on the Jacobian matrix

of parameters. When a convergence criterion is satisﬁed, the

last step node hidden states are forwarded to a readout layer.

GNN* alternates the stage of node state propagation and the

stage of parameter gradient computation to minimize a train-

ing objective. This strategy enables GNN* to handle cyclic

graphs. In the follow-up works, the graph echo state network

(GraphESN) [16] extends echo state networks to improve the

training efﬁciency of GNN*. GraphESN consists of an encoder

and an output layer. The encoder is randomly initialized and

requires no training. It implements a contractive state transition

function to recurrently update node states until the global

graph state reaches convergence. Afterward, the output layer

is trained by taking the ﬁxed node states as inputs.

Gated GNN (GGNN) [17] employs a gated recurren t un it

(GRU) [81] as a recurrent function, reducing the recurrence

to a ﬁxed number of steps. The advantage is that it no longer

needs to constrain parameters to ensure convergence. A node

hidden state is updated by its previous hidden states and its

neighboring hidden states, deﬁned as

(t)

= GRU

⎛

⎝

(t−1)



u∈N (v)

(t−1)

⎞

⎠

(2)

where h

(0)

= x

. Different from GNN* and GraphESN,

GGNN uses the backpropagation through time (BPTT) algo-

rithm to learn the model parameters. This can be problematic

As GNN is used to represent broad graph neural networks in this article,

we name this particular method GNN* to avoid ambiguity.

Authorized licensed use limited to: Fujian Normal University. Downloaded on March 27,2021 at 01:56:03 UTC from IEEE Xplore. Restrictions apply.

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