图神经网络详解：方法与应用综述

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"这篇论文是2018年由清华大学的研究团队发表在arXiv上的《Graph Neural Networks: A Review of Methods and Applications》，是一份关于图神经网络（GNN）的综合综述。" 正文: 图神经网络（Graph Neural Networks, GNN）是一种强大的机器学习模型，特别适用于处理具有复杂结构和关系数据的任务。这些任务包括但不限于模拟物理系统、学习分子指纹、预测蛋白质接口以及疾病分类。GNNs能够从图输入中学习，并捕获节点之间丰富的关联信息。论文作者包括Jie Zhou、Ganqu Cui、Zhengyan Zhang、Cheng Yang、Zhiyuan Liu和Maosong Sun等，他们都是清华大学的学者。这些专家在相关的研究项目中也有深入的工作，如Entity Alignment和Sememe项目。论文的预印本于2018年12月发布，截至2019年1月24日，已获得1440次阅读，但尚未有引用记录。用户Jie Zhou上传了文件，并请求增强下载文件的功能。在GNN的方法部分，论文可能涵盖了基础的图卷积网络（Graph Convolutional Networks, GCN）、图注意力网络（Graph Attention Networks, GAT）、递归神经网络（Recursive Neural Networks, RNN）在图数据上的应用，以及如何在图上进行消息传递和聚合操作。此外，可能还讨论了如何通过GNN处理异质图（Heterogeneous Graphs）、动态图（Dynamic Graphs）以及图数据的嵌入表示（Node Embeddings）。在应用方面，论文可能会探讨GNN在化学领域的应用，如药物发现和分子性质预测；在生物信息学中的蛋白质相互作用预测；在社交网络分析中的用户行为建模；以及在推荐系统中的上下文依赖关系捕捉。此外，论文可能还涉及了GNN的挑战和未来发展方向，例如如何更好地处理大规模图数据、提高模型的解释性、以及在无监督或半监督学习场景下的性能优化。这篇论文提供了一个全面的视角，对GNN的各种方法进行了深入解析，并展示了它们在不同领域的广泛应用。对于想要进入图神经网络领域的研究人员和实践者来说，这是一份非常有价值的参考资料。

loss.

• The weights W are updated according to the gradi-

ent computed in the last step.

Limitations Though experimental results showed that

GNN is a powerful architecture for modeling structural

data, there are still several limitations of the original GNN.

Firstly, it is inefﬁcient to update the hidden states of nodes

iteratively for the ﬁxed point. If relaxing the assumption

of the ﬁxed point, we can design a multi-layer GNN to

get a stable representation of node and its neighborhood.

Secondly, GNN uses the same parameters in the iteration

while most popular neural networks use different parame-

ters in different layers, which serve as a hierarchical feature

extraction method. Moreover, the update of node hidden

states is a sequential process which can beneﬁt from the

RNN kernel like GRU and LSTM. Thirdly, there are also

some informative features on the edges which cannot be

effectively modeled in the original GNN. For example, the

edges in the knowledge graph have the type of relations and

the message propagation through different edges should

be different according to their types. Besides, how to learn

the hidden states of edges is also an important problem.

Lastly, it is unsuitable to use the ﬁxed points if we focus on

the representation of nodes instead of graphs because the

distribution of representation in the ﬁxed point will be much

smooth in value and less informative for distinguishing each

node.

2.2 Variants of Graph Neural Networks

In this subsection, we present several variants of graph

neural networks. Sec 2.2.1 focuses on variants operating

on different graph types. These variants extend the rep-

resentation capability of the original model. Sec 2.2.2 lists

several modiﬁcations (convolution, gate mechanism, atten-

tion mechanism and skip connection) on the propagation

step and these models could learn representations with

higher quality. Sec 2.2.3 describes variants using advanced

training methods, which improve the training efﬁciency. An

overview of different variants of graph neural networks

could be found in Fig. 2.

2.2.1 Graph Types

In the original GNN [18], the input graph consists of nodes

with label information and undirected edges, which is the

simplest graph format. However, there are many variants

of graph in the world. In this subsection, we will introduce

some methods designed to model different kinds of graphs.

Directed Graphs The ﬁrst variant of graph is directed

graph. Undirected edge which can be treated as two directed

edges shows that there is a relation between two nodes.

However, directed edges can bring more information than

undirected edges. For example, in a knowledge graph where

the edge starts from the head entity and ends at the tail

entity, the head entity is the parent class of the tail entity,

which suggests we should treat the information propagation

process from parent classes and child classes differently.

ADGPM [29] uses two kinds of weight matrix, W

and

, to incorporate more precise structural information. The

propagation rule is shown as follows:

= σ(D

−1

σ(D

−1

t−1

) (7)

where D

−1

, D

−1

are the normalized adjacency matrix

for parents and children respectively.

Heterogeneous Graphs The second variant of graph

is heterogeneous graph, where there are several kinds of

nodes. The simplest way to process heterogeneous graph

is to convert the type of each node to a one-hot feature

vector which is concatenated with the original feature.

What’s more, GraphInception [30] introduces the concept of

metapath into the propagation on the heterogeneous graph.

With metapath, we can group the neighbors according to

their node types and distances. For each neighbor group,

GraphInception treats it as a sub-graph in a homogeneous

graph to do propagation and concatenates the propagation

results from different homogeneous graphs to do a collective

node representation.

Graphs with Edge Information In the ﬁnal variant of

graph, each edge also has its information like the weight

or the type of the edge. There are two ways to handle

this kind of graphs: Firstly, we can convert the graph to a

bipartite graph where the original edges also become nodes

and one original edge is split into two new edges which

means there are two new edges between the edge node

and begin/end nodes. The encoder of G2S [31] uses the

following aggregation function for neighbors:

= ρ(

u∈N

 h

t−1

) + b

) (8)

where W

and b

are the propagation parameters for

different types of edges (relations). Secondly, we can adapt

different weight matrices for the propagation on different

kinds of edges. When the number of relations is very large,

r-GCN [32] introduces two kinds of regularization to reduce

the number of parameters for modeling amounts of rela-

tions: basis- and block-diagonal-decomposition. With the basis

decomposition, each W

is deﬁned as follows:

(9)

i.e. as a linear combination of basis transformations V

∈

×d

out

with coefﬁcients a

such that only the coefﬁcients

depend on r. In the block-diagonal decomposition, r-GCN

deﬁnes each W

through the direct sum over a set of low-

dimensional matrices, which needs more parameters than

the ﬁrst one.

2.2.2 Propagation Types

The propagation step and output step are of vital impor-

tance in the model to obtain the hidden states of nodes

(or edges). As we list below, there are several major mod-

iﬁcations in the propagation step from the original graph

neural network model while researchers usually follow a

simple feed-forward neural network setting in the output

step. The comparison of different variants of GNN could be

found in Table 2. The variants utilize different aggregators to

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