图神经网络：方法综述与应用深度探讨
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图卷积神经网络（Graph Neural Networks, GNNs）是近年来在计算机科学领域引起广泛关注的研究热点，尤其在处理具有丰富关系信息的非结构化数据时展现出了强大的潜力。本文旨在提供对图神经网络方法及其应用的一次全面回顾。
1. **图神经网络基础**：
图神经网络是一种连接主义模型，其核心思想是通过节点之间的消息传递来捕捉图数据中的依赖关系。与传统的神经网络不同，GNNs能够保留节点状态，从而能反映任意深度邻域的信息。这使得它们特别适合于处理各种任务，如分子指纹学习、蛋白质界面预测、疾病分类等，这些领域往往依赖于元素间的复杂关系。
2. **挑战与困难**：
初始的图神经网络设计在达到固定点的训练过程中遇到了挑战，这通常涉及到梯度消失或爆炸问题，使得模型难以收敛。然而，随着研究的深入，网络架构、优化技巧以及并行计算技术的进步，已经极大地改善了图神经网络的学习能力和性能。
3. **网络架构创新**：
近年来，研究人员提出了多种创新的图神经网络架构，如Graph Convolutional Networks (GCN)，它利用邻接矩阵进行卷积操作；Graph Attention Networks (GAT) 引入了注意力机制，赋予节点不同的学习权重；还有GraphSAGE，通过聚合邻居节点的特征生成当前节点的表示。这些创新有助于更好地捕捉图结构中的复杂性。
4. **优化技术**：
优化技术的进步也对GNNs的训练效果产生了重大影响。例如，通过引入残差连接（Residual Connections）、正则化策略和更高效的优化器，如Adam，使模型能够在处理大规模图数据时更稳定地收敛。
5. **跨领域应用**：
图神经网络的应用并不仅限于物理系统和分子科学。在自然语言处理领域，它们可以用于分析句子的依赖树，而在计算机视觉中，可以构建图像场景图的推理模型。此外，GNNs还被用于社交网络分析、推荐系统、网络安全等领域，展示出广泛的应用潜力。
6. **未来趋势与挑战**：
随着技术的发展，图神经网络仍面临许多挑战，如如何处理动态图、如何处理稀疏数据以及如何提高模型的解释性和可扩展性。尽管如此，随着研究人员不断探索和改进，图神经网络的应用前景一片光明。
总结来说，图卷积神经网络是解决多模态数据中关系建模的重要工具，其不断进化的架构和优化方法使其在多个领域展现出强大的表现力。随着技术的深入，我们期待看到更多的创新和突破，进一步推动图神经网络在实际问题中的广泛应用。
4
• The states h
t
v
are iteratively updated by Eq. 1 until
a time T . They approach the fixed point solution of
Eq. 3: H(T ) ≈ H.
• The gradient of weights W is computed from the
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
p
and
W
c
, to incorporate more precise structural information. The
propagation rule is shown as follows:
H
t
= σ(D
−1
p
A
p
σ(D
−1
c
A
c
H
t−1
W
c
)W
p
) (7)
where D
−1
p
A
p
, D
−1
c
A
c
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:
h
t
v
= ρ(
1
|N
v
|
X
u∈N
v
W
r
(r
t
v
h
t−1
u
) + b
r
) (8)
where W
r
and b
r
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
r
is defined as follows:
W
r
=
B
X
1
a
rb
V
b
(9)
i.e. as a linear combination of basis transformations V
b
∈
R
d
in
×d
out
with coefficients a
rb
such that only the coefficients
depend on r. In the block-diagonal decomposition, r-GCN
defines each W
r
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
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