胶囊图神经网络：提升图嵌入性能

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"胶囊图神经网络(Capsule Graph Neural Network, CapsGNN)是一篇于2019年在国际计算机视觉与模式识别会议(ICLR)上发表的研究论文。该工作由张欣怡和李辉（来自新加坡南洋理工大学电气与电子工程学院）提出，其研究背景是针对图神经网络(GNN)在生成图嵌入时存在的局限性。GNNs在学习高质量节点嵌入方面表现出色，被广泛应用于各种基于节点的任务，并在一些场景下达到了最先进的性能。然而，当将GNN学习到的节点嵌入用于生成全局的图嵌入时，传统的标量表示可能不足以有效地保留节点和图的复杂属性，从而导致图嵌入效果不理想。作者受Capsule Neural Network (CapsNet, Sabouret al., 2017) 的启发，提出了CapsGNN。核心思想在于借鉴胶囊网络的结构，通过胶囊形式来提取节点特征，而非仅仅依赖单一的标量表示。胶囊网络的特点在于它能够捕捉和表达物体的不同部分及其相对关系，这使得CapsGNN能够在处理图数据时更好地捕捉图形结构的全局信息。 CapsGNN利用路由机制，通过对胶囊进行动态分配和聚合，生成多个图嵌入，每个嵌入代表图的不同方面或层次，这样不仅增加了模型的表达能力，还能更好地反映出图的内在复杂性和结构特征。这种方法旨在改进现有的GNN方法，提升图嵌入的质量和适应性，使之更适用于各种图数据分析任务，如社区检测、节点分类和图聚类等。该研究在图神经网络领域引入了新的视角和方法，有望推动图学习算法的进一步发展和优化。"

Published as a conference paper at ICLR 2019

Figure 1: Framework of CapsGNN. At ﬁrst, GNN is used to extract node embeddings and form

primary capsules. Attention module is used to scale node embeddings which is followed by Dynamic

Routing to generate graph capsules. At the last stage, Dynamic Routing is applied again to perform

graph classiﬁcation.

where W

∈ R

d×d

is the trainable weights matrix. It serves as the channel ﬁlters from the ith

channel at the lth layer to the jth channel at the (l + 1)th layer. Here, we choose f (·) = tanh(·)

as the activation function. Z

l+1

∈ R

N×d

, Z

= X,

A = A + I

and

D =

. To

preserve features of sub-components with different sizes, we use nodes features extracted from all

GNN layers to generate high-level capsules.

3.2 HIGH-LEVEL GRAPH CAPSULES

After getting local node capsules, global routing mechanism is applied to generate graph capsules.

The input of this block contains N sets of node capsules, each set is S

= {s

, .., s

, ..., s

∈ R

, where C

is the number of channels at the lth layer of GNN, d is the dimension of each

capsule. The output of this block is a set of graph capsules H ∈ R

P ×d

. Each of the capsules

reﬂects the properties of the graph from different aspects. The length of these capsules reﬂects

the probability of the presence of these properties and the angle reﬂects the details of the graph

properties. Before generating graph capsules with node capsules, an Attention Module is introduced

to scale node capsules.

Attention Module. In CapsGNN, primary capsules are extracted based on each node which means

the number of primary capsules depends on the size of input graphs. In this case, if the routing

mechanism is directly applied, the value of the generated high-level capsules will highly depend on

the number of primary capsules (graph size) which is not the ideal case. Hence, an Attention Module

is introduced to combat this issue.

The attention measure we choose is a two-layer fully connected neural network F

attn

(·). The num-

ber of input units of F

attn

(·) is d × C

all

where C

all

and the number of output units equals

to C

all

. We apply node-based normalization to generate attention value in each channel and then

scale the original node capsules. The details of Attention Module is shown in Figure 2 and the

procedure can be written as:

scaled(s

(n,i)

) =

attn

(

)

attn

(

)

(n,i)

(3)

where

∈ R

1×C

all

is obtained by concatenating all capsules of the node n. s

(n,i)

∈ R

1×d

represents the ith capsule of the node n and F

attn

(

) ∈ R

1×C

all

is the generated attention value. In

this way, the generated graph capsules can be independent to the size of graphs and the architecture

will focus on more important parts of the input graph.

I represents identity matrix.

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