DEMO-Net：图神经网络的新视角

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"DEMO-Net是针对节点和图分类的一种度特定图神经网络模型，旨在解决现有图神经网络在图卷积属性分析、节点度特有结构表达以及图级池化理论解释上的局限性。" DEMO-Net: 度特定图神经网络在信息技术领域，图数据在许多具有高影响力的应用中普遍存在，如社交网络、生物信息学和推荐系统等。随着深度学习在网格结构数据中的成功应用，研究人员提出了图神经网络（GNN）来学习强大的节点级或图级表示。然而，现有的大多数图神经网络面临着几个关键问题： 1. 图卷积属性分析不足：大多数模型缺乏对图卷积特性的深入分析，例如种子导向、度感知和无序性分析。这些特性对于理解和优化模型性能至关重要。 2. 节点度特定结构未明确表达：在图卷积过程中，节点的度（连接到该节点的边的数量）是决定其邻域结构的重要因素。现有的方法往往未能明确考虑这一点，导致结构敏感的节点邻域无法被有效区分。 3. 图级池化的理论基础不清晰：图级别的聚合操作，如池化，对于生成全局图表示至关重要。但关于这些池化策略的理论解释尚不明确，这限制了我们对模型工作原理的理解和改进。 DEMO-Net模型的提出，受到Weisfeiler-Lehman图同构测试的启发，该测试通过递归地识别1-hop邻居来增强节点的表示。DEMO-Net旨在解决上述问题，它设计了一种通用的度特定图神经网络架构，强调了节点的度信息在图卷积过程中的重要性，并且试图提供更清晰的图级池化理论基础。具体来说，DEMO-Net的创新点包括： 1. 度敏感的图卷积：DEMO-Net明确考虑了节点的度信息，为不同度的节点设计了不同的卷积操作，从而能够区分结构上不同的邻域，提高对图结构的捕捉能力。 2. 结构增强表示：借鉴Weisfeiler-Lehman测试，DEMO-Net通过迭代更新节点特征，增强了节点的表示能力，使其能更好地反映其1-hop邻域的信息。 3. 清晰的图级池化机制：尽管没有在摘要中详细描述，可以推测DEMO-Net可能提出了一种新的或改进的图级池化方法，以提供更坚实的理论基础，帮助模型理解和学习图的整体结构。 DEMO-Net是对现有图神经网络模型的重要补充，它提升了图数据处理的效率和准确性，特别是在节点和图分类任务中。通过度特定的处理方式，DEMO-Net有望在图数据密集的应用场景中展现出更强的性能。

DEMO-Net: Degree-specific Graph Neural Networks for

Node and Graph Classification

Jun Wu

Arizona State University

junwu6@asu.edu

Jingrui He

Arizona State University

Jingrui.he@asu.edu

Jiejun Xu

HRL Laboratories, LLC

jxu@hrl.com

ABSTRACT

Graph data widely exist in many high-impact applications. Inspired

by the success of deep learning in grid-structured data, graph neural

network models have been proposed to learn powerful node-level

or graph-level representation. However, most of the existing graph

neural networks suer from the following limitations: (1) there is

limited analysis regarding the graph convolution properties, such

as seed-oriented, degree-aware and order-free; (2) the node’s degree-

specic graph structure is not explicitly expressed in graph con-

volution for distinguishing structure-aware node neighborhoods;

(3) the theoretical explanation regarding the graph-level pooling

schemes is unclear.

To address these problems, we propose a generic degree-specic

graph neural network named DEMO-Net motivated by Weisfeiler-

Lehman graph isomorphism test that recursively identies 1-hop

neighborhood structures. In order to explicitly capture the graph

topology integrated with node attributes, we argue that graph con-

volution should have three properties: seed-oriented, degree-aware,

order-free. To this end, we propose multi-task graph convolution

where each task represents node representation learning for nodes

with a specic degree value, thus leading to preserving the degree-

specic graph structure. In particular, we design two multi-task

learning methods: degree-specic weight and hashing functions

for graph convolution. In addition, we propose a novel graph-level

pooling/readout scheme for learning graph representation provably

lying in a degree-specic Hilbert kernel space. The experimental

results on several node and graph classication benchmark data

sets demonstrate the eectiveness and eciency of our proposed

DEMO-Net over state-of-the-art graph neural network models.

KEYWORDS

Graph Neural Network, Degree-specic Convolution, Multi-task

Learning, Graph Isomorphism Test

ACM Reference Format:

Jun Wu, Jingrui He, and Jiejun Xu. 2019. DEMO-Net: Degree-specic Graph

Neural Networks for Node and Graph Classication. In The 25th ACM

SIGKDD Conference on Knowledge Discovery and Data Mining (KDD’19),

June 22–24, 2019, Anchorage, AK, USA. ACM, New York, NY, USA, 10 pages.

https://doi.org/10.1145/3292500.3330950

Permission to make digital or hard copies of all or part of this work for personal or

classroom use is granted without fee provided that copies are not made or distributed

for prot or commercial advantage and that copies bear this notice and the full citation

on the rst page. Copyrights for components of this work owned by others than ACM

must be honored. Abstracting with credit is permitted. To copy otherwise, or republish,

to post on servers or to redistribute to lists, requires prior specic permission and/or a

fee. Request permissions from permissions@acm.org.

KDD ’19, August 4–8, 2019, Anchorage, AK, USA

ACM ISBN 978-1-4503-6201-6/19/08.. . $15.00

https://doi.org/10.1145/3292500.3330950

1 INTRODUCTION

Nowadays, graph data is being generated across multiple high-

impact application domains, ranging from bioinformatics [

] to

nancial fraud detection [

], from genome-wide association

study [

] to social network analysis [

]. In order to leverage the

rich information in graph-structured data, it is of great impor-

tance to learn eective node or graph representation from both

node/edge attributes and the graph topological structure. To this

end, numerous graph neural network models have been proposed

recently inspired by the success of deep learning architectures on

grid-structured data (e.g., images, videos, languages, etc.). One intu-

ition behind this line of approaches is that the topological structure

as well as node attributes could be integrated by recursively aggre-

gating and compressing the continuous feature vectors from local

neighborhoods in an end-to-end training architecture.

One key component of graph neural networks [

] is the graph

convolution (or feature aggregation function) that aggregates and

transforms the feature vectors from a node’s local neighborhood. By

integrating the node attributes with the graph structure information

using Laplacian smoothing [

] or advanced attention mecha-

nism [

], graph neural networks learn the node representation in

a low-dimensional feature space where nearby nodes in the graph

would share a similar representation. Moreover, in order to learn the

representation for the entire graph, researchers have proposed the

graph-level pooling schemes [

] that compress the nodes’ represen-

tation into a global feature vector. The node or graph representation

learned by graph neural networks has achieved state-of-the-art per-

formance in many downstream graph mining tasks, such as node

classication [26], graph classication [22], etc.

However, most of the existing graph neural networks suer

from the following limitations.

(L1)

There is limited analysis on

graph convolution properties that could guide the design of graph

neural networks when learning node representation.

(L2)

In or-

der to preserve the node proximity, the graph convolution applies

a special form of Laplacian smoothing [

], which simply mixes

the attributes from node’s neighborhood. This leads to the loss of

degree-specic graph structure information for the learned repre-

sentation. An illustrative example is shown in Figure 1: although

nodes 4 and 5 are structurally dierent, they would be mapped

to similar representation due to rst-order node proximity using

existing methods. Moreover, the neighborhood sub-sampling meth-

ods used to improve model eciency [

] signicantly degraded

the discrimination of degree-specic graph structure.

(L3)

The

theoretical explanation regarding the graph-level pooling schemes

is largely missing.

To address the above problems, in this paper, we propose a

generic graph neural network model DEMO-Net that considers the

arXiv:1906.02319v1 [cs.LG] 5 Jun 2019

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