Graph Representation Learning学习笔记-chapter1

Posted 2022-10-29 Dodo·D·Caster

Chapter1 Introduction

Graphs are a ubiquitous data structure and a universal language for describing complex systems.

1.1 What is a graph

Definition of Graph

G=(V,E)

• V : node
• E : edge
• (u, v) : an edge from node u to node v

Presentation of Graph

adjacency matrix A

• A[u, v] = 1 if (u, v) ∈ E
• A[u, v] = 0 otherwise

Types of Graph

undirected graph

• A will be a symmetric matrix

directed graph

• not necessarily a symmetric matrix

weighted graph

• A[u, v] = w

multi-relational graph

• $A\in R^{|V|\times |R|\times |V|}$

  • R : the set of relations

• Heterogeneous graphs 异构图

  • 节点的类型+边的类型>2
  • 边满足一定的条件，如某类型的边只连接特定类型的节点

• Multiplex graphs 多重图

  

1.2 Machine learning on graphs

node classification

explicitly leverage the connections between nodes

• exploit homophily
  • tendency for nodes to share attributes with their neighbors in the graph
• structural equivalence
  • nodes with similar local neighborhood structures will have similar labels
• heterophily
  • nodes will be preferentially connected to nodes with different labels

graph : semi-supervised learning

• 训练图的时候会把整个图作为输入，有的节点带有标签，有的节点没有标签，但对于没有标签的节点，仍然可以使用他们邻居的信息

elation prediction

• use machine learning to infer the edges between nodes in a graph

Community detection : graph analogue of unsupervised clustering

graph clustering : straightforward extension of unsupervised clustering for graph data

• given a dataset of multiple different graphs and our goal is to make independent predictions specific to each graph