J. Y. Choi. SNU

Graph Convolution Networks

Jin Young Choi

Seoul National University

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J. Y. Choi. SNU

Graphs from social networks

people and their interactions

directed (Twitter) and undirected (Facebook)

typical ML tasks

Link(edge) prediction

advertising (recommendation)

product placement

node

edge

Social Graphs

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J. Y. Choi. SNU

Graphs from utility and technology networks

power grids, roads, internet, sensor networks

structure is either hand designed or not

typical ML tasks

best routing under unknown or variable costs

identify nodes of interest

Transportation Graphs

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J. Y. Choi. SNU

Graphs from information networks

web

blogs

wikipedia

typical ML tasks

find influential sources

search (page rank)Web Graphs

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J. Y. Choi. SNU

Graphs from biological networks

protein-protein interactions

gene regulatory networks

typical ML tasks

discover unexplored interactions

learn or reconstruct the structure (graph auto-encoder)

recognize a similar structure for personalized cancer treatment (graph classification)

Gene Graphs

Cell Graphs

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J. Y. Choi. SNU

Graphs from similarity networks

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J. Y. Choi. SNU

Graphs from similarity networks

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J. Y. Choi. SNU

Graphs from similarity networks

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J. Y. Choi. SNU

Graphs from similarity networks

vision

audio

text

typical ML tasks

semi-supervised learning

spectral clustering (unsupervised learning, graph auto-encoder)

manifold learning (hyperbolic representation learning)

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J. Y. Choi. SNU

What will you learn in the Graphs in ML course?

Concepts and methods to work with graphs in ML.

Theoretical tools to analyze graph-based algorithms.

Specific applications of graphs in ML.

How to tackle: large graphs, online setting, graph construction …

One example: Online Semi-Supervised Face Recognition

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J. Y. Choi. SNU

Online Semi-Supervised Face Recognition

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J. Y. Choi. SNU

Online Semi-Supervised Face Recognition

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J. Y. Choi. SNU

Online Semi-Supervised Face Recognition

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J. Y. Choi. SNU

Unsupervised Graph Clustering of Data

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Non-Euclidean distance:Geodesic distancein tangent space of manifold→Geometric deep learning

J. Y. Choi. SNU

Data as Graphs

Jian Xu. Representing Big Data as Networks.

PhD Dissertation, University of Notre Dame

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J. Y. Choi. SNU

Deep Learning Meets Graphs: Challenges

Traditional DL is designed for simple grids or sequences

CNNs for fixed-size images/grids

RNNs for text/sequences

But nodes on graphs have different connections

Arbitrary neighbor size

Complex topological structure

No fixed node ordering

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J. Y. Choi. SNU

Graph Neural Networks

Graph-level

Node-level

Graph Convolutions Graph Convolutions

Activation Function

Representations

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J. Y. Choi. SNU

Machine Learning with Graphs

Node classification (semi-supervised Learning)

Predict a type of a given node

Link prediction

Predict whether two nodes are linked

Community detection (node clustering, unsupervised learning)

Identify densely linked clusters of nodes

Network similarity

How similar are two (sub)networks

Ranking

Page ranking in Web.

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56 7

node

edge

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J. Y. Choi. SNU

Course Objective

To be sure to grasp new concepts related with GCN

To become familiar with the new terms related with GCN

To learn the underlying theory for GCN (graph spectral theory)

To derive formulas related with GCN

To introduce recent GCN structures

To be experienced with the coding for GCN and applications

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J. Y. Choi. SNU

References:

Graphs in Machine Learning, Michal Valko, DeepMind Paris and Inria Lille

Graph Spectral Theory

Graph Cut

Graph Node Clustering

Graph Laplacian

Laplacian Smoothing

Semi-supervised Learning (SSL) with Graph

Online SSL and SSL for large graph

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J. Y. Choi. SNU

References:

Graph Neural Networks: Models and Applications(AAAI 2020 Tutorial), Yao Ma, Wei Jin, and Jiliang Tang, Michigan State University; Lingfei Wu and Tengfei Ma, IBM Research

Graph Convolution Networks (GCN)

Graph Filtering in GCN

Graph Pooling in GCN

Spectral Filtering in GCN

Spatial Filtering in GCN

Recent GCN papers

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J. Y. Choi. SNU

References:

Geometric Deep Learning on graph and manifolds, Michael Bronstein, SIAM 2018, Imperial College London

Basics of deep learning

Basics of graph theory and differential geometry

Spectral analysis on graphs and manifolds (in Hilbert Space)

Spectral-domain geometric deep learning methods

Spatial-domain geometric deep learning methods

Applications: network analysis, recommender systems, computer graphics and vision, chemistry, high-energy physics, drug design, etc

Geometric Deep Learning, Gong et al., Imperial College London

Machine Learning with Graphs, Jurij Leskovec, Stanford University

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J. Y. Choi. SNU

Course Plan

(1 주)

• Definition of Graph

• Node, Edge

• Affinity Matrix

(2 주)

• Spectral Clustering

• Graph Laplacian

(3 주)

• Graph Random Walk

• Diffusion

• Applications of Graph

(4 주)

• Node classification

• Link prediction

• Community detection

(5 주)

• Network similarity

• Feature Learning in Graphs

• Node embedding

(6주)

• Adjacency-based Similarity

• Multi-hop Similarity

• Random-walk Embedding

• Graph Neural Networks (GNN)

(7 주)

• Embedding Nodes

• Deep Encoder

(8 주)

• 중간고사 (50%)

• Review

(9주)

• Similarity function

• Neighborhood Aggregation

(10 주)

• Neighborhood Convolutions

• Training for Embedding

• Graph Convolutional Networks (GCN)

(11 주)

• Basic GCN configuration

• MPNN (Message Passing Neural Networks)

(12 주)

• GraphSage (Aggregate then Update)

• SGC (Simplifying GCN)

(13 주)

• GAT (Graph AttentionNetworks)

• GIN (Graph IsomorphismNetworks)

(14 주)

• JK (Jumping Knowledge)

• APPNP (Approximated Personalized Propagation of Neural Predictions)

• PAG (Position Aware Graph Neural Networks)

• Applications of Graph Convolutional Networks (GCN)

(15주)

• Select one paper and Reproducing (Term Project 50%)

• Presentation

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