Introduction to Graph Neural Networks
Chapter 1: Foundations of Graph-Based Learning
What is Graph Data?
Limitations of Standard Neural Networks on Graphs
Common Graph Machine Learning Tasks
Representing Graphs: Adjacency and Feature Matrices
Graph Properties and Measurements
Introduction to the NetworkX Library
Hands-on: Loading and Inspecting a Graph Dataset
Chapter 2: The Message Passing Mechanism
The Neighborhood Aggregation Idea
A General GNN Layer: Aggregate and Update
Common Aggregation Functions
Update Functions and Non-Linearities
Permutation Invariance and Equivariance
Stacking Layers to Form a Deep GNN
Practice: A Simple GNN Layer with NumPy
Chapter 3: Foundational GNN Architectures
Graph Convolutional Networks (GCN)
A Spatial Interpretation of Graph Convolutions
GraphSAGE: Sampling and Aggregating Neighborhoods
Inductive Learning with GraphSAGE
Graph Attention Networks (GAT)
The Attention Mechanism in GATs
Comparing GCN, GraphSAGE, and GAT
Hands-on: Implementing a GCN from Scratch
Chapter 4: Training GNN Models
Setting up a GNN for Node Classification
Loss Functions for Graph Tasks
The Training Loop for GNNs
Data Splitting in Graphs: Transductive vs. Inductive
Evaluation Metrics for Node Classification
Overfitting and Regularization in GNNs
Practice: Training and Evaluating your GCN
Chapter 5: GNN Implementation with PyTorch Geometric
Introduction to PyTorch Geometric (PyG)
The PyG Data Object
Working with PyG Datasets
Building Models with PyG GNN Layers
Mini-Batching for Large Graphs
A Complete Training Script in PyG
Hands-on: Node Classification on the Cora Dataset with PyG
Update Functions and Non-Linearities
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- Semi-Supervised Classification with Graph Convolutional Networks, Thomas N. Kipf and Max Welling, 2017 International Conference on Learning Representations (ICLR) DOI: 10.48550/arXiv.1609.02907 - This foundational paper introduces Graph Convolutional Networks (GCNs), which use a specific update function combining separate linear transformations and summation before a non-linearity. This approach is explicitly mentioned as an alternative in the section and illustrates how non-linearities are integrated into GNN updates.
- Inductive Representation Learning on Large Graphs, William L. Hamilton, Rex Ying, and Jure Leskovec, 2017 Advances in Neural Information Processing Systems (NIPS) DOI: 10.48550/arXiv.1706.02216 - This paper introduces GraphSAGE, a prominent GNN architecture that employs update mechanisms similar to the general concatenation approach described in the section, often combining aggregated messages with self-features and applying non-linear transformations.
- Graph Representation Learning, William L. Hamilton, 2020 Synthesis Lectures on Artificial Intelligence and Machine Learning, Vol. 14 (Morgan & Claypool Publishers) DOI: 10.2200/S01045ED1V01Y202009AIM046 - This textbook provides a comprehensive theoretical and practical treatment of GNNs, including detailed explanations of message passing paradigms, aggregation and update functions, and the role of non-linearities in different GNN architectures.
- Graph Neural Networks: A Review of Methods and Applications, Jie Zhou, Ganqu Cui, Zhengyan Li, Mingxuan Wang, Lei Wang, 2021 AI Open, Vol. 2 (Elsevier) DOI: 10.1016/j.aiopen.2021.01.001 - This survey paper categorizes and reviews various GNN models, discussing their message passing mechanisms, including different aggregation and update function designs, and the importance of non-linear transformations in building expressive GNN layers.