Joint Embedding of Graphs.

Area of Science:

• Graph Theory
• Network Analysis
• Machine Learning

Background:

• Feature extraction and dimension reduction are crucial for network analysis across various domains.
• Learning features for multiple graphs is essential for statistical inference on graphs.

Purpose of the Study:

• To propose a novel method for jointly embedding multiple undirected graphs.
• To develop a generalized random graph model for multiple graphs.

Main Methods:

• The joint embedding method identifies a linear subspace and projects graph adjacency matrices.
• Projection coefficients serve as graph features, and embedding components represent vertex features.
• A new random graph model is proposed, generalizing classical models.

Main Results:

• The joint embedding method yields parameter estimates with minimal errors under the proposed model.
• Simulation experiments show state-of-the-art performance in graph classification using extracted features.
• Application to human brain graphs reveals interpretable features and high prediction accuracy.

Conclusions:

• The joint embedding method effectively extracts features from multiple graphs.
• This approach achieves superior performance in graph classification tasks.
• Interpretable features are extracted for applications like human brain network analysis.