Embedding graphs on Grassmann manifold.

Area of Science:

• Graph representation learning
• Machine learning on graphs
• Manifold learning

Background:

• Efficient graph representation is crucial for downstream tasks like property prediction.
• Non-Euclidean graph data requires specialized methods to preserve similarity in embeddings.
• Existing techniques may struggle with capturing higher-order graph structures.

Purpose of the Study:

• To develop a novel graph representation learning scheme named Egg.
• To embed approximated second-order graph characteristics into a Grassmann manifold.
• To improve the accuracy of node and graph property prediction.

Main Methods:

• Leveraging graph convolutions to learn hidden representations.
• Mapping graph representations to a Grassmann manifold via truncated Singular Value Decomposition (SVD).
• Utilizing a symmetric matrix space for Euclidean calculations to approximate denoised attribute correlationships.

Main Results:

• The Egg method demonstrates effectiveness in both node-level and graph-level clustering and classification tasks.
• Egg outperforms existing baseline models across various benchmark datasets.
• The learned embeddings approximate denoised correlationships of node attributes.

Conclusions:

• Egg provides an effective approach for learning graph representations by utilizing Grassmann manifolds.
• The method shows strong performance on diverse graph-based machine learning tasks.
• Egg offers a promising direction for capturing complex graph structures and relationships.