Embedding Graphs on Grassmann Manifold

Abstract

Learning efficient graph representation is the key to favorably addressing downstream tasks on graphs, such as node or graph property prediction. Given the non-Euclidean structural property of graphs, preserving the original graph data's similarity relationship in the embedded space needs specific tools and a similarity metric. This paper develops a new graph representation learning scheme, namely EGG, which embeds approximated second-order graph characteristics into a Grassmann manifold. The proposed strategy leverages graph convolutions to learn hidden representations of the corresponding subspace of the graph, which is then mapped to a Grassmann point of a low dimensional manifold through truncated singular value decomposition (SVD). The established graph embedding approximates denoised correlationship of node attributes, as implemented in the form of a symmetric matrix space for Euclidean calculation. The effectiveness of EGG is demonstrated using both clustering and classification tasks at the node level and graph level. It outperforms baseline models on various benchmarks.

References in corpus (20)

• A Comprehensive Survey on Graph Neural Networks
• Semi-Supervised Classification with Graph Convolutional Networks
• Inductive Representation Learning on Large Graphs
• Geometric deep learning: going beyond Euclidean data
• Spectral Networks and Locally Connected Networks on Graphs
• Fast Graph Representation Learning with PyTorch Geometric
• Representation Learning on Graphs with Jumping Knowledge Networks
• Open Graph Benchmark: Datasets for Machine Learning on Graphs
• TUDataset: A collection of benchmark datasets for learning with graphs
• Revisiting Semi-Supervised Learning with Graph Embeddings
• Clustering on Multi-Layer Graphs via Subspace Analysis on Grassmann Manifolds
• Towards Sparse Hierarchical Graph Classifiers
• How to Find Your Friendly Neighborhood: Graph Attention Design with Self-Supervision
• Edge Contraction Pooling for Graph Neural Networks
• Second-Order Pooling for Graph Neural Networks
• Understanding Attention and Generalization in Graph Neural Networks
• GNN-FiLM: Graph Neural Networks with Feature-wise Linear Modulation
• Path Integral Based Convolution and Pooling for Graph Neural Networks
• Wiki-CS: A Wikipedia-Based Benchmark for Graph Neural Networks
• MathNet: Haar-Like Wavelet Multiresolution-Analysis for Graph Representation and Learning