Graph Embedding via Spectral Ego-Graph Analysis
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Solution Overview
Problem
Existing graph embedding techniques fail to accurately reflect structural characteristics of graphs, leading to degraded performance in tasks that rely on these features, such as isomorphic graph determination.
Innovation Solution
A method that calculates spectral information from ego-graphs and sub-graphs, incorporating eigenvalues, eigenvectors, and angle information, and uses this information along with node data to generate embedding representations through a modified Weisfeiler-Lehman algorithm and graph neural networks, ensuring the structural characteristics are preserved and aggregated effectively.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If graph embedding techniques use only node information aggregation through GNN, then the processing is simple, but structural characteristics of the graph are not reflected
Solution Approach 1:
The patent merges node information aggregation (through GNN) with spectral information aggregation (through eigenvalue/eigenvector calculations) to create a comprehensive graph embedding that preserves both local node characteristics and global structural properties. This combination resolves the contradiction by integrating multiple information sources rather than relying on a single approach.
Solution Approach 2:
The patent creates a composite embedding representation that combines different types of graph information (node features, spectral features, structural features) similar to how composite materials combine different substances. This composite approach ensures that structural characteristics are not lost while maintaining processing efficiency through the synergistic effect of multiple information types.
2Loss of information
If spectral information is calculated from the entire graph, then global structural information is captured, but computational complexity increases significantly
Solution Approach 1:
The patent segments the graph into ego-graphs (local subgraphs centered at each node) and calculates spectral information for each segment independently. This segmentation approach captures local structural characteristics without requiring computation on the entire graph, thereby reducing computational complexity while preserving essential structural information.
Solution Approach 2:
The patent calculates spectral information for partial graphs (ego-graphs) rather than the complete graph. This partial action is sufficient to capture the necessary structural characteristics for embedding purposes, avoiding the excessive computational burden of processing the entire graph while maintaining information quality.
3Measurement precision
If multiple types of graph information are aggregated, then embedding expressiveness improves, but information loss during aggregation increases
Solution Approach 1:
The patent introduces spectral information (eigenvalues and eigenvectors) as an intermediary representation that bridges node information and global graph structure. This intermediary captures structural characteristics in a compressed form that can be aggregated with node information without significant loss, acting as a mediator that preserves essential structural properties during the aggregation process.
Solution Approach 2:
The patent transforms graph structural information into spectral parameters (eigenvalues and eigenvectors) that provide a different representation of the same underlying structure. This parameter transformation allows for more efficient aggregation with node information while preserving structural characteristics, as the spectral parameters encode structural properties in a form that is easier to combine with node features without information loss.
Data Source
AI summary
Provided are a method for processing a graph and system therefor. The method according to some embodiments may include calculating spectral information associated with a target graph, and generating an embedding representation of the target graph based on information on nodes constituting the target graph and the spectral information.