Graph Embedding via Edge Filtration and Topology Extraction
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Solution Overview
Problem
Existing graph embedding techniques, such as those based on the Weisfeiler-Lehman algorithm and node filtration, fail to capture topology information effectively, limiting their expressive power and performance in graph tasks like classification and distinction.
Innovation Solution
A method that calculates edge weights based on node color values and generates edge filtrations using these weights as a connectivity metric, extracting topology information to create a more expressive embedding representation through neural networks.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If graph embedding techniques based on Weisfeiler-Lehman algorithm and neighboring node aggregation are used, then computational efficiency is maintained, but topology information capture capability deteriorates
Solution Approach 1:
The patent segments the graph embedding process into distinct stages: first performing node filtration to capture local topology, then performing edge filtration to capture global connectivity patterns. This segmentation allows each stage to focus on specific topology aspects, improving overall topology capture capability while maintaining manageable computational complexity through staged processing.
Solution Approach 2:
The patent transitions from node-centric filtration to edge-centric filtration, adding a new dimension to the embedding process. By filtering edges based on their connectivity patterns and using edge filtrations in conjunction with node filtrations, the method captures topology information that was previously inaccessible to node-based approaches alone.
2Measurement precision
If node filtration-based graph embedding is used, then node-level topology is captured, but edge-level connectivity information is lost
Solution Approach 1:
The patent merges node filtration and edge filtration into a unified embedding framework. Node filtrations capture local topology around each node, while edge filtrations capture global connectivity patterns. By combining both types of filtrations and their corresponding embeddings, the method recovers both node-level and edge-level information that would otherwise be lost separately.
3Productivity
If traditional graph embedding methods are used, then computational resources are efficient, but expressive power for graph tasks deteriorates
Solution Approach 1:
The patent performs preliminary node filtration and edge filtration to extract topological features before the final embedding computation. This preliminary action organizes the graph data into structured representations (node filtrations and edge filtrations) that can be efficiently processed in subsequent embedding stages, maintaining computational efficiency while enhancing expressive power for downstream graph tasks.
Data Source
AI summary
A method for embedding a graph and a system therefor are provided. The method according to some embodiments may include acquiring a colored graph for a target graph, calculating an edge weight for the colored graph based on node color values of the colored graph, generating an edge filtration for the colored graph using the edge weight as a connectivity metric between nodes, and generating an embedding representation of the target graph based on topology information extracted from the edge filtration.