Multi-view Hyperbolic Graph Neural Network for Hierarchical Structure Preservation
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Solution Overview
Problem
Existing graph neural networks primarily use single-view information, leading to information loss and distortion when representing graphs with scale-free or hierarchical structures, as they embed graphs in Euclidean space, which fails to preserve hyperbolic geometry and hierarchical information effectively.
Innovation Solution
A multi-view hyperbolic-hyperbolic graph representation learning method is proposed, constructing multiple views from graph topological structures and node features, using hyperbolic geometry to minimize distortion by performing graph operations in the hyperbolic space, including hyperbolic graph convolution, pooling, and attention fusion to obtain accurate node representations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If graphs are embedded in Euclidean space, then the embedding process is simple and computationally efficient, but the hierarchical structure and scale-free properties of real-world graphs are distorted and cannot be preserved
Solution Approach 1:
The patent changes the geometric parameter of the embedding space from Euclidean (flat) to hyperbolic (curved with constant negative curvature). This parameter change allows the space to naturally accommodate hierarchical and scale-free structures by providing exponential volume growth with radius, matching the structural properties of real-world graphs while maintaining mathematical tractability through well-defined transformation operations.
Solution Approach 2:
The patent applies curvature by using hyperbolic space instead of flat Euclidean space. The hyperbolic geometry's negative curvature provides the necessary geometric properties to preserve hierarchical relationships and power-law degree distributions. The curvature enables exponential expansion of available embedding space, allowing accurate representation of tree-like and hierarchical graph structures without the distortion inherent in Euclidean embeddings.
2Device complexity
If single-view information is used for graph representation learning, then the model complexity is reduced, but information loss occurs and the representation accuracy decreases
Solution Approach 1:
The patent segments the graph representation into multiple views, where each view captures different aspects of the graph structure and node properties. By dividing the complex graph data into multiple complementary perspectives (e.g., different topological structures, different feature representations), the model can process each view separately and then integrate them, reducing the complexity of processing the entire graph at once while preserving comprehensive information.
Solution Approach 2:
The patent merges multiple view representations into a unified graph representation. By combining the information from different views through appropriate fusion mechanisms, the model recovers the complete graph information that would be lost in single-view approaches. This merging process allows the model to leverage complementary information from each view, achieving more accurate and robust node representations.
3Ease of operation
If tangent space is used for neighborhood aggregation in hyperbolic graph neural networks, then the computation is simplified, but the hyperbolic geometry properties and hierarchical structure are not strictly preserved
Solution Approach 1:
The patent introduces proper hyperbolic operations and transformations as intermediaries to bridge the gap between computational simplicity and geometric fidelity. Instead of directly using Euclidean tangent space operations that approximate hyperbolic geometry, the patent employs dedicated hyperbolic linear algebra operations, hyperbolic activation functions, and geodesic-based neighborhood aggregation that strictly preserve hyperbolic geometry while remaining computationally tractable through well-designed algorithms.
Data Source
AI summary
The present disclosure belongs to application in the field of deep learning and graph neural networks, and particularly relates to a multi-view hyperbolic-hyperbolic graph representation learning method. Two views are constructed based on a topological relation of nodes and node attributes, then an adjacency matrix and the two views generated are input into a hyperbolic-hyperbolic graph neural network to obtain node representations of three views, graph embedding representations of different views are obtained by performing hyperbolic-hyperbolic convolution and pooling on the node representations of the three views, the graph embedding representations are concatenated and input into a Lorentz multilayer perceptron (MLP) layer to obtain attention scores of the views, and with a hyperbolic-hyperbolic weighted representation, a multi-view based node embedding representation is obtained.