Graph Embedding in the Graph Fractional Fourier Transform Domain

2025-08-04

AI Summary

Traditional spectral graph embedding methods are limited by the representational capacity of the Fourier domain, struggling to capture multiscale and non-local graph structural patterns. To address this, we propose Generalized Fractional Filtering Embedding (GEFRFE), the first framework to incorporate the Graph Fractional Fourier Transform (GFrFT) into spectral graph embedding, thereby constructing a novel embedding space in the fractional-order domain. GEFRFE introduces a dual-strategy dynamic order selection mechanism to adaptively match graph structural complexity, integrates fractional-order graph Laplacian eigendecomposition, learnable fractional-domain filtering, ResNet18-based feature fusion, and efficient search optimization. Evaluated on six benchmark datasets, GEFRFE achieves significant improvements in both node and graph classification accuracy, while maintaining computational complexity comparable to the baseline GEFFE. These results empirically validate the effectiveness and efficiency of fractional-order representations for modeling complex graph structures.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding

Abstract

Spectral graph embedding plays a critical role in graph representation learning by generating low-dimensional vector representations from graph spectral information. However, the embedding space of traditional spectral embedding methods often exhibit limited expressiveness, failing to exhaustively capture latent structural features across alternative transform domains. To address this issue, we use the graph fractional Fourier transform to extend the existing state-of-the-art generalized frequency filtering embedding (GEFFE) into fractional domains, giving birth to the generalized fractional filtering embedding (GEFRFE), which enhances embedding informativeness via the graph fractional domain. The GEFRFE leverages graph fractional domain filtering and a nonlinear composition of eigenvector components derived from a fractionalized graph Laplacian. To dynamically determine the fractional order, two parallel strategies are introduced: search-based optimization and a ResNet18-based adaptive learning. Extensive experiments on six benchmark datasets demonstrate that the GEFRFE captures richer structural features and significantly enhance classification performance. Notably, the proposed method retains computational complexity comparable to GEFFE approaches.

Problem

• Enhances graph embedding expressiveness in fractional domains
• Captures latent structural features via fractional Fourier transform
• Dynamically optimizes fractional order for improved classification

Innovation

• Extends GEFFE to fractional Fourier domains
• Uses graph fractional domain filtering
• Adaptive fractional order learning via ResNet18