Graph Embedding Using Frequency Filtering.

Area of Science:

• Graph theory
• Machine learning
• Signal processing

Background:

• Graph embedding aims to represent graphs as feature vectors capturing similarities and differences.
• Existing spectral embedding methods have limitations in adapting to diverse graph datasets.

Purpose of the Study:

• To propose a novel graph embedding method, Frequency Filtering Embedding (FFE), and its generalized version, GeFFE.
• To enhance graph feature extraction using graph Fourier transform and frequency filtering.
• To address limitations of previous spectral embedding techniques and the cospectrality problem.

Main Methods:

• Developed Frequency Filtering Embedding (FFE) utilizing graph Fourier transform and frequency filtering.
• Introduced novel filter sets: heat, anti-heat, part-sine, and identity.
• Proposed a generalized version, GeFFE, with pseudo-Fourier operators for adaptability.
• Demonstrated GeFFE's capability as a general framework for existing invariants.

Main Results:

• FFE and GeFFE effectively extract graph features by amplifying or attenuating selected frequencies.
• GeFFE demonstrated superior classification accuracy compared to existing methods, especially with the part-sine filter set.
• GeFFE successfully resolved the cospectrality problem across tested datasets.
• GeFFE's flexibility allows adaptation to specific graph dataset properties.

Conclusions:

• Frequency Filtering Embedding (FFE) and its generalized version (GeFFE) offer a powerful approach to graph embedding.
• GeFFE provides a flexible framework that enhances classification accuracy and overcomes the cospectrality problem.
• The proposed filtering techniques and generalized operators represent a significant advancement in spectral graph embedding.