# Graph Embedding Using Frequency Filtering

### Abstract

The target of graph embedding is to embed graphs in vector space such that the embedded feature vectors follow the differences and similarities of the source graphs. In this paper, a novel method named Frequency Filtering Embedding (FFE) is proposed which uses graph Fourier transform and Frequency filtering as a graph Fourier domain operator for graph feature extraction. Frequency filtering amplifies or attenuates selected frequencies using appropriate filter functions. Here, heat, anti-heat, part-sine and identity filter sets are proposed as the filter functions. A generalized version of FFE named GeFFE is also proposed by defining pseudo-Fourier operators. This method can be considered as a general framework for formulating some previously defined invariants in other works by choosing a suitable filter bank and defining suitable pseudo-Fourier operators. This flexibility empowers GeFFE to adapt itself to the properties of each graph dataset unlike the previous spectral embedding methods and leads to superior classification accuracy relative to the others. Utilizing the proposed part-sine filter set which its members filter different parts of the spectrum in turn improves the classification accuracy of GeFFE method. Additionally GeFFE resolves the cospectrality problem entirely in tested datasets.

Publication
IEEE Transactions on Pattern Analysis and Machine Intelligence
Date

## Bibtex

@ARTICLE{8778695,
author={H. {Bahonar} and A. {Mirzaei} and S. {Sadri} and R. {Wilson}},
journal={IEEE Transactions on Pattern Analysis and Machine Intelligence},
title={Graph Embedding Using Frequency Filtering},
year={2019},
volume={},
number={},
pages={1-1},
keywords={Feature extraction;Frequency-domain analysis;Pattern recognition;Fourier transforms;Eigenvalues and eigenfunctions;Filtering;Signal processing;Spectral graph embedding;graph Fourier transform;heat kernel;frequency filtering;graph classification},
doi={10.1109/TPAMI.2019.2929519},
ISSN={},
month={},}