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Graph Embedding Using Frequency Filtering

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JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
DateAccepted/In press - 15 Jul 2019
DateE-pub ahead of print - 29 Jul 2019
DatePublished (current) - 1 Feb 2021
Issue number2
Volume43
Number of pages12
Pages (from-to)473-484
Early online date29/07/19
Original languageEnglish

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.

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