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Open AccessFeature PaperArticle

A New Surrogating Algorithm by the Complex Graph Fourier Transform (CGFT)

1
Institute of Telecommunications and Multimedia Applications, Universitat Politècnica de València, 46022 València, Spain
2
Sciling SL, C/Camí a La Mar 75, 46022 València, Spain
*
Author to whom correspondence should be addressed.
Entropy 2019, 21(8), 759; https://doi.org/10.3390/e21080759
Received: 4 July 2019 / Revised: 31 July 2019 / Accepted: 2 August 2019 / Published: 4 August 2019
(This article belongs to the Special Issue Information Theory and Graph Signal Processing)
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Abstract

The essential step of surrogating algorithms is phase randomizing the Fourier transform while preserving the original spectrum amplitude before computing the inverse Fourier transform. In this paper, we propose a new method which considers the graph Fourier transform. In this manner, much more flexibility is gained to define properties of the original graph signal which are to be preserved in the surrogates. The complex case is considered to allow unconstrained phase randomization in the transformed domain, hence we define a Hermitian Laplacian matrix that models the graph topology, whose eigenvectors form the basis of a complex graph Fourier transform. We have shown that the Hermitian Laplacian matrix may have negative eigenvalues. We also show in the paper that preserving the graph spectrum amplitude implies several invariances that can be controlled by the selected Hermitian Laplacian matrix. The interest of surrogating graph signals has been illustrated in the context of scarcity of instances in classifier training. View Full-Text
Keywords: surrogates; graph Fourier transform; Hermitian Laplacian matrix surrogates; graph Fourier transform; Hermitian Laplacian matrix
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Belda, J.; Vergara, L.; Safont, G.; Salazar, A.; Parcheta, Z. A New Surrogating Algorithm by the Complex Graph Fourier Transform (CGFT). Entropy 2019, 21, 759.

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