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.
Highlights
Surrogate means that the (Fourier) spectrum amplitude of the original signal is retained while the phase is randomized
We propose a new method for generating surrogates which exploit the concept of graph signal processing [8,9,10]
14.82 any arbitrary domain are defined on the vertices of a graph, much more flexibility can be obtained byConclusions the new algorithms in comparison with traditional surrogating methods based on the Fourier transform (FT)
Summary
Starting from an available original signal, synthetic signals can be generated which are surrogates of it. In spite of its attractive approach, existing surrogating methods are too constrained due to the use of the Fourier transform (FT)—Both the original signal and its surrogates share the same autocorrelation function. This implies that pairwise interrelations are assumed to be the same for pairs of samples separated. The GFT represents the graph signal in a domain expanded by the eigenvectors of the graph Laplacian matrix This may lead to further extensions of the work presented here) [8,13]. The good results of this novel approach suggest continuing to working on it
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
