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

Jordi Belda1, Luis Vergara1, Gonzalo Safont1

  • 1Institute of Telecommunications and Multimedia Applications, Universitat Politècnica de València, 46022 València, Spain.

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Summary
This summary is machine-generated.

This study introduces a novel graph Fourier transform method for creating surrogate graph signals. This approach offers greater flexibility in preserving signal properties, aiding classifier training with limited data.

Keywords:
Hermitian Laplacian matrixgraph Fourier transformsurrogates

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Area of Science:

  • Graph Signal Processing
  • Machine Learning
  • Data Augmentation

Background:

  • Surrogating algorithms typically involve phase randomization of the Fourier transform while maintaining spectrum amplitude.
  • This process is crucial for generating synthetic data that preserves essential signal characteristics.

Purpose of the Study:

  • To propose a new method for surrogating graph signals using the graph Fourier transform.
  • To enhance flexibility in defining and preserving properties of original graph signals in their surrogates.
  • To address the challenge of limited data instances in classifier training.

Main Methods:

  • Development of a complex graph Fourier transform based on a Hermitian Laplacian matrix.
  • Utilizing eigenvectors of the Hermitian Laplacian matrix as the basis for the transform.
  • Allowing unconstrained phase randomization in the transformed domain for the complex case.

Main Results:

  • Demonstration that the Hermitian Laplacian matrix can exhibit negative eigenvalues.
  • Showing that preserving graph spectrum amplitude leads to controllable invariances defined by the Hermitian Laplacian matrix.
  • Validation of the method's utility in scenarios with scarce data for classifier training.

Conclusions:

  • The proposed graph Fourier transform method provides a flexible framework for generating graph signal surrogates.
  • This technique is particularly valuable for data augmentation in machine learning, especially when dealing with limited datasets.
  • The control over invariances through the Hermitian Laplacian matrix offers new possibilities in signal processing and analysis.