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Vector-Valued Graph Trend Filtering with Non-Convex Penalties.

Rohan Varma1, Harlin Lee1, Jelena Kovačević2

  • 1Dept. of Electrical and Computer Engineering, Carnegie Mellon University.

IEEE Transactions on Signal and Information Processing Over Networks
|March 22, 2021
PubMed
Summary
This summary is machine-generated.

This study introduces non-convex regularizers for denoising vector-valued graph signals, improving recovery performance. The proposed graph trend filtering method offers statistically sound error rates and efficient algorithmic solutions.

Keywords:
graph signal processinggraph trend filteringnon-convex optimizationsemi-supervised classification

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Area of Science:

  • Graph Signal Processing
  • Machine Learning
  • Optimization

Background:

  • Graph signals can be vector-valued and exhibit varying smoothness.
  • Existing convex regularizers have limitations in denoising such signals.

Purpose of the Study:

  • To develop a robust framework for denoising vector-valued piecewise smooth graph signals.
  • To introduce non-convex regularizers that outperform convex alternatives.
  • To analyze the statistical properties and algorithmic convergence of the proposed method.

Main Methods:

  • Extension of the graph trend filtering framework.
  • Application of a family of non-convex regularizers.
  • Statistical error rate analysis using oracle inequalities.
  • Development of an Alternating Direction Method of Multipliers (ADMM)-based algorithm.

Main Results:

  • Superior signal recovery performance compared to convex regularizers.
  • Established statistical error rates for first-order stationary points.
  • Demonstrated convergence of the ADMM-based algorithm.
  • Successful application in denoising, support recovery, event detection, and semi-supervised classification.

Conclusions:

  • The proposed non-convex approach provides a powerful tool for vector-valued graph signal denoising.
  • The method is statistically rigorous and computationally efficient.
  • The framework is versatile, applicable to various graph-based data analysis tasks.