Eigendecomposition-Free Sampling Set Selection for Graph Signals

TL;DR

This paper introduces an eigendecomposition-free sampling set selection method for graph signals that efficiently considers frequency information without eigendecomposition, improving prediction accuracy and computational speed.

Contribution

The proposed method offers a novel approach to sampling set selection on graphs that avoids eigendecomposition while incorporating spectral domain localization.

Findings

Reduces computation time compared to eigendecomposition-based methods.

Achieves comparable or better prediction accuracy.

Demonstrates effectiveness through empirical evaluations.

Abstract

This paper addresses the problem of selecting an optimal sampling set for signals on graphs. The proposed sampling set selection (SSS) is based on a localization operator that can consider both vertex domain and spectral domain localization. We clarify the relationships among the proposed method, sensor position selection methods in machine learning, and conventional SSS methods based on graph frequency. In contrast to the conventional graph signal processing-based approaches, the proposed method does not need to compute the eigendecomposition of a variation operator, while still considering (graph) frequency information. We evaluate the performance of our approach through comparisons of prediction errors and execution time.