کنفرانس مهندسی برق ایران

صفحه اصلی / سی و دومین کنفرانس بین المللی مهندسی برق

Partitioning-based Graph Signal Denoising via Heat Kernel Smoothing

نویسندگان :

Mohammadreza Fattahi¹ Hamid Saeedi-Sourck² Vahid Abootalebi³

1- دانشگاه یزد 2- دانشگاه یزد 3- دانشگاه یزد

کلمات کلیدی :

Graph signal processing،denoising،partitioning،Fiedler’s theorem

چکیده :

Abstract—The objective of graph signal denoising is to extract a clean signal from a noisy dataset while maintaining the graph’s inherent structure. Dealing with large-scale graphs introduce significant computational complexities, urging us to explore low-complexity methods that leverage their potential decomposability. This study focuses on graph signal denoising using two techniques: heat kernel smoothing and Fiedler’s method for graph partitioning. Fiedler’s theorem divides the graph recursively based on the sign of the Fiedler vector, which corresponds to the second smallest eigenvalue of the graph Laplacian. Our findings demonstrate that parallelly applying heat kernel smoothing separately to each subgraph yields less computational complexity compared to its application to the entire graph. This improvement stems from the decomposability of subgraphs, effectively preventing kernel approximation issues on the primary graph. Additionally, we aggregate the denoised signals from different subgraphs into a unified denoised signal. We evaluate the effectiveness of our method across various graphs by comparing input and output signal-to-noise ratios, highlighting its performance relative to kernel estimation, especially on larger graphs.