A Graph Downsampling Technique Based On Graph Fourier Transform

TL;DR

This paper introduces a novel graph downsampling method based on the Graph Fourier Transform that applies to various graph types, providing a quality measure and a greedy algorithm for effective signal reduction.

Contribution

It presents a spectral property-based downsampling approach applicable to directed and undirected graphs, along with a new quality measure and a greedy algorithm.

Findings

The method effectively downscales signals on different graph types.

The proposed quality measure correlates well with existing metrics like normalized cuts.

Experiments demonstrate improved flexibility and applicability over existing approaches.

Abstract

In this paper, we provide a Graph Fourier Transform based approach to downsample signals on graphs. For bandlimited signals on a graph, a test is provided to identify whether signal reconstruction is possible from the given downsampled signal. Moreover, if the signal is not bandlimited, we provide a quality measure for comparing different downsampling schemes. Using this quality measure, we propose a greedy downsampling algorithm. Most of the prevailing approaches consider undirected graphs, and exploit the topological properties of the graph in order to downsample the grid, while the proposed method exploits spectral properties of graph signals, and is applicable to directed graphs, undirected graphs, and graphs with negative edge-weights. We provide several experiments demonstrating our downsampling scheme, and compare our quality measure with measures like normalized cuts.