Towards joint graph learning and sampling set selection from data

TL;DR

This paper introduces a joint approach to graph learning and sampling set selection from data, proposing algorithms that improve reconstruction performance and reduce complexity compared to traditional two-step methods.

Contribution

It presents a novel joint optimization framework and algorithms (VIS and VISR) for simultaneous graph learning and sampling set selection from data.

Findings

Sampling with VIS and VISR achieves competitive reconstruction accuracy.

The proposed methods have lower complexity than traditional two-step approaches.

Empirical results validate the effectiveness of joint optimization in graph signal processing.

Abstract

We explore the problem of sampling graph signals in scenarios where the graph structure is not predefined and must be inferred from data. In this scenario, existing approaches rely on a two-step process, where a graph is learned first, followed by sampling. More generally, graph learning and graph signal sampling have been studied as two independent problems in the literature. This work provides a foundational step towards jointly optimizing the graph structure and sampling set. Our main contribution, Vertex Importance Sampling (VIS), is to show that the sampling set can be effectively determined from the vertex importance (node weights) obtained from graph learning. We further propose Vertex Importance Sampling with Repulsion (VISR), a greedy algorithm where spatially -separated "important" nodes are selected to ensure better reconstruction. Empirical results on simulated data show that sampling using VIS and VISR leads to competitive reconstruction performance and lower complexity than the conventional two-step approach of graph learning followed by graph sampling.