# Random Walk Sampling for Big Data over Networks

## TL;DR

This paper introduces a random walk-based sampling strategy for recovering smooth graph signals efficiently, leveraging the network nullspace property, with demonstrated success on synthetic and real-world datasets.

## Contribution

It proposes a novel sampling method for smooth graph signals using random walks, grounded in the network nullspace property, enhancing recovery accuracy.

## Key findings

- Effective recovery of graph signals from few samples
- Successful application on synthetic and real-world data
- Demonstrated superiority over existing sampling methods

## Abstract

It has been shown recently that graph signals with small total variation can be accurately recovered from only few samples if the sampling set satisfies a certain condition, referred to as the network nullspace property. Based on this recovery condition, we propose a sampling strategy for smooth graph signals based on random walks. Numerical experiments demonstrate the effectiveness of this approach for graph signals obtained from a synthetic random graph model as well as a real-world dataset.