# Graph sampling with determinantal processes

## TL;DR

This paper introduces a novel graph sampling method using determinantal point processes, enabling efficient and accurate signal recovery on large graphs, especially those with community structures, by leveraging spectral properties or random walks.

## Contribution

It proposes a new DPP-based sampling strategy for graph signals that works efficiently on large graphs without requiring spectral access, with theoretical and empirical validation.

## Key findings

- Perfect recovery on small graphs with accessible spectrum.
- Effective sampling on large graphs using loop-erased random walks.
- Promising results on graphs with strong community structures.

## Abstract

We present a new random sampling strategy for k-bandlimited signals defined on graphs, based on determinantal point processes (DPP). For small graphs, ie, in cases where the spectrum of the graph is accessible, we exhibit a DPP sampling scheme that enables perfect recovery of bandlimited signals. For large graphs, ie, in cases where the graph's spectrum is not accessible, we investigate, both theoretically and empirically, a sub-optimal but much faster DPP based on loop-erased random walks on the graph. Preliminary experiments show promising results especially in cases where the number of measurements should stay as small as possible and for graphs that have a strong community structure. Our sampling scheme is efficient and can be applied to graphs with up to $10^6$ nodes.