Sampling Large Data on Graphs

TL;DR

This paper introduces methods to precisely compute the cut-off frequency for bandlimited signals on graphs and develops algorithms to select optimal sampling nodes, improving data reconstruction efficiency on large graphs.

Contribution

It provides an exact computation of the cut-off frequency and algorithms for optimal node subset selection based on spectral graph theory.

Findings

Exact computation of the cut-off frequency for graph signals.

Algorithms for selecting node subsets with optimal spectral properties.

Analysis of random sampling performance versus optimal algorithms.

Abstract

We consider the problem of sampling from data defined on the nodes of a weighted graph, where the edge weights capture the data correlation structure. As shown recently, using spectral graph theory one can define a cut-off frequency for the bandlimited graph signals that can be reconstructed from a given set of samples (i.e., graph nodes). In this work, we show how this cut-off frequency can be computed exactly. Using this characterization, we provide efficient algorithms for finding the subset of nodes of a given size with the largest cut-off frequency and for finding the smallest subset of nodes with a given cut-off frequency. In addition, we study the performance of random uniform sampling when compared to the centralized optimal sampling provided by the proposed algorithms.