On the Impact of Sample Size in Reconstructing Graph Signals

TL;DR

This paper investigates how increasing the number of observations affects the accuracy of reconstructing signals on graphs, revealing that more data does not always lead to better results under certain noisy conditions.

Contribution

It provides a theoretical and experimental analysis showing that additional observations may not always improve graph signal reconstruction accuracy in noisy settings.

Findings

Adding observations does not always reduce reconstruction error.

Theoretical characterization of when more data helps or hinders.

Experimental validation of the non-monotonic behavior.

Abstract

Reconstructing a signal on a graph from observations on a subset of the vertices is a fundamental problem in the field of graph signal processing. It is often assumed that adding additional observations to an observation set will reduce the expected reconstruction error. We show that under the setting of noisy observation and least-squares reconstruction this is not always the case, characterising the behaviour both theoretically and experimentally.