On the Coherence Properties of Random Euclidean Distance Matrices

TL;DR

This paper investigates the coherence properties of random Euclidean distance matrices and establishes conditions for their successful recovery in matrix completion tasks, relevant to applications like sensor network localization.

Contribution

It provides new theoretical conditions for the recoverability of Euclidean distance matrices based on their coherence properties, advancing understanding in matrix completion.

Findings

Derived sufficient conditions for EDM recovery

Linked coherence properties to successful matrix completion

Applicable to sensor network localization scenarios

Abstract

In the present paper we focus on the coherence properties of general random Euclidean distance matrices, which are very closely related to the respective matrix completion problem. This problem is of great interest in several applications such as node localization in sensor networks with limited connectivity. Our results can directly provide the sufficient conditions under which an EDM can be successfully recovered with high probability from a limited number of measurements.