The Phantom Alignment Strength Conjecture: Practical use of graph matching alignment strength to indicate a meaningful graph match

The alignment strength of a graph matching is a quantity that gives the practitioner a measure of the correlation of the two graphs, and it can also give the practitioner a sense for whether the graph matching algorithm found the true matching. Unfortunately, when a graph matching algorithm fails to...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2021-08
Main Authors: Fishkind, Donniell E, Parker, Felix, Hamilton Sawczuk, Meng, Lingyao, Bridgeford, Eric, Athreya, Avanti, Priebe, Carey E, Lyzinski, Vince
Format: Article
Language:English
Subjects:
Algorithms
Alignment
Correlation analysis
Graph matching
Random noise
Strength
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The alignment strength of a graph matching is a quantity that gives the practitioner a measure of the correlation of the two graphs, and it can also give the practitioner a sense for whether the graph matching algorithm found the true matching. Unfortunately, when a graph matching algorithm fails to find the truth because of weak signal, there may be "phantom alignment strength" from meaningless matchings that, by random noise, have fewer disagreements than average (sometimes substantially fewer); this alignment strength may give the misleading appearance of significance. A practitioner needs to know what level of alignment strength may be phantom alignment strength and what level indicates that the graph matching algorithm obtained the true matching and is a meaningful measure of the graph correlation. The {\it Phantom Alignment Strength Conjecture} introduced here provides a principled and practical means to approach this issue. We provide empirical evidence for the conjecture, and explore its consequences.
ISSN:2331-8422
DOI:10.48550/arxiv.2103.00624