Ranking and synchronization from pairwise measurements via SVD - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Journal of Machine Learning Research Year : 2021

Ranking and synchronization from pairwise measurements via SVD


Given a measurement graph $G= (V,E)$ and an unknown signal $r \in \mathbb{R}^n$, we investigate algorithms for recovering $r$ from pairwise measurements of the form $r_i - r_j$; $\{i,j\} \in E$. This problem arises in a variety of applications, such as ranking teams in sports data and time synchronization of distributed networks. Framed in the context of ranking, the task is to recover the ranking of $n$ teams (induced by $r$) given a small subset of noisy pairwise rank offsets. We propose a simple SVD-based algorithmic pipeline for both the problem of time synchronization and ranking. We provide a detailed theoretical analysis in terms of robustness against both sampling sparsity and noise perturbations with outliers, using results from matrix perturbation and random matrix theory. Our theoretical findings are complemented by a detailed set of numerical experiments on both synthetic and real data, showcasing the competitiveness of our proposed algorithms with other state-of-the-art methods.
Fichier principal
Vignette du fichier
19-542.pdf (11.25 Mo) Télécharger le fichier
Origin Publisher files allowed on an open archive

Dates and versions

hal-02340372 , version 1 (29-05-2024)




Alexandre d'Aspremont, Mihai Cucuringu, Hemant Tyagi. Ranking and synchronization from pairwise measurements via SVD. Journal of Machine Learning Research, 2021, 22 (19), pp.1-63. ⟨10.48550/arXiv.1906.02746⟩. ⟨hal-02340372⟩
4581 View
2 Download



Gmail Mastodon Facebook X LinkedIn More