Phase transitions and optimal algorithms in high-dimensional Gaussian mixture clustering - Université Pierre et Marie Curie Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2016

Phase transitions and optimal algorithms in high-dimensional Gaussian mixture clustering

Résumé

We consider the problem of Gaussian mixture clustering in the high-dimensional limit where the data consists of $m$ points in $n$ dimensions, $n,m \rightarrow \infty$ and $\alpha = m/n$ stays finite. Using exact but non-rigorous methods from statistical physics, we determine the critical value of $\alpha$ and the distance between the clusters at which it becomes information-theoretically possible to reconstruct the membership into clusters better than chance. We also determine the accuracy achievable by the Bayes-optimal estimation algorithm. In particular, we find that when the number of clusters is sufficiently large, $r > 4 + 2 \sqrt{\alpha}$, there is a gap between the threshold for information-theoretically optimal performance and the threshold at which known algorithms succeed.
Fichier principal
Vignette du fichier
1610.02918v1.pdf (479.09 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

cea-01448112 , version 1 (27-01-2017)

Identifiants

Citer

Thibault Lesieur, Caterina de Bacco, Jess Banks, Florent Krzakala, Cris Moore, et al.. Phase transitions and optimal algorithms in high-dimensional Gaussian mixture clustering. 2016. ⟨cea-01448112⟩
217 Consultations
333 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More