(Un)detectable cluster structure in sparse networks
| dc.creator | Reichardt, Joerg | |
| dc.creator | Leone, Michele | |
| dc.date | 2007-11-09 | |
| dc.date.accessioned | 2026-07-07T12:11:30Z | |
| dc.date.available | 2026-07-07T12:11:30Z | |
| dc.description | We study the problem of recovering a known cluster structure in a sparse network, also known as the planted partitioning problem, by means of statistical mechanics. We find a sharp transition from un-recoverable to recoverable structure as a function of the separation of the clusters. For multivariate data, such transitions have been observed frequently, but always as a function of the number of data points provided, i.e. given a large enough data set, two point clouds can always be recognized as different clusters, as long as their separation is non-zero. In contrast, for the sparse networks studied here, a cluster structure remains undetectable even in an infinitely large network if a critical separation is not exceeded. We give analytic formulas for this critical separation as a function of the degree distribution of the network and calculate the shape of the recoverability-transition. Our findings have implications for unsupervised learning and data-mining in relational data bases and provide bounds on the achievable performance of graph clustering algorithms. | |
| dc.description | 4 Pages, 2 Figures | |
| dc.identifier | https://arxiv.org/abs/0711.1452 | |
| dc.identifier | http://arxiv.org/abs/0711.1452 | |
| dc.identifier | Phys. Rev. Lett. 101, 078701 (2008) | |
| dc.identifier | doi:10.1103/PhysRevLett.101.078701 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/210238 | |
| dc.subject | Disordered Systems and Neural Networks | |
| dc.subject | Statistical Mechanics | |
| dc.title | (Un)detectable cluster structure in sparse networks | |
| dc.type | text |