A simple spectral algorithm for recovering planted partitions

• Autorzy: Sam Cole , Shmuel Friedland , Lev Reyzin
• Języki publikacji: EN

Abstrakty

EN

In this paper, we consider the planted partition model, in which n = ks vertices of a random graph are partitioned into k “clusters,” each of size s. Edges between vertices in the same cluster and different clusters are included with constant probability p and q, respectively (where 0 ≤ q < p ≤ 1). We give an efficient algorithm that, with high probability, recovers the clusters as long as the cluster sizes are are least (√n). Informally, our algorithm constructs the projection operator onto the dominant k-dimensional eigenspace of the graph’s adjacency matrix and uses it to recover one cluster at a time. To our knowledge, our algorithm is the first purely spectral algorithm which runs in polynomial time and works even when s = Θ (√n), though there have been several non-spectral algorithms which accomplish this. Our algorithm is also among the simplest of these spectral algorithms, and its proof of correctness illustrates the usefulness of the Cauchy integral formula in this domain.

• Wydawca: De Gruyter Open
• Czasopismo: Special Matrices
• Rocznik: 2017
• Tom: 5
• Numer: 1
• Strony: 139-157

Daty

wydano

2017-01-26

otrzymano

2016-11-24

zaakceptowano

2017-07-14

online

2017-08-18

Twórcy

autor

Sam Cole

• , Illinois 60607-7045,

autor

Shmuel Friedland

• , Illinois 60607-7045,

autor

Lev Reyzin

• , Illinois 60607-7045,

Identyfikatory

DOI

10.1515/spma-2017-0013