Localization of dominant eigenpairs and planted communities by means of Frobenius inner products

Title:

Localization of dominant eigenpairs and planted communities by means of Frobenius inner products

Creator:

Fasino, Dario and Tudisco, Francesco

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:046a267c-5ca9-448a-ab99-357868773ef8
uuid:046a267c-5ca9-448a-ab99-357868773ef8
issn:0011-4642

Subject:

matematika, mathematics, dominant eigenpair, cone of matrices, spectral method, community detection, 13, and 51

Type:

model:article and TEXT

Format:

print, bez média, and svazek

Description:

We propose a new localization result for the leading eigenvalue and eigenvector of a symmetric matrix A. The result exploits the Frobenius inner product between A and a given rank-one landmark matrix X. Different choices for X may be used, depending on the problem under investigation. In particular, we show that the choice where X is the all-ones matrix allows to estimate the signature of the leading eigenvector of A, generalizing previous results on Perron-Frobenius properties of matrices with some negative entries. As another application we consider the problem of community detection in graphs and networks. The problem is solved by means of modularity-based spectral techniques, following the ideas pioneered by Miroslav Fiedler in mid-’70s. We show that a suitable choice of X can be used to provide new quality guarantees of those techniques, when the network follows a stochastic block model., Dario Fasino, Francesco Tudisco., and Obsahuje seznam literatury

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

881-893

Source:

Czechoslovak Mathematical Journal | 2016 Volume:66 | Number:3

Harvested from:

CDK

Metadata only:

false