Geodesic
Localization of dominant eigenpairs and planted communities by means of Frobenius inner products
Czechoslovak Mathematical Journal, Tome 66 (2016) no. 3, pp. 881-893.

Voir la notice de l'article dans Czech Digital Mathematics Library

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. \endgraf 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.
DOI : 10.1007/s10587-016-0298-2
Classification : 15A18, 15B48
Mots-clés : dominant eigenpair; cone of matrices; spectral method; community detection 
@article{10_1007_s10587_016_0298_2,
     author = {Fasino, Dario and Tudisco, Francesco},
     title = {Localization of dominant eigenpairs and planted communities by means of {Frobenius} inner products},
     journal = {Czechoslovak Mathematical Journal},
     pages = {881--893},
     publisher = {mathdoc},
     volume = {66},
     number = {3},
     year = {2016},
     doi = {10.1007/s10587-016-0298-2},
     mrnumber = {3556873},
     zbl = {06644039},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-016-0298-2/}
}
TY  - JOUR
AU  - Fasino, Dario
AU  - Tudisco, Francesco
TI  - Localization of dominant eigenpairs and planted communities by means of Frobenius inner products
JO  - Czechoslovak Mathematical Journal
PY  - 2016
SP  - 881
EP  - 893
VL  - 66
IS  - 3
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-016-0298-2/
DO  - 10.1007/s10587-016-0298-2
LA  - en
ID  - 10_1007_s10587_016_0298_2
ER  - 
%0 Journal Article
%A Fasino, Dario
%A Tudisco, Francesco
%T Localization of dominant eigenpairs and planted communities by means of Frobenius inner products
%J Czechoslovak Mathematical Journal
%D 2016
%P 881-893
%V 66
%N 3
%I mathdoc
%U https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-016-0298-2/
%R 10.1007/s10587-016-0298-2
%G en
%F 10_1007_s10587_016_0298_2
Fasino, Dario; Tudisco, Francesco. Localization of dominant eigenpairs and planted communities by means of Frobenius inner products. Czechoslovak Mathematical Journal, Tome 66 (2016) no. 3, pp. 881-893. doi : 10.1007/s10587-016-0298-2. https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-016-0298-2/

Cité par Sources :