Reference:
Pekka Orponen, Satu Elisa Schaeffer, and Vanesa Avalos Gaytán. Locally computable approximations for spectral clustering and absorption times of random walks. Technical Report cs.DM/0810.4061, arXiv.org, October 2008.
Abstract:
We address the problem of determining a natural local neighbourhood or ``cluster'' associated to a given seed vertex in an undirected graph. We formulate the task in terms of absorption times of random walks from other vertices to the vertex of interest, and observe that these times are well approximated by the components of the principal eigenvector of the corresponding fundamental matrix of the graph's adjacency matrix. We further present a locally computable gradientdescent method to estimate this DirichletFiedler vector, based on minimising the respective Rayleigh quotient. Experimental evaluation shows that the approximations behave well and yield welldefined local clusters.
Keywords:
graph clustering, spectral clustering, random walk, absorption time, gradient method
Suggested BibTeX entry:
@techreport{OrSA08,
author = {Pekka Orponen and Satu Elisa Schaeffer and Vanesa Avalos Gaytán},
institution = {arXiv.org},
month = {October},
number = {cs.DM/0810.4061},
pages = {21},
title = {Locally computable approximations for spectral clustering and absorption times of random walks},
type = {Technical Report},
year = {2008},
}
