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SUMMARY:Limit theorems for eigenvectors of the normalized Laplacian for ra
 ndom graphs - Carey Priebe (Johns Hopkins University)
DTSTART:20161006T130000Z
DTEND:20161006T140000Z
UID:TALK67922@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:We prove a central limit theorem for the components of the eig
 envectors corresponding to the $d$ largest eigenvalues of the normalized L
 aplacian matrix of a finite dimensional random dot product graph. As a cor
 ollary\, we show that for stochastic blockmodel graphs\, the rows of the s
 pectral embedding of the normalized Laplacia converge to multivariate norm
 als and furthermore the mean and the covariance matrix of each row are fun
 ctions of the associated vertex&#39\;s block membership. Together with pri
 or results for the eigenvectors of the adjacency matrix\, we then compare\
 , via the Chernoff information between multivariate normal distributions\,
  how the choice of embedding method impacts subsequent inference. We demon
 strate that neither embedding method dominates with respect to the inferen
 ce task of recovering the latent block assignments.  <span>(<a target="_bl
 ank" rel="nofollow" href="http://arxiv.org/abs/1607.08601">http://arxiv.or
 g/abs/1607.08601</a>)</span>
LOCATION:Seminar Room 2\, Newton Institute
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