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Limit theorems for eigenvectors of the normalized Laplacian for random graphs
http://sms.cam.ac.uk/media/2352116
Carey Priebe
Thursday 6th October 2016  14:00 to 15:00
40
Limit theorems for eigenvectors of the normalized Laplacian for random graphs
http://sms.cam.ac.uk/media/2352116
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Limit theorems for eigenvectors of the normalized Laplacian for random graphs
ucs_sms_2283481_2352116
http://sms.cam.ac.uk/media/2352116
Limit theorems for eigenvectors of the normalized Laplacian for random graphs
Carey Priebe
Thursday 6th October 2016  14:00 to 15:00
Thu, 03 Nov 2016 12:46:54 +0000
Isaac Newton Institute
Carey Priebe
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Carey Priebe
Thursday 6th October 2016  14:00 to 15:00
Carey Priebe
Thursday 6th October 2016  14:00 to 15:00
Cambridge University
3780
http://sms.cam.ac.uk/media/2352116
Limit theorems for eigenvectors of the normalized Laplacian for random graphs
Carey Priebe
Thursday 6th October 2016  14:00 to 15:00
We prove a central limit theorem for the components of the eigenvectors corresponding to the d largest eigenvalues of the normalized Laplacian matrix of a finite dimensional random dot product graph. As a corollary, we show that for stochastic blockmodel graphs, the rows of the spectral embedding of the normalized Laplacia converge to multivariate normals and furthermore the mean and the covariance matrix of each row are functions of the associated vertex's block membership. Together with prior 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 demonstrate that neither embedding method dominates with respect to the inference task of recovering the latent block assignments. (http://arxiv.org/abs/1607.08601)
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