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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Limit theorems for eigenvectors of the normalized Laplacian for random graphs

## Limit theorems for eigenvectors of the normalized Laplacian for random graphsAdd to your list(s) Download to your calendar using vCal - Carey Priebe (Johns Hopkins University)
- Thursday 06 October 2016, 14:00-15:00
- Seminar Room 2, Newton Institute.
If you have a question about this talk, please contact info@newton.ac.uk. SNA - Theoretical foundations for statistical network analysis 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) This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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