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Poster

Latent distance estimation for random geometric graphs

Ernesto Araya Valdivia · De Castro Yohann

East Exhibition Hall B, C #186

Keywords: [ Applications ] [ Network Analysis ] [ Spectral Methods ] [ Algorithms ]


Abstract: Random geometric graphs are a popular choice for a latent points generative model for networks. Their definition is based on a sample of n points X1,X2,,Xn on the Euclidean sphere~Sd1 which represents the latent positions of nodes of the network. The connection probabilities between the nodes are determined by an unknown function (referred to as the link'' function) evaluated at the distance between the latent points. We introduce a spectral estimator of the pairwise distance between latent points and we prove that its rate of convergence is the same as the nonparametric estimation of a function on Sd1, up to a logarithmic factor. In addition, we provide an efficient spectral algorithm to compute this estimator without any knowledge on the nonparametric link function. As a byproduct, our method can also consistently estimate the dimension d of the latent space.

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