A consistent dot product embedding for stochastic blockmodel graphs

Details A consistent dot product embedding for stochastic blockmodel graphs A consistent dot product embedding for stochastic blockmodel graphs

2011-08-10

arxiv.org/abs/1108.2228v2

Statistics

Machine Learning

17 pages

Scientific paper

We present a method to estimate block membership of nodes in a random graph generated by a stochastic blockmodel. We use an embedding procedure motivated by the random dot product graph model, a particular example of the latent position model. The embedded vectors are clustered through minimization of a mean square error/criteria. We prove that this method is consistent for assigning nodes to blocks, as only a negligible number of nodes will be mis-assigned. We prove consistency of the method for directed and undirected graphs. The consistent block assignment makes possible consistent parameter estimation for a stochastic blockmodel. We extend the result for when the number of blocks grows slowly with the number of nodes. Our method is also computationally feasible even for very large graphs.

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