SMS scnews item created by John Ormerod at Wed 27 Jan 2016 1201
Type: Seminar
Distribution: World
Expiry: 29 Jan 2016
Calendar1: 28 Jan 2016 1400-1500
CalLoc1: AGR Carslaw 829
CalTitle1: Latent structure of sparse random networks
Auth: jormerod@pjormerod5.pc (assumed)

# Statistics Seminar: Can Le (University of Michigan) -- Latent structure of sparse random networks


Abstract:

Network analysis has become an important area in many research domains.
A common way to study real-world networks is to model them as random
graphs whose structure is encoded in the expectation matrix. We consider
a general model of networks on $n$ nodes, known as the inhomogeneous
Erdos-Renyi model, where edges between nodes are formed independently
and possibly with different probabilities. We study the behavior of
such random networks through the concentration of their adjacency and
Laplacian matrices in the spectral norm. Sparse random networks whose
expected average degrees grow slower than $\log n$ fail to concentrate.
The obstruction is caused by vertices with abnormally high and low
degrees. We show that concentration can be restored if we regularize
the degrees of such vertices, and one can do this in various ways. As
an immediate consequence, we establish the validity of one of the
simplest and fastest approaches to community detection â€“ regularized
spectral clustering, under the stochastic block model. We also discuss
how to choose the regularization parameter and estimate the number of
communities.


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