est.LG: Estimate graphons based on empirical degrees

Description Usage Arguments Value References See Also Examples

View source: R/est.LG.R

Description

est.LG takes a 2-stage approach. First it adopts largest gap criterion on empirical degrees to estimate blocks of a given network under Stochastic Blockmodel framework. Then a consistent histogram estimator is utilized to estimate graphons based on estimated blocks in a given network.

Usage

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est.LG(A, K)

Arguments

A

an (n-by-n) binary adjacency matrix.

K

the number of blocks provided by an user.

Value

a named list containing

H

a (K-by-K) matrix of 3D histogram.

P

an (n-by-n) corresponding probability matrix.

B

a length-K list where each element is a vector of nodes/indices for each cluster.

References

Channarond, A., Daudin, J., and Robin, S. (2012) Classification and estimation in the SBM based on empirical degrees. Electronic Journal of Statistics, Vol.6:2574-2601.

Chan, S.H. and Airoldi, E.M. (2014) A consistent histogram estimator for exchangeable graph models. Journal of Machine Learning Research Workshop and Conference Proceedings, Vol.32, No.1:208-216.

See Also

est.SBA

Examples

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## generate a graphon of type No.10 with 3 clusters
W = gmodel.preset(3,id=10)

## create a probability matrix for 100 nodes
graphW = gmodel.block(W,n=100)
P = graphW$P

## draw 23 observations from a given probability matrix
A = gmodel.P(P,rep=23)

## run LG algorithm with a rough guess for K=2,3,4
res2 = est.LG(A,K=2)
res3 = est.LG(A,K=3)
res4 = est.LG(A,K=4)

## compare true probability matrix and estimated ones
par(mfrow=c(1,4))
image(P); title("main")
image(res2$P); title("LG with K=2")
image(res3$P); title("LG with K=3")
image(res4$P); title("LG with K=4")

graphon documentation built on Nov. 17, 2017, 5:28 a.m.

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