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.
the number of blocks provided by an user.
a named list containing
(K-by-K) matrix of 3D histogram.
(n-by-n) corresponding probability matrix.
K list where each element is a vector of nodes/indices
for each cluster.
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.
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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")
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