est.SBA: Estimate graphons based on Stochastic Blockmodel...

Description Usage Arguments Value References See Also Examples

View source: R/est.SBA.R

Description

est.SBA takes a 2-stage approach for estimating graphons based on exchangeable random graph models. First, it finds a Stochastic Blockmodel Approximation (SBA) of the graphon. Then, it uses clustering information to estimate graphon using a consistent histogram estimator.

Usage

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est.SBA(A, delta = 0.5)

Arguments

A

either

Case 1.

an (n-by-n) binary adjacency matrix, or

Case 2.

a vector containing multiple of (n-by-n) binary adjacency matrices.

delta

a precision parameter larger than 0.

Value

a named list containing

H

a (K-by-K) matrix fo 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

Airoldi, E.M., Costa, T.B., and Chan, S.H. (2013) Stochastic blockmodel approximation of a graphon: Theory and consistent estimation. Advances in Neural Information Processing Systems, 692-700.

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.LG

Examples

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## generate a graphon of type No.6 with 3 clusters
W = gmodel.preset(3,id=6)

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

## draw 17 observations from a given probability matrix
A = gmodel.P(P,rep=17)

## run SBA algorithm with different deltas (0.2,0.5,0.8)
res2 = est.SBA(A,delta=0.2)
res3 = est.SBA(A,delta=0.5)
res4 = est.SBA(A,delta=0.8)

## compare true probability matrix and estimated ones
par(mfrow=c(1,4))
image(P); title("original P")
image(res2$P); title("SBA with delta=0.2")
image(res3$P); title("SBA with delta=0.5")
image(res4$P); title("SBA with delta=0.8")

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

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