randnet (version 0.7)

reg.SSP: detects communities by regularized spherical spectral clustering

Description

community detection by regularized spherical spectral clustering

Usage

reg.SSP(A, K, tau = 1, lap = FALSE,nstart=30,iter.max=100)

Value

a list of

cluster

cluster labels

loss

the loss of Kmeans algorithm

Arguments

A

adjacency matrix

K

number of communities

tau

reguarlization parameter. Default value is one. Typically set between 0 and 1. If tau=0, no regularization is applied.

lap

indicator. If TRUE, the Laplacian matrix for clustering. If FALSE, the adjacency matrix will be used.

nstart

number of random initializations for K-means

iter.max

maximum number of iterations for K-means

Author

Tianxi Li, Elizaveta Levina, Ji Zhu

Maintainer: Tianxi Li <[e-mail]>

Details

The regularlization is done by adding a small constant to each element of the adjacency matrix. It is shown by such perturbation helps concentration in sparse networks. The difference from spectral clustering (reg.SP) comes from its extra step to normalize the rows of spectral vectors. It is proved that it gives consistent clustering under DCSBM.

References

T. Qin and K. Rohe. Regularized spectral clustering under the degree-corrected stochastic blockmodel. In Advances in Neural Information Processing Systems, pages 3120-3128, 2013.

J. Lei and A. Rinaldo. Consistency of spectral clustering in stochastic block models. The Annals of Statistics, 43(1):215-237, 2014.

See Also

reg.SP

Examples

dt <- BlockModel.Gen(30,300,K=3,beta=0.2,rho=0.9,simple=FALSE,power=TRUE)


A <- dt$A

ssc <- reg.SSP(A,K=3,lap=TRUE)

NMI(ssc$cluster,dt$g)