randnet (version 0.7)

reg.SP: clusters nodes by regularized spectral clustering

Description

community detection by regularized spectral clustering

Usage

reg.SP(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. It is shown to give consistent clustering under SBM.

References

K. Rohe, S. Chatterjee, and B. Yu. Spectral clustering and the high-dimensional stochastic blockmodel. The Annals of Statistics, pages 1878-1915, 2011.

A. A. Amini, A. Chen, P. J. Bickel, and E. Levina. Pseudo-likelihood methods for community detection in large sparse networks. The Annals of Statistics, 41(4):2097-2122, 2013.

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

C. M. Le, E. Levina, and R. Vershynin. Concentration and regularization of random graphs. Random Structures & Algorithms, 2017.

See Also

reg.SP

Examples

dt <- BlockModel.Gen(30,300,K=3,beta=0.2,rho=0)


A <- dt$A


sc <- reg.SP(A,K=3,lap=TRUE)


NMI(sc$cluster,dt$g)