detects communities by regularized spherical spectral clustering
community detection by regularized spherical spectral clustering
reg.SSP(A, K, tau = 1, lap = FALSE)
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. |
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.
a list of
cluster |
cluster labels |
loss |
the loss of Kmeans algorithm |
Tianxi Li, Elizaveta Levina, Ji Zhu
Maintainer: Tianxi Li <tianxili@umich.edu>
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.
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)
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