reg.SP | R Documentation |

community detection by regularized spectral clustering

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

`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 |

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.

a list of

`cluster ` |
cluster labels |

`loss ` |
the loss of Kmeans algorithm |

Tianxi Li, Elizaveta Levina, Ji Zhu

Maintainer: Tianxi Li <tianxili@virginia.edu>

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.

`reg.SP`

```
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)
```

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