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The network analysis plays an important role in numerous application domains including biomedicine.
Estimation of the number of communities is a fundamental and critical issue in network analysis. Most existing studies assume that the number of communities is known a priori, or lack of rigorous theoretical guarantee on the estimation consistency. This method proposes a regularized network embedding model to simultaneously estimate the community structure and the number of communities in a unified formulation.
The proposed model equips network embedding with a novel composite regularization term, which pushes the embedding vector towards its center and collapses similar community centers with each other. A rigorous theoretical analysis is conducted, establishing asymptotic consistency in terms of community detection and estimation of the number of communities.
Reference:
Ren, M., Zhang S. and Wang J. (2022). "Consistent Estimation of the Number of Communities via Regularized Network Embedding". Biometrics, <doi:10.1111/biom.13815>.

Mingyang Ren

cencrne

Consistent Estimation of the Number of Communities via
Regularized Network Embedding

Sanguo Zhang

Junhui Wang

example.data function

<p>A list including:
A: An observed n * n adjacency matrix of undirected graph, n=360.
K.true: The estimated number of communities.
Z.true: A n * r matrix, the true embedding vectors corresponding to n nodes, n=360, r=5.
B.true: A n * r matrix, the true community centers corresponding to n nodes.
P.true: A n * n true probability matrix.
Theta.true: A n * n true matrix: Z.true %*% t(Z.true).
cluster.matrix.true: A n * n true membership matrix, whose (i,j)-element is 1, if nodes i and j belong to the same community, and 0, otherwise.</p>

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Some example data

example.data: Some example data

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