evaluation

The evaluation function for Consistent Estimation of the Number of Communities via Regularized Network Embedding.

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

evaluation function

<dl><dt>Z.hat</dt>
<dd>A n * r matrix, the estimated embedding vectors corresponding to n nodes.</dd>
<dt>Z.true</dt>
<dd>A n * r matrix, the true embedding vectors corresponding to n nodes.</dd>
<dt>cluster.matrix.hat</dt>
<dd>A n * n estimated membership matrix, whose (i,j)-element is 1, if nodes i and j are estimated to belong to the same community, and 0, otherwise.</dd>
<dt>cluster.matrix.true</dt>
<dd>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.</dd>
<dt>P.true</dt>
<dd>A n * n true probability matrix.</dd>
<dt>Theta.true</dt>
<dd>A n * n true matrix: Z.true %*% t(Z.true).</dd>
<dt>K.hat</dt>
<dd>The true number of communities.</dd>
<dt>K.true</dt>
<dd>The estimated number of communities.</dd></dl>

Arguments

Author

Consistent Estimation of the Number of Communities via Regularized Network Embedding. — evaluation

<dl>

<dt>Z.hat</dt>
<dd>A n * r matrix, the estimated embedding vectors corresponding to n nodes.</dd>


<dt>Z.true</dt>
<dd>A n * r matrix, the true embedding vectors corresponding to n nodes.</dd>


<dt>cluster.matrix.hat</dt>
<dd>A n * n estimated membership matrix, whose (i,j)-element is 1, if nodes i and j are estimated to belong to the same community, and 0, otherwise.</dd>


<dt>cluster.matrix.true</dt>
<dd>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.</dd>


<dt>P.true</dt>
<dd>A n * n true probability matrix.</dd>


<dt>Theta.true</dt>
<dd>A n * n true matrix: Z.true %*% t(Z.true).</dd>


<dt>K.hat</dt>
<dd>The true number of communities.</dd>


<dt>K.true</dt>
<dd>The estimated number of communities.</dd>

</dl>

evaluation: Consistent Estimation of the Number of Communities via Regularized Network Embedding.

Description

Usage

Value

Arguments

Author