generated_sol_kernel

Output of mainVEM obtained on dataset <code>generated_Q3</code> with <code>kernel</code> method and Qmin=Qmax=5.

datasets

Stochastic block model used for dynamic graphs represented by Poisson processes.
To model recurrent interaction events in continuous time, an extension of the stochastic block model is proposed where every individual belongs to a latent group and interactions between two individuals follow a conditional inhomogeneous Poisson process with intensity driven by the individuals’ latent groups. The model is shown to be identifiable and its estimation is based on a semiparametric variational expectation-maximization algorithm. Two versions of the method are developed, using either a nonparametric histogram approach (with an adaptive choice of the partition size) or kernel intensity estimators. The number of latent groups can be selected by an integrated classification likelihood criterion.
Y. Baraud and L. Birgé (2009). <doi:10.1007/s00440-007-0126-6>.
C. Biernacki, G. Celeux and G. Govaert (2000). <doi:10.1109/34.865189>.
M. Corneli, P. Latouche and F. Rossi (2016). <doi:10.1016/j.neucom.2016.02.031>.
J.-J. Daudin, F. Picard and S. Robin (2008). <doi:10.1007/s11222-007-9046-7>.
A. P. Dempster, N. M. Laird and D. B. Rubin (1977). <http://www.jstor.org/stable/2984875>.
G. Grégoire (1993). <http://www.jstor.org/stable/4616289>.
L. Hubert and P. Arabie (1985). <doi:10.1007/BF01908075>.
M. Jordan, Z. Ghahramani, T. Jaakkola and L. Saul (1999). <doi:10.1023/A:1007665907178>.
C. Matias, T. Rebafka and F. Villers (2018). <doi:10.1093/biomet/asy016>.
C. Matias and S. Robin (2014). <doi:10.1051/proc/201447004>.
H. Ramlau-Hansen (1983). <doi:10.1214/aos/1176346152>.
P. Reynaud-Bouret (2006). <doi:10.3150/bj/1155735930>.

Daphnc3<a9> Giorgi

ppsbm

Clustering in Longitudinal Networks

Daphné Giorgi

Catherine Matias

Tabea Rebafka

Fanny Villers

generated_sol_kernel function

Solution for Q=5 clusters, containing 5 components:<dl>
 <dt><code>tau</code></dt>
<dd>Matrix with size \(Q\times n\) containing the estimated probability in \((0,1)\) that cluster \(q\) contains node \(i\).</dd> <dt><code>J</code></dt>
<dd>Estimated value of the ELBO</dd> <dt><code>run</code></dt>
<dd>Which run of the algorithm gave the best solution. A run relies on a specific initialization of the algorithm. A negative value maybe obtained in the decreasing phase (for Q) of the algorithm.</dd>
 
 <dt><code>converged</code></dt>
<dd>Boolean. If TRUE, the algorithm stopped at convergence. Otherwise it stopped at the maximal number of iterations.</dd>
 </dl>

Format

Output example of mainVEM — generated_sol_kernel

Solution for Q=5 clusters, containing 5 components:<dl>
 <dt><code>tau</code></dt>
<dd>Matrix with size \(Q\times n\) containing the estimated probability in \((0,1)\) that cluster \(q\) contains node \(i\).</dd>

 <dt><code>J</code></dt>
<dd>Estimated value of the ELBO</dd>

 <dt><code>run</code></dt>
<dd>Which run of the algorithm gave the best solution. A run relies on a specific initialization of the algorithm. A negative value maybe obtained in the decreasing phase (for Q) of the algorithm.</dd>
 
 <dt><code>converged</code></dt>
<dd>Boolean. If TRUE, the algorithm stopped at convergence. Otherwise it stopped at the maximal number of iterations.</dd>
 

</dl>

generated_sol_kernel: Output example of mainVEM

Description

Usage

Arguments

Format

Details

References