generated_Q3

Example of undirected dataset with \(n=50\) individuals in \(Q=3\) clusters and final observation Time=1.

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_Q3 function

A list of 3 components:<dl>
 <dt><code>data</code></dt>
<dd>Observed data is itself a list of 3 components:<ul>
<li><code>time.seq</code> - Vector containing the times (in [0,1]) of the events (length M).</li>
<li><code>type.seq</code> - Vector containing the types in \(\{1,\dots, N\}\) of the events (length M). Here, \(N=n(n-1)/2\) (undirected).</li>
<li><code>Time</code> - Positive real number. [0,Time] is the total time interval of observation.</li>
</ul></dd> <dt><code>z</code></dt>
<dd>Latent variables. A matrix with size \(Q\times n\) and entries 1 (cluster q contains node i) or 0 (else).</dd> <dt><code>intens</code></dt>
<dd>Intensities used to simulate data. A list of \(Q(Q+1)/2\) intensity functions. Each one is given as a list of 2 components:<ul>
<li><code>intens</code> - a positive function. The intensity function \(\alpha^{(q,l)}\)</li>
<li><code>max</code> - positive real number. An upper bound on function \(\alpha^{(q,l)}\)</li>
</ul></dd>
</dl>

Format

Example dataset — generated_Q3

A list of 3 components:<dl>
 <dt><code>data</code></dt>
<dd>Observed data is itself a list of 3 components:<ul>
<li><code>time.seq</code> - Vector containing the times (in [0,1]) of the events (length M).</li>
<li><code>type.seq</code> - Vector containing the types in \(\{1,\dots, N\}\) of the events (length M). Here, \(N=n(n-1)/2\) (undirected).</li>
<li><code>Time</code> - Positive real number. [0,Time] is the total time interval of observation.</li>
</ul></dd>

 <dt><code>z</code></dt>
<dd>Latent variables. A matrix with size \(Q\times n\) and entries 1 (cluster q contains node i) or 0 (else).</dd>

 <dt><code>intens</code></dt>
<dd>Intensities used to simulate data. A list of \(Q(Q+1)/2\) intensity functions. Each one is given as a list of 2 components:<ul>
<li><code>intens</code> - a positive function. The intensity function \(\alpha^{(q,l)}\)</li>
<li><code>max</code> - positive real number. An upper bound on function \(\alpha^{(q,l)}\)</li>
</ul></dd>


</dl>

generated_Q3: Example dataset

Description

Usage

Arguments

Format

Details

References