tauInitial

Same function whatever directed or undirected case

internal

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

tauInitial function

<dl><dt>data</dt>
<dd>Data : only needs the \(N_{ijk}\) field of data</dd>
<dt>n</dt>
<dd>Total number of nodes</dd>
<dt>Q</dt>
<dd>Total number of groups</dd>
<dt>d_part</dt>
<dd>Maximal level for finest partitions of time interval [0,T], used for kmeans initializations.<ul>
<li>Algorithm takes partition up to depth \(2^d\) with \(d=1,...,d_{part}\)</li>
<li>Explore partitions \([0,T], [0,T/2], [T/2,T], ... [0,T/2^d], ...[(2^d-1)T/2^d,T]\)</li>
<li>Total number of partitions \(npart= 2^{(d_part +1)} - 1\)</li>
</ul></dd>
<dt>n_perturb</dt>
<dd>Number of different perturbations on k-means result</dd>
<dt>perc_perturb</dt>
<dd>Percentage of labels that are to be perturbed (= randomly switched)</dd>
<dt>n_random</dt>
<dd>Number of completely random initial points. If not zero there will be n_random taus uniformly sampled in the initialization.</dd>
<dt>directed</dt>
<dd>Boolean for directed (TRUE) or undirected (FALSE) case</dd></dl>

Arguments

List of initial values for \(\tau\) — tauInitial

<dl>

<dt>data</dt>
<dd>Data : only needs the \(N_{ijk}\) field of data</dd>


<dt>n</dt>
<dd>Total number of nodes</dd>


<dt>Q</dt>
<dd>Total number of groups</dd>


<dt>d_part</dt>
<dd>Maximal level for finest partitions of time interval [0,T], used for kmeans initializations.<ul>
<li>Algorithm takes partition up to depth \(2^d\) with \(d=1,...,d_{part}\)</li>
<li>Explore partitions \([0,T], [0,T/2], [T/2,T], ... [0,T/2^d], ...[(2^d-1)T/2^d,T]\)</li>
<li>Total number of partitions \(npart= 2^{(d_part +1)} - 1\)</li>
</ul></dd>


<dt>n_perturb</dt>
<dd>Number of different perturbations on k-means result</dd>


<dt>perc_perturb</dt>
<dd>Percentage of labels that are to be perturbed (= randomly switched)</dd>


<dt>n_random</dt>
<dd>Number of completely random initial points. If not zero there will be n_random taus uniformly sampled in the initialization.</dd>


<dt>directed</dt>
<dd>Boolean for directed (TRUE) or undirected (FALSE) case</dd>

</dl>

tauInitial: List of initial values for \(\tau\)

Description

Usage

Value

Arguments

Details