kernelIntensities

List with 3 components:<ul>
<li>data$time.seq : sequence of observed time points of the m-th event (M-vector)</li>
<li>data$type.seq : sequence of observed values convertNodePair(i,j,n,directed) (auxiliary.R)
 of process that produced the mth event (M-vector)</li>
<li>$Time - [0,data$Time] is the total time interval of observation</li>
</ul>

data

Boolean for directed (TRUE) or undirected (FALSE) case

directed

Boolean for sparse (TRUE) or not sparse (FALSE) case

sparse

nb.points

Compute smooth intensities with direct kernel estimation of intensities relying on a classification tau.
This can be used with the values $\tau$ obtained on a dataset with mainVEM function run with 'hist' method.

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

kernelIntensities function

<dl><dt>data</dt>
<dd>List with 3 components:<ul>
<li>data$time.seq : sequence of observed time points of the m-th event (M-vector)</li>
<li>data$type.seq : sequence of observed values convertNodePair(i,j,n,directed) (auxiliary.R)
 of process that produced the mth event (M-vector)</li>
<li>$Time - [0,data$Time] is the total time interval of observation</li>
</ul></dd>
<dt>tau</dt>
<dd>$\tau$</dd>
<dt>Q</dt>
<dd>Total number of groups</dd>
<dt>n</dt>
<dd>Total number of nodes</dd>
<dt>directed</dt>
<dd>Boolean for directed (TRUE) or undirected (FALSE) case</dd>
<dt>rho</dt>
<dd>$\rho$</dd>
<dt>sparse</dt>
<dd>Boolean for sparse (TRUE) or not sparse (FALSE) case</dd>
<dt>nb.points</dt>
<dd>Number of points</dd></dl>

Arguments

Direct kernel estimator intensities — kernelIntensities

<dl>

<dt>data</dt>
<dd>List with 3 components:<ul>
<li>data$time.seq : sequence of observed time points of the m-th event (M-vector)</li>
<li>data$type.seq : sequence of observed values convertNodePair(i,j,n,directed) (auxiliary.R)
 of process that produced the mth event (M-vector)</li>
<li>$Time - [0,data$Time] is the total time interval of observation</li>
</ul></dd>


<dt>tau</dt>
<dd>$\tau$</dd>


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


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


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


<dt>rho</dt>
<dd>$\rho$</dd>


<dt>sparse</dt>
<dd>Boolean for sparse (TRUE) or not sparse (FALSE) case</dd>


<dt>nb.points</dt>
<dd>Number of points</dd>

</dl>

kernelIntensities: Direct kernel estimator intensities

Description

Usage

Arguments

Details

Examples