Output of mainVEM obtained on dataset generated_Q3 with hist method and Qmin=1, Qmax=5.
generated_sol_histList of 5 components. Each one is the output of the algorithm with a different value of the number of clusters \(Q\) for \(1\le Q \le 5\) and given as a list of 8 components:
tauMatrix with size \(Q\times n\) containing the estimated probability in \((0,1)\) that cluster \(q\) contains node \(i\).
rhoSparsity parameter - 1 in this case (non sparse method).
betaSparsity parameter - 1 in this case (non sparse method).
logintensities.qlMatrix with size \(Q(Q+1)/2\times K\). Each row contains estimated values of the log of the intensity function \(\log(\alpha^{(q,l)})\) on a regular partition (in \(K\) parts) of the time interval [0,Time].
best.dVector with length \(Q(Q+1)/2\) (undirected case) with estimated value for the exponent of the best partition to estimate intensity \(\alpha^{(q,l)}\). The best number of parts is \(K=2^d\).
JEstimated value of the ELBO
runWhich 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.
convergedBoolean. If TRUE, the algorithm stopped at convergence. Otherwise it stopped at the maximal number of iterations.
This solution was (randomly) obtained using the following code
Nijk <- statistics(generated_Q3$data,n=50,K=8,directed=FALSE)
generated_sol_hist <- mainVEM(list(Nijk=Nijk,Time=1),n=50,Qmin=1,Qmax=5,directed=FALSE,method='hist')
MATIAS, C., REBAFKA, T. & VILLERS, F. (2018). A semiparametric extension of the stochastic block model for longitudinal networks. Biometrika. 105(3): 665-680.