DcSbm function

Degree Corrected Stochastic Block Model Prior class

An S4 class to represent a Degree Corrected Stochastic Block Model. Such model can be used to cluster graph vertex, and model a square adjacency matrix $X$ with the following generative model : [REMOVE_ME]$\pi \sim Dirichlet(\alpha) [REMOVE_ME_2]$

[REMOVE_ME]$Z_i \sim \mathcal{M}(1,\pi) [REMOVE_ME_2]$

[REMOVE_ME]$\theta_{kl} \sim Exponential(p) [REMOVE_ME_2]$

[REMOVE_ME]$\gamma_i^+,\gamma_i^- \sim \mathcal{U}(S_k) [REMOVE_ME_2]$

[REMOVE_ME]$X_{ij}|Z_{ik}Z_{jl}=1 \sim \mathcal{P}(\gamma_i^+\theta_{kl}\gamma_j^-) [REMOVE_ME_2]$

The individuals parameters $\gamma_i^+,\gamma_i^-$ allow to take into account the node degree heterogeneity. These parameters have uniform priors over the simplex $S_k$ ie. $\sum_{i:z_{ik}=1}\gamma_i^+=1$. These classes mainly store the prior parameters value $\alpha,p$ of this generative model. The DcSbm-class must be used when fitting a simple Degree Corrected Stochastic Block Model whereas the DcSbmPrior-class must be used when fitting a CombinedModels-class. class

DcSbmPrior(p = NaN, type = "guess")

DcSbm(alpha = 1, p = NaN, type = "guess")

Arguments

• p: Exponential prior parameter (default to NaN, in this case p will be estimated from data as the mean connection probability)
• type: define the type of networks (either "directed", "undirected" or "guess", default to "guess")
• alpha: Dirichlet prior parameter over the cluster proportions (default to 1)

Returns

a DcSbmPrior-class object

a DcSbm-class object

Description

An S4 class to represent a Degree Corrected Stochastic Block Model. Such model can be used to cluster graph vertex, and model a square adjacency matrix $X$ with the following generative model :

The individuals parameters $\gamma_i^+,\gamma_i^-$ allow to take into account the node degree heterogeneity. These parameters have uniform priors over the simplex $S_k$ ie. $\sum_{i:z_{ik}=1}\gamma_i^+=1$. These classes mainly store the prior parameters value $\alpha,p$ of this generative model. The DcSbm-class must be used when fitting a simple Degree Corrected Stochastic Block Model whereas the DcSbmPrior-class must be used when fitting a CombinedModels-class.

Examples

DcSbmPrior()
DcSbmPrior(type = "undirected")
DcSbm()
DcSbm(type = "undirected")

See Also

DcSbmFit-class, DcSbmPath-class

Other DlvmModels: CombinedModels, DcLbm, DiagGmm, DlvmPrior-class, Gmm, Lca, MoM, MoR, MultSbm, Sbm, greed()