DcLbm function

Degree Corrected Latent Block Model for bipartite graph class

An S4 class to represent a degree corrected stochastic block model for co_clustering of bipartite graph. Such model can be used to cluster graph vertex, and model a bipartite graph adjacency matrix $X$ with the following generative model : [REMOVE_ME]$\pi \sim Dirichlet(\alpha) [REMOVE_ME_2]$

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

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

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

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

[REMOVE_ME]$\gamma_i^c\sim \mathcal{U}(S_l) [REMOVE_ME_2]$

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

The individuals parameters $\gamma_i^r,\gamma_j^c$ allow to take into account the node degree heterogeneity. These parameters have uniform priors over simplex $S_k$. These classes mainly store the prior parameters value $\alpha,p$ of this generative model. The DcLbm-class must be used when fitting a simple Diagonal Gaussian Mixture Model whereas the DcLbmPrior-class must be sued when fitting a CombinedModels-class. class

DcLbmPrior(p = NaN)

DcLbm(alpha = 1, p = NaN)

Arguments

• p: Exponential prior parameter (default to Nan, in this case p will be estimated from data as the average intensities of X)
• alpha: Dirichlet prior parameter over the cluster proportions (default to 1)

Returns

a DcLbmPrior-class

a DcLbm-class object

Description

An S4 class to represent a degree corrected stochastic block model for co_clustering of bipartite graph. Such model can be used to cluster graph vertex, and model a bipartite graph adjacency matrix $X$ with the following generative model :

$$\pi \sim Dirichlet(\alpha)$$ $$Z_i^r \sim \mathcal{M}(1,\pi^r)$$ $$Z_j^c \sim \mathcal{M}(1,\pi^c)$$ $$\theta_{kl} \sim Exponential(p)$$ $$\gamma_i^r\sim \mathcal{U}(S_k)$$ $$\gamma_i^c\sim \mathcal{U}(S_l)$$ $$X_{ij}|Z_{ik}^cZ_{jl}^r=1 \sim \mathcal{P}(\gamma_i^r\theta_{kl}\gamma_j^c)$$

The individuals parameters $\gamma_i^r,\gamma_j^c$ allow to take into account the node degree heterogeneity. These parameters have uniform priors over simplex $S_k$. These classes mainly store the prior parameters value $\alpha,p$ of this generative model. The DcLbm-class must be used when fitting a simple Diagonal Gaussian Mixture Model whereas the DcLbmPrior-class must be sued when fitting a CombinedModels-class.

Examples

DcLbmPrior()
DcLbmPrior(p = 0.7)
DcLbm()
DcLbm(p = 0.7)

See Also

DcLbmFit-class, DcLbmPath-class

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