---
title: "Illustration on a simulated multipartite network"
author: "Sophie Donnet, Pierre Barbillon"
date: "`r Sys.Date()`"
output:
rmarkdown::html_vignette:
toc: true
toc_depth: 4
bibliography: references.bib
link-citations: yes
vignette: >
%\VignetteEngine{knitr::rmarkdown}
%\VignetteIndexEntry{Illustration on a simulated multipartite network}
%\VignetteEncoding{UTF-8}
---
<!-- README.md is generated from README.Rmd. Please edit that file -->
```{r, include = FALSE}
knitr::opts_chunk$set(
collapse = TRUE,
comment = "#>",
# fig.path = "man/figures/README-",
out.width = "100%"
)
```
<!-- badges: start -->
<!-- badges: end -->
We present the performances of GREMLINS on a simulated multipartite network. GREMLINS includes a function `rMBM` to simulate multipartite networks. Mathematical details can be found in @multipartite.
## Simulation of a complex multipartite network.
We use the function `rMBM` provided in the package to simulate a multipartite network involving $2$ functional groups (namely A and B) of respective sizes
$$n_A = 60, \quad, n_B = 50.$$
A and B are divided respectively into $3$ and $2$ blocks. The sizes of the blocks are generated randomly. For reproductibility, we fix the random seed to an arbitrarily chosen value.
```{r param FG}
namesFG <- c('A','B')
v_NQ <- c(60,50) #size of each FG
list_pi = list(c(0.16 ,0.40 ,0.44),c(0.3,0.7)) #proportion of each block in each FG
list_pi[[1]]
```
We assume that we observe $3$ interactions matrices
- A-B : continuous weighted interactions
- B-B : binary interactions
- A-A : counting directed interactions
```{r param 1 net}
E <- rbind(c(1,2),c(2,2),c(1,1))
typeInter <- c( "inc","diradj", "adj")
v_distrib <- c('ZIgaussian','bernoulli','poisson')
```
Note that the distributions may be `Bernoulli`, `Poisson`, `Gaussian` or `Laplace` (with null mean). For the Gaussian distribution, a mean and a variance must be given.
We generate randomly the emission parameters $\theta$.
```{r param net}
list_theta <- list()
list_theta[[1]] <- list()
list_theta[[1]]$mean <- matrix(c(6.1, 8.9, 6.6, 9.8, 2.6, 1.0), 3, 2)
list_theta[[1]]$var <- matrix(c(1.6, 1.6, 1.8, 1.7 ,2.3, 1.5),3, 2)
list_theta[[1]]$p0 <- matrix(c(0.4, 0.1, 0.6, 0.5 , 0.2, 0),3, 2)
list_theta[[2]] <- matrix(c(0.7,1.0, 0.4, 0.6),2, 2)
m3 <- matrix(c(2.5, 2.6 ,2.2 ,2.2, 2.7 ,3.0 ,3.6, 3.5, 3.3),3,3 )
list_theta[[3]] <- (m3 + t(m3))/2# for symetrisation
```
We are now ready to simulate the data
```{r simul 2, eval = TRUE, echo = TRUE}
library(GREMLINS)
dataSim <- rMBM(v_NQ,E , typeInter, v_distrib, list_pi,
list_theta, namesFG = namesFG, seed = 4,keepClassif = TRUE)
list_Net <- dataSim$list_Net
length(list_Net)
names(list_Net[[1]])
list_Net[[1]]$typeInter
list_Net[[1]]$rowFG
list_Net[[1]]$colFG
```
## Inference with model selection
The model selection and the estimation are performed with the function `multipartiteBM`.
```{r MBM simul, echo = TRUE, eval = TRUE}
res_MBMsimu <- multipartiteBM(list_Net,
v_distrib = v_distrib,
namesFG = c('A','B'),
v_Kinit = c(2,2),
nbCores = 2,
initBM = FALSE,
keep = FALSE)
```
We can now get the estimated parameters.
```{r estim param, eval=TRUE}
res_MBMsimu$fittedModel[[1]]$paramEstim$list_theta$AB$mean
```
`extractClustersMBM` produces the clusters in each functional group.
```{r extract cluster, eval=TRUE}
Cl <- extractClustersMBM(res_MBMsimu)
```
## Inference without model selection
One may also want to estimate the parameters for given numbers of clusters. The function `multipartiteBMFixedModel` is designed for this task.
```{r MBM fixed, echo = TRUE, eval = TRUE}
res_MBMsimu_fixed <- multipartiteBMFixedModel(list_Net, v_distrib = v_distrib, nbCores = 2,namesFG = namesFG, v_K = c(3,2))
res_MBMsimu_fixed$fittedModel[[1]]$paramEstim$v_K
extractClustersMBM(res_MBMsimu_fixed)$A
```
## Missing data
GREMLINS is also able to handle missing data. In the following experiment, we artificially set missing data in the previously simulated matrices.
```{r sim NA}
############# NA data at random in any matrix
epsilon = 10/100
list_Net_NA <- list_Net
for (m in 1:nrow(E)){
U <- sample(c(1,0),v_NQ[E[m,1]]*v_NQ[E[m,2]],replace=TRUE,prob = c(epsilon, 1-epsilon))
matNA <- matrix(U,v_NQ[E[m,1]],v_NQ[E[m,2]])
list_Net_NA[[m]]$mat[matNA== 1] = NA
if (list_Net_NA[[m]]$typeInter == 'adj') {
M <- list_Net_NA[[m]]$mat
diag(M) <- NA
M[lower.tri(M)] = t(M)[lower.tri(M)]
list_Net_NA[[m]]$mat <- M
}
}
```
```{r MBM simul NA, echo = TRUE, eval = TRUE}
res_MBMsimuNA <- multipartiteBM(list_Net_NA,
v_distrib = v_distrib,
namesFG = c('A','B'),
v_Kinit = c(2,2),
nbCores = 2,
keep = FALSE)
```
We then have a function to predict the missing edges (probability if binary or intensity if weighted)
```{r MBM predict NA, echo = TRUE, eval = TRUE}
pred <- predictMBM(res_MBMsimuNA)
```
## References