From 767f2f86c7fc1c9f8cd9ce0872929f81714d016e Mon Sep 17 00:00:00 2001 From: Polarolouis Date: Fri, 7 Jul 2023 10:44:15 +0200 Subject: [PATCH] Adding work BOD 7/7/23 --- .vscode/settings.json | 2 +- Rcodes/simulation/inference_analyze.Rmd | 196 ++++++++++ Rcodes/simulation/inference_analyze.tex | 205 ++++++++++ Rcodes/simulation/model_selection_analyze.Rmd | 41 +- Rcodes/simulation/model_selection_analyze.tex | 352 +++--------------- Rcodes/simulation/netclustering_analyze.R | 7 +- Rcodes/simulation/netclustering_analyze.Rmd | 19 + Rcodes/simulation/netclustering_analyze.tex | 1 + Rmd2Latex-fragment.R | 11 +- img/plot_model_function_eps.png | Bin 19840 -> 66583 bytes presentation_UMR.tex | 4 +- rapport.pdf | Bin 848569 -> 860297 bytes rapport.tex | 31 +- references.bib | 19 + 14 files changed, 545 insertions(+), 343 deletions(-) create mode 100644 Rcodes/simulation/inference_analyze.tex create mode 100644 Rcodes/simulation/netclustering_analyze.Rmd create mode 100644 Rcodes/simulation/netclustering_analyze.tex diff --git a/.vscode/settings.json b/.vscode/settings.json index b087b8f..6523ba8 100644 --- a/.vscode/settings.json +++ b/.vscode/settings.json @@ -4,7 +4,7 @@ { "match": ".*\\.Rmd", "isAsync": true, - "cmd": "Rscript Rmd2Latex-fragment.R '${file}' " + "cmd": "/bin/bash -c \"Rscript Rmd2Latex-fragment.R '${file}'\"" }, { "match": ".*", diff --git a/Rcodes/simulation/inference_analyze.Rmd b/Rcodes/simulation/inference_analyze.Rmd index e69de29..503c687 100644 --- a/Rcodes/simulation/inference_analyze.Rmd +++ b/Rcodes/simulation/inference_analyze.Rmd @@ -0,0 +1,196 @@ +```{r libraries, echo = FALSE, include = FALSE} +require("ggplot2") +require("tidyr") +require("dplyr") +require("stringr") +require("knitr") +require("pander") +require("patchwork") +require("latex2exp") +``` + +```{r setup, echo = FALSE} +options(dplyr.summarise.inform = FALSE) +knitr::opts_knit$set(kable.force.latex = TRUE) + +meanse <- function(x, ...) { + mean1 <- signif(round(mean(x, na.rm = T), 2), 5) # calculate mean and round + se1 <- signif(round(sd(x, na.rm = T) / sqrt(sum(!is.na(x))), 2), 2) # std error - round adding zeros + out <- paste(mean1, "$\\pm$", se1) # paste together mean plus/minus and standard error + if (str_detect(out, "NA")) { + out <- "NA" + } # if missing do not add plusminus + if (se1 == 0) { + out <- paste(mean1) + } + return(out) +} +``` + +```{r import-data, echo = FALSE} +filenames <- list.files( + path = "./data/", + pattern = "inference_testing_2023-07-*", + full.names = TRUE +) +data_list <- lapply(filenames, readRDS) +col_id_BICLS <- c(11, 16, 23, 30, 37) +result_data_frame <- dplyr::bind_rows(data_list) + +# Compute the preferred model +result_data_frame <- cbind(result_data_frame, preferred_model = sapply(seq_len(nrow(result_data_frame)), function(n) sub("_BICL", "", names(which.max(result_data_frame[n, col_id_BICLS]))))) + +``` + +# Efficiency of the inference + +\paragraph{Simulation settings} For this simulation the data is simulated with +$M = 2, n_{1}^{m} = 120, n_{2}^{m} = 120, Q_1 = Q_2 = 4$, $\bm{\alpha}, \bm{\pi}$ +and $\bm{\rho}$ are set as follows: +\begin{align*} + &&\bm{\alpha} = .25 + + \begin{pmatrix} + 3 \eps[\alpha] & 2 \eps[\alpha] & \eps[\alpha] & - \eps[\alpha]\\ + 2 \eps[\alpha] & 2 \eps[\alpha] & - \eps[\alpha] & \eps[\alpha]\\ + \eps[\alpha] & - \eps[\alpha] & \eps[\alpha] & 2 \eps[\alpha]\\ + - \eps[\alpha] & \eps[\alpha] & 2 \eps[\alpha] & 0 + \end{pmatrix}, \\ \bm{\pi}^1 = \sigma_1 + \begin{pmatrix} + 0.2 & 0.4 & 0.4 & 0 + \end{pmatrix}, + && \bm{\pi}^2 = + \begin{pmatrix} + 0.25 & 0.25 & 0.25 & 0.25 + \end{pmatrix}, \\ + \bm{\rho}^1 = + \begin{pmatrix} + 0.25 & 0.25 & 0.25 & 0.25 + \end{pmatrix}, && + \bm{\rho}^2 = \sigma_2 + \begin{pmatrix} + 0 & 0.33 & 0.33 & 0.33 + \end{pmatrix}, && +\end{align*} +with $\eps[\alpha]$ taking nine equally spaced values ranging from 0 to 0.24. +For each value of $\eps[\alpha]$, 108 datasets ($X_1, X_2$) are simulated, +resulting in $9 \times 108 = 972$ datasets. More precisely, for each dataset, +we pick uniformly at random two permutations of $\{ 1, \dots , 4 \}$ +($\sigma_1, \sigma_2$) with the constraint that $\sigma_1(4) \neq \sigma_2(1)$. +This ensures that each of the two networks have a non-empty block that is empty +in the other one. Then the networks are simulated with +$\mathcal{B}$ern-$BiSBM_{120}(4, \bm{\alpha}, \bm{\pi}^m, \bm{\rho}^m)$ +with the previous parameters. Each network has 2 blocks in common and their +connectivity structures encompass a mix of core-periphery, assortative +community and disassortative community structures, depending on which 3 of the 4 +blocks are selected for each network. $\eps[\alpha]$ represents the strength of +these structures, the larger, the easier it is to tell apart one block from +another. + +\paragraph{Inference} We want to measure the quality of the +inference procedure, for this we use the inference described in the section +\ref{sec:variational-estimation-of-the-parameters}. + +\paragraph{Quality indicators} To assess the quality of the inference, we will +use the following indicators: +\begin{itemize} + \item First, for each dataset, we put in competition $\pi\text{-}colBiSBM$ with + $sep\text{-}BiSBM$, $iid\text{-}colBiSBM$, $\rho\text{-}colBiSBM$, + $\pi\rho\text{-}colBiSBM$ + respectively. To do so, for each dataset, we compute the + BIC-L of each model $\pi\text{-}colBiSBM$ is preferred to $sep\text{-}BiSBM$ + (resp. $iid\text{-}colBiSBM$, $\rho\text{-}colBiSBM$, + $\pi\rho\text{-}colBiSBM$) if + its BIC-L is greater. + \item When considering $\pi\text{-}colBiSBM$, $\rho\text{-}colBiSBM$, + $\pi\rho\text{-}colBiSBM$ we compare $\widehat{Q_1}$, $\widehat{Q_2}$ to + their true values. ($Q_1 = 4$ and $Q_2 = 4$) + \item Finally, we assess the quality of the node grouping by computing the + Adjusted Rand Index \parencite[][, ARI = 0 for a random grouping, ARI = 1 for a perfect recovery]{hubertComparingPartitions1985}. For each network, for the + $\pi\text{-}colBiSBM$, $\rho\text{-}colBiSBM$, + $\pi\rho\text{-}colBiSBM$ we compare the inferred block memberships to the + real ones by computing the mean of the ARI per axis over the two networks + \begin{equation*} + \overline{\text{ARI}}_d = \frac{1}{2} \text{ARI}\big( \text{ARI}(\widehat{\bm{Z}^1_d},\bm{Z}^1_d) + \text{ARI}(\widehat{\bm{Z}^2_d},\bm{Z}^2_d) \big) + \end{equation*} + where $d$ is the dimension or axis (i.e., rows, $d=1$, or columns, $d=2$) of + the block memberships. + And we compute the ARI of the whole set of nodes to account for block + pairing between networks + \begin{equation*} + \text{ARI}_d = \text{ARI}\big((\widehat{\bm{Z}^1_d},\widehat{\bm{Z}^2_d}),(\bm{Z}^1_d,\bm{Z}^2_d) \big) + \end{equation*} +\end{itemize} + +All these quality indicators are averaged over the 108 datasets. The results are +provided in the tables \ref{tab:per_model_sep} to \ref{tab:per_model_pirho}. Each line corresponds to the +108 datasets for a given value of value of $\eps[\alpha]$. + +```{r inference_table, echo = FALSE} +averaged_data <- result_data_frame %>% + group_by(epsilon_alpha) %>% + summarise(across(-preferred_model, list("avrg" = meanse))) %>% + select(-c(2:10)) +averaged_data <- averaged_data %>% + select(which(!grepl("*_BICL_*", colnames(averaged_data)), + arr.ind = TRUE)) +``` + +```{r function_per_model, echo = FALSE} +dataframe_per_model <- function(model) { + averaged_data %>% + select(epsilon_alpha, starts_with(paste0(model, "_"))) +} +``` + +```{r per_model_table, echo = FALSE, results='asis', message=FALSE, warning = FALSE} +for (model in c("sep", "iid", "pi", "rho", "pirho")) { + kable_colnames <- c( + "$\\eps[\\alpha]$", #"BIC-L", + "$\\overline{\\text{ARI}}_{1}$", + "$\\overline{\\text{ARI}}_{2}$", "$\\text{ARI}_{1}$", "$\\text{ARI}_{2}$" + ) + model_name <- model + if (model != "sep") { + kable_colnames <- c( + kable_colnames, "Recovered $Q_1$", + "Recovered $Q_2$" + ) + } + if (model == "pirho") { + model_name <- "$\\pi\\rho$" + } else { + if (model != "iid" && model != "sep") model_name <- paste0("$\\", model, "$") + } + print(kable(dataframe_per_model(model), + escape = FALSE, + booktabs = TRUE, + digits = 2, + position = "!h", + caption = paste0( + "\\label{tab:per_model_", model, + "}Quality metrics for ", + paste0(model_name, "-colBiSBM") + ), + col.names = kable_colnames + )) +} +``` + + +```{r proportion-preferred_model, echo = FALSE} +proportion_preferred_table <- result_data_frame %>% + group_by(epsilon_alpha, preferred_model) %>% + summarise(n = n()) %>% + mutate(freq = n / sum(n)) %>% + ungroup() %>% + select(-n) %>% + pivot_wider( + names_from = preferred_model, + values_from = freq, values_fill = 0 + ) +``` + +\paragraph{Results} For the model comparison, when $\eps[\alpha]$ is small +($\eps[\alpha]\in[0, .04]$), the simulation model is close to the +Erd\H{o}s-Reńyi network and it is very hard to find any structure beyond the one +of a single block on each dimension. \ No newline at end of file diff --git a/Rcodes/simulation/inference_analyze.tex b/Rcodes/simulation/inference_analyze.tex new file mode 100644 index 0000000..da0f782 --- /dev/null +++ b/Rcodes/simulation/inference_analyze.tex @@ -0,0 +1,205 @@ +\hypertarget{efficiency-of-the-inference}{% +\section{Efficiency of the +inference}\label{efficiency-of-the-inference}} + +\paragraph{Simulation settings} + +For this simulation the data is simulated with +\(M = 2, n_{1}^{m} = 120, n_{2}^{m} = 120, Q_1 = Q_2 = 4\), +\(\bm{\alpha}, \bm{\pi}\) and \(\bm{\rho}\) are set as follows: +\begin{align*} + &&\bm{\alpha} = .25 + + \begin{pmatrix} + 3 \eps[\alpha] & 2 \eps[\alpha] & \eps[\alpha] & - \eps[\alpha]\\ + 2 \eps[\alpha] & 2 \eps[\alpha] & - \eps[\alpha] & \eps[\alpha]\\ + \eps[\alpha] & - \eps[\alpha] & \eps[\alpha] & 2 \eps[\alpha]\\ + - \eps[\alpha] & \eps[\alpha] & 2 \eps[\alpha] & 0 + \end{pmatrix}, \\ \bm{\pi}^1 = \sigma_1 + \begin{pmatrix} + 0.2 & 0.4 & 0.4 & 0 + \end{pmatrix}, + && \bm{\pi}^2 = + \begin{pmatrix} + 0.25 & 0.25 & 0.25 & 0.25 + \end{pmatrix}, \\ + \bm{\rho}^1 = + \begin{pmatrix} + 0.25 & 0.25 & 0.25 & 0.25 + \end{pmatrix}, && + \bm{\rho}^2 = \sigma_2 + \begin{pmatrix} + 0 & 0.33 & 0.33 & 0.33 + \end{pmatrix}, && +\end{align*} with \(\eps[\alpha]\) taking nine equally spaced values +ranging from 0 to 0.24. For each value of \(\eps[\alpha]\), 108 datasets +(\(X_1, X_2\)) are simulated, resulting in \(9 \times 108 = 972\) +datasets. More precisely, for each dataset, we pick uniformly at random +two permutations of \(\{ 1, \dots , 4 \}\) (\(\sigma_1, \sigma_2\)) with +the constraint that \(\sigma_1(4) \neq \sigma_2(1)\). This ensures that +each of the two networks have a non-empty block that is empty in the +other one. Then the networks are simulated with +\(\mathcal{B}\)ern-\(BiSBM_{120}(4, \bm{\alpha}, \bm{\pi}^m, \bm{\rho}^m)\) +with the previous parameters. Each network has 2 blocks in common and +their connectivity structures encompass a mix of core-periphery, +assortative community and disassortative community structures, depending +on which 3 of the 4 blocks are selected for each network. +\(\eps[\alpha]\) represents the strength of these structures, the +larger, the easier it is to tell apart one block from another. + +\paragraph{Inference} + +We want to measure the quality of the inference procedure, for this we +use the inference described in the section +\ref{sec:variational-estimation-of-the-parameters}. + +\paragraph{Quality indicators} + +To assess the quality of the inference, we will use the following +indicators: + +\begin{itemize} + \item First, for each dataset, we put in competition $\pi\text{-}colBiSBM$ with + $sep\text{-}BiSBM$, $iid\text{-}colBiSBM$, $\rho\text{-}colBiSBM$, + $\pi\rho\text{-}colBiSBM$ + respectively. To do so, for each dataset, we compute the + BIC-L of each model $\pi\text{-}colBiSBM$ is preferred to $sep\text{-}BiSBM$ + (resp. $iid\text{-}colBiSBM$, $\rho\text{-}colBiSBM$, + $\pi\rho\text{-}colBiSBM$) if + its BIC-L is greater. + \item When considering $\pi\text{-}colBiSBM$, $\rho\text{-}colBiSBM$, + $\pi\rho\text{-}colBiSBM$ we compare $\widehat{Q_1}$, $\widehat{Q_2}$ to + their true values. ($Q_1 = 4$ and $Q_2 = 4$) + \item Finally, we assess the quality of the node grouping by computing the + Adjusted Rand Index \parencite[][, ARI = 0 for a random grouping, ARI = 1 for a perfect recovery]{hubertComparingPartitions1985}. For each network, for the + $\pi\text{-}colBiSBM$, $\rho\text{-}colBiSBM$, + $\pi\rho\text{-}colBiSBM$ we compare the inferred block memberships to the + real ones by computing the mean of the ARI per axis over the two networks + \begin{equation*} + \overline{\text{ARI}}_d = \frac{1}{2} \text{ARI}\big( \text{ARI}(\widehat{\bm{Z}^1_d},\bm{Z}^1_d) + \text{ARI}(\widehat{\bm{Z}^2_d},\bm{Z}^2_d) \big) + \end{equation*} + where $d$ is the dimension or axis (i.e., rows, $d=1$, or columns, $d=2$) of + the block memberships. + And we compute the ARI of the whole set of nodes to account for block + pairing between networks + \begin{equation*} + \text{ARI}_d = \text{ARI}\big((\widehat{\bm{Z}^1_d},\widehat{\bm{Z}^2_d}),(\bm{Z}^1_d,\bm{Z}^2_d) \big) + \end{equation*} +\end{itemize} + +All these quality indicators are averaged over the 108 datasets. The +results are provided in the tables \ref{tab:per_model_sep} to +\ref{tab:per_model_pirho}. Each line corresponds to the 108 datasets for +a given value of value of \(\eps[\alpha]\). + +\begin{table}[!h] + +\caption{\label{tab:per_model_table}\label{tab:per_model_sep}Quality metrics for sep-colBiSBM} +\centering +\begin{tabular}[t]{rllll} +\toprule +$\eps[\alpha]$ & $\overline{\text{ARI}}_{1}$ & $\overline{\text{ARI}}_{2}$ & $\text{ARI}_{1}$ & $\text{ARI}_{2}$\\ +\midrule +0.00 & 0 & 0 & 0 & 0\\ +0.03 & 0 & 0 & 0 & 0\\ +0.06 & 0.1 $\pm$ 0.01 & 0.08 $\pm$ 0.01 & 0.06 $\pm$ 0.01 & 0.05 $\pm$ 0.01\\ +0.09 & 0.71 $\pm$ 0.02 & 0.7 $\pm$ 0.01 & 0.37 $\pm$ 0.02 & 0.37 $\pm$ 0.02\\ +0.12 & 0.94 $\pm$ 0.01 & 0.93 $\pm$ 0.01 & 0.5 $\pm$ 0.02 & 0.49 $\pm$ 0.02\\ +\addlinespace +0.15 & 0.99 & 0.99 & 0.54 $\pm$ 0.02 & 0.49 $\pm$ 0.01\\ +0.18 & 0.99 & 0.99 & 0.52 $\pm$ 0.02 & 0.52 $\pm$ 0.02\\ +0.21 & 0.99 & 0.99 & 0.54 $\pm$ 0.02 & 0.52 $\pm$ 0.02\\ +0.24 & 1 & 1 & 0.55 $\pm$ 0.02 & 0.52 $\pm$ 0.02\\ +\bottomrule +\end{tabular} +\end{table} +\begin{table}[!h] + +\caption{\label{tab:per_model_table}\label{tab:per_model_iid}Quality metrics for iid-colBiSBM} +\centering +\begin{tabular}[t]{rllllll} +\toprule +$\eps[\alpha]$ & $\overline{\text{ARI}}_{1}$ & $\overline{\text{ARI}}_{2}$ & $\text{ARI}_{1}$ & $\text{ARI}_{2}$ & Recovered $Q_1$ & Recovered $Q_2$\\ +\midrule +0.00 & 0 & 0 & 0 & 0 & 1 & 1\\ +0.03 & 0 & 0 & 0 & 0 & 1 & 1\\ +0.06 & 0.08 $\pm$ 0.01 & 0.08 $\pm$ 0.01 & 0.08 $\pm$ 0.01 & 0.07 $\pm$ 0.01 & 1.4 $\pm$ 0.05 & 1.49 $\pm$ 0.05\\ +0.09 & 0.72 $\pm$ 0.01 & 0.71 $\pm$ 0.01 & 0.53 $\pm$ 0.02 & 0.52 $\pm$ 0.02 & 3.4 $\pm$ 0.06 & 3.41 $\pm$ 0.06\\ +0.12 & 0.94 & 0.93 & 0.75 $\pm$ 0.03 & 0.72 $\pm$ 0.03 & 4.06 $\pm$ 0.02 & 3.97 $\pm$ 0.02\\ +\addlinespace +0.15 & 0.98 & 0.98 & 0.77 $\pm$ 0.03 & 0.76 $\pm$ 0.03 & 4.11 $\pm$ 0.03 & 4.11 $\pm$ 0.03\\ +0.18 & 0.99 & 0.99 & 0.82 $\pm$ 0.03 & 0.82 $\pm$ 0.03 & 4.15 $\pm$ 0.04 & 4.13 $\pm$ 0.03\\ +0.21 & 0.99 & 0.99 & 0.8 $\pm$ 0.02 & 0.79 $\pm$ 0.03 & 4.35 $\pm$ 0.06 & 4.19 $\pm$ 0.04\\ +0.24 & 0.99 & 0.99 & 0.77 $\pm$ 0.03 & 0.77 $\pm$ 0.03 & 4.3 $\pm$ 0.06 & 4.43 $\pm$ 0.07\\ +\bottomrule +\end{tabular} +\end{table} +\begin{table}[!h] + +\caption{\label{tab:per_model_table}\label{tab:per_model_pi}Quality metrics for $\pi$-colBiSBM} +\centering +\begin{tabular}[t]{rllllll} +\toprule +$\eps[\alpha]$ & $\overline{\text{ARI}}_{1}$ & $\overline{\text{ARI}}_{2}$ & $\text{ARI}_{1}$ & $\text{ARI}_{2}$ & Recovered $Q_1$ & Recovered $Q_2$\\ +\midrule +0.00 & 0 & 0 & 0 & 0 & 1 & 1\\ +0.03 & 0 & 0 & 0 & 0 & 1.01 $\pm$ 0.01 & 1\\ +0.06 & 0.07 $\pm$ 0.01 & 0.08 $\pm$ 0.01 & 0.07 $\pm$ 0.01 & 0.06 $\pm$ 0.01 & 1.49 $\pm$ 0.05 & 1.5 $\pm$ 0.05\\ +0.09 & 0.73 $\pm$ 0.02 & 0.72 $\pm$ 0.01 & 0.56 $\pm$ 0.02 & 0.53 $\pm$ 0.02 & 3.78 $\pm$ 0.07 & 3.37 $\pm$ 0.07\\ +0.12 & 0.96 & 0.93 & 0.79 $\pm$ 0.02 & 0.74 $\pm$ 0.03 & 4.46 $\pm$ 0.07 & 3.95 $\pm$ 0.02\\ +\addlinespace +0.15 & 0.99 & 0.97 & 0.82 $\pm$ 0.02 & 0.76 $\pm$ 0.03 & 4.62 $\pm$ 0.08 & 4\\ +0.18 & 1 & 0.98 & 0.83 $\pm$ 0.02 & 0.79 $\pm$ 0.03 & 4.65 $\pm$ 0.09 & 4\\ +0.21 & 1 & 0.98 & 0.84 $\pm$ 0.02 & 0.79 $\pm$ 0.03 & 4.69 $\pm$ 0.1 & 4\\ +0.24 & 1 & 0.99 & 0.86 $\pm$ 0.02 & 0.79 $\pm$ 0.03 & 4.74 $\pm$ 0.11 & 4.01 $\pm$ 0.01\\ +\bottomrule +\end{tabular} +\end{table} +\begin{table}[!h] + +\caption{\label{tab:per_model_table}\label{tab:per_model_rho}Quality metrics for $\rho$-colBiSBM} +\centering +\begin{tabular}[t]{rllllll} +\toprule +$\eps[\alpha]$ & $\overline{\text{ARI}}_{1}$ & $\overline{\text{ARI}}_{2}$ & $\text{ARI}_{1}$ & $\text{ARI}_{2}$ & Recovered $Q_1$ & Recovered $Q_2$\\ +\midrule +0.00 & 0 & 0 & 0 & 0 & 1 & 1\\ +0.03 & 0 & 0 & 0 & 0 & 1.01 $\pm$ 0.01 & 1.01 $\pm$ 0.01\\ +0.06 & 0.08 $\pm$ 0.01 & 0.08 $\pm$ 0.01 & 0.06 $\pm$ 0.01 & 0.07 $\pm$ 0.01 & 1.39 $\pm$ 0.05 & 1.6 $\pm$ 0.06\\ +0.09 & 0.72 $\pm$ 0.01 & 0.72 $\pm$ 0.01 & 0.53 $\pm$ 0.02 & 0.54 $\pm$ 0.02 & 3.39 $\pm$ 0.07 & 3.74 $\pm$ 0.07\\ +0.12 & 0.93 & 0.95 & 0.71 $\pm$ 0.03 & 0.75 $\pm$ 0.02 & 3.95 $\pm$ 0.02 & 4.5 $\pm$ 0.07\\ +\addlinespace +0.15 & 0.97 & 0.99 & 0.78 $\pm$ 0.03 & 0.81 $\pm$ 0.02 & 4 & 4.49 $\pm$ 0.07\\ +0.18 & 0.98 & 1 & 0.76 $\pm$ 0.03 & 0.81 $\pm$ 0.02 & 4.01 $\pm$ 0.01 & 4.71 $\pm$ 0.09\\ +0.21 & 0.98 & 1 & 0.76 $\pm$ 0.03 & 0.81 $\pm$ 0.02 & 4.03 $\pm$ 0.02 & 4.72 $\pm$ 0.09\\ +0.24 & 0.98 & 1 & 0.74 $\pm$ 0.03 & 0.8 $\pm$ 0.02 & 4.06 $\pm$ 0.02 & 4.8 $\pm$ 0.1\\ +\bottomrule +\end{tabular} +\end{table} +\begin{table}[!h] + +\caption{\label{tab:per_model_table}\label{tab:per_model_pirho}Quality metrics for $\pi\rho$-colBiSBM} +\centering +\begin{tabular}[t]{rllllll} +\toprule +$\eps[\alpha]$ & $\overline{\text{ARI}}_{1}$ & $\overline{\text{ARI}}_{2}$ & $\text{ARI}_{1}$ & $\text{ARI}_{2}$ & Recovered $Q_1$ & Recovered $Q_2$\\ +\midrule +0.00 & 0 & 0 & 0 & 0 & 1 & 1\\ +0.03 & 0 & 0 & 0 & 0 & 1.01 $\pm$ 0.01 & 1.01 $\pm$ 0.01\\ +0.06 & 0.07 $\pm$ 0.01 & 0.07 $\pm$ 0.01 & 0.07 $\pm$ 0.01 & 0.06 $\pm$ 0.01 & 1.48 $\pm$ 0.05 & 1.57 $\pm$ 0.06\\ +0.09 & 0.74 $\pm$ 0.01 & 0.73 $\pm$ 0.01 & 0.56 $\pm$ 0.03 & 0.55 $\pm$ 0.02 & 3.69 $\pm$ 0.06 & 3.66 $\pm$ 0.06\\ +0.12 & 0.96 $\pm$ 0.01 & 0.95 $\pm$ 0.01 & 0.73 $\pm$ 0.03 & 0.73 $\pm$ 0.03 & 4.31 $\pm$ 0.05 & 4.26 $\pm$ 0.05\\ +\addlinespace +0.15 & 0.99 & 0.99 & 0.79 $\pm$ 0.02 & 0.78 $\pm$ 0.03 & 4.31 $\pm$ 0.05 & 4.35 $\pm$ 0.05\\ +0.18 & 1 & 1 & 0.83 $\pm$ 0.02 & 0.83 $\pm$ 0.02 & 4.31 $\pm$ 0.05 & 4.25 $\pm$ 0.04\\ +0.21 & 1 & 1 & 0.77 $\pm$ 0.03 & 0.77 $\pm$ 0.03 & 4.42 $\pm$ 0.05 & 4.34 $\pm$ 0.05\\ +0.24 & 1 & 1 & 0.82 $\pm$ 0.02 & 0.82 $\pm$ 0.02 & 4.25 $\pm$ 0.04 & 4.31 $\pm$ 0.05\\ +\bottomrule +\end{tabular} +\end{table} + +\paragraph{Results} + +For the model comparison, when \(\eps[\alpha]\) is small +(\(\eps[\alpha]\in[0, .04]\)), the simulation model is close to the +Erd\H{o}s-Reńyi network and it is very hard to find any structure beyond +the one of a single block on each dimension. diff --git a/Rcodes/simulation/model_selection_analyze.Rmd b/Rcodes/simulation/model_selection_analyze.Rmd index 564e373..d21af4a 100644 --- a/Rcodes/simulation/model_selection_analyze.Rmd +++ b/Rcodes/simulation/model_selection_analyze.Rmd @@ -1,11 +1,18 @@ ```{r libraries, echo = FALSE, include = FALSE} require("ggplot2") +require("knitr") +# require("kableExtra") require("tidyr") require("dplyr") require("patchwork") require("latex2exp") ``` +```{r setup, echo = FALSE, include= FALSE} +options(knitr.table.knitr.table.format = "latex") +``` + + ```{r import-data, echo = FALSE} filenames <- list.files( path = "./data/", @@ -113,7 +120,7 @@ Finally, when $\eps[\pi] > 0$ or $\bm{\pi}^1 \neq \bm{\pi}^2$ and $\eps[\rho] > 0$ or $\bm{\rho}^1 \neq \bm{\rho}^2$, the model is a $\pi\rho\text{-}colBiSBM$. -```{r tables, echo = FALSE} +```{r tables, echo = FALSE, results='asis'} kable( (model_comparison_eps_pi %>% select(-one_of("n")) %>% @@ -121,23 +128,28 @@ kable( names_from = preferred_model, values_from = prop_model, values_fill = 0 - ) %>% group_by(epsilon_pi) %>% - summarise(rec_Q1 = mean(rec_Q1), - iid = sum(iid), - pi = sum(pi), - rho = sum(rho), - pirho = sum(pirho)))[,c(1,3:6, 2)], + ) %>% group_by(epsilon_pi) %>% + summarise( + rec_Q1 = mean(rec_Q1), + iid = sum(iid), + pi = sum(pi), + rho = sum(rho), + pirho = sum(pirho) + ))[, c(1, 3:6, 2)], digits = 2, col.names = c( "$\\eps[\\pi]$", - "$iid\\text{-}colBiSBM$", + "$iid\\text{-}colBiSBM$ ", "$\\pi\\text{-}colBiSBM$", "$\\rho\\text{-}colBiSBM$", "$\\pi\\rho\\text{-}colBiSBM$", "Recovered $Q_1$" ), align = "lcccc", + booktab = TRUE, + position = "!h", + escape = FALSE, caption = "\\label{tab:pi-model-sel}Model selection for varying $\\pi$ mixture parameters" -) +) %>% kableExtra::add_header_above(c(" " = 1, "Proportions of model selection" = 4, "Blocks" = 1)) kable( (model_comparison_eps_rho %>% select(-one_of("n")) %>% @@ -154,14 +166,17 @@ kable( digits = 2, col.names = c( "$\\eps[\\rho]$", - "$iid\\text{-}colBiSBM$", + "$iid\\text{-}colBiSBM$ ", "$\\pi\\text{-}colBiSBM$", "$\\rho\\text{-}colBiSBM$", "$\\pi\\rho\\text{-}colBiSBM$", "Recovered $Q_2$" ), align = "lcccc", + booktab = TRUE, + position = "!h", + escape = FALSE, caption = "\\label{tab:rho-model-sel}Model selection for varying $\\rho$ mixture parameters" -) +) %>% kableExtra::add_header_above(c(" " = 1, "Proportions of model selection" = 4, "Blocks" = 1)) ``` \begin{figure}[H] @@ -170,7 +185,7 @@ kable( \label{fig:pref_model_func_eps} \end{figure} -On the figure \ref{fig:pref_model_func_eps} and tables \ref{tab:pi-model-sel} +\paragraph{Results:}On the figure \ref{fig:pref_model_func_eps} and tables \ref{tab:pi-model-sel} and \ref{tab:rho-model-sel}, one can see that there is a turning point around $\eps[\pi] = 0.2$ (resp. $\eps[\rho] = 0.2$), before which $iid\text{-}colBiSBM$ @@ -180,5 +195,5 @@ $\rho\text{-}colBiSBM$) and $\pi\rho\text{-}colBiSBM$ gets more and more selected, highlighting our capacity to recover the simulated structure. -Please note that when "Recovered $Q_1$(or $Q_2$)" is not an integer it's because +\paragraph*{Remark:} Please note that when "Recovered $Q_1$(or $Q_2$)" is not an integer it's because some procedures returned a value other than 3. \ No newline at end of file diff --git a/Rcodes/simulation/model_selection_analyze.tex b/Rcodes/simulation/model_selection_analyze.tex index 70ad597..754b600 100644 --- a/Rcodes/simulation/model_selection_analyze.tex +++ b/Rcodes/simulation/model_selection_analyze.tex @@ -49,315 +49,53 @@ is a \(\rho\text{-}colBiSBM\). Finally, when \(\eps[\pi] > 0\) or \(\bm{\rho}^1 \neq \bm{\rho}^2\), the model is a \(\pi\rho\text{-}colBiSBM\). -\begin{longtable}[]{@{}lccccl@{}} -\caption{\label{tab:pi-model-sel}Model selection for varying \(\pi\) -mixture parameters}\tabularnewline -\toprule -\begin{minipage}[b]{0.08\columnwidth}\raggedright -\(\eps[\pi]\)\strut -\end{minipage} & \begin{minipage}[b]{0.15\columnwidth}\centering -\(iid\text{-}colBiSBM\)\strut -\end{minipage} & \begin{minipage}[b]{0.15\columnwidth}\centering -\(\pi\text{-}colBiSBM\)\strut -\end{minipage} & \begin{minipage}[b]{0.16\columnwidth}\centering -\(\rho\text{-}colBiSBM\)\strut -\end{minipage} & \begin{minipage}[b]{0.18\columnwidth}\centering -\(\pi\rho\text{-}colBiSBM\)\strut -\end{minipage} & \begin{minipage}[b]{0.11\columnwidth}\raggedright -Recovered \(Q_1\)\strut -\end{minipage}\tabularnewline -\midrule -\endfirsthead -\toprule -\begin{minipage}[b]{0.08\columnwidth}\raggedright -\(\eps[\pi]\)\strut -\end{minipage} & \begin{minipage}[b]{0.15\columnwidth}\centering -\(iid\text{-}colBiSBM\)\strut -\end{minipage} & \begin{minipage}[b]{0.15\columnwidth}\centering -\(\pi\text{-}colBiSBM\)\strut -\end{minipage} & \begin{minipage}[b]{0.16\columnwidth}\centering -\(\rho\text{-}colBiSBM\)\strut -\end{minipage} & \begin{minipage}[b]{0.18\columnwidth}\centering -\(\pi\rho\text{-}colBiSBM\)\strut -\end{minipage} & \begin{minipage}[b]{0.11\columnwidth}\raggedright -Recovered \(Q_1\)\strut -\end{minipage}\tabularnewline -\midrule -\endhead -\begin{minipage}[t]{0.08\columnwidth}\raggedright -0.00\strut -\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering -0.65\strut -\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering -0.00\strut -\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\centering -0.35\strut -\end{minipage} & \begin{minipage}[t]{0.18\columnwidth}\centering -0.00\strut -\end{minipage} & \begin{minipage}[t]{0.11\columnwidth}\raggedright -3.00\strut -\end{minipage}\tabularnewline -\begin{minipage}[t]{0.08\columnwidth}\raggedright -0.04\strut -\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering -0.66\strut -\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering -0.00\strut -\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\centering -0.34\strut -\end{minipage} & \begin{minipage}[t]{0.18\columnwidth}\centering -0.00\strut -\end{minipage} & \begin{minipage}[t]{0.11\columnwidth}\raggedright -3.00\strut -\end{minipage}\tabularnewline -\begin{minipage}[t]{0.08\columnwidth}\raggedright -0.07\strut -\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering -0.64\strut -\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering -0.01\strut -\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\centering -0.34\strut -\end{minipage} & \begin{minipage}[t]{0.18\columnwidth}\centering -0.01\strut -\end{minipage} & \begin{minipage}[t]{0.11\columnwidth}\raggedright -3.01\strut -\end{minipage}\tabularnewline -\begin{minipage}[t]{0.08\columnwidth}\raggedright -0.11\strut -\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering -0.63\strut -\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering -0.03\strut -\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\centering -0.31\strut -\end{minipage} & \begin{minipage}[t]{0.18\columnwidth}\centering -0.03\strut -\end{minipage} & \begin{minipage}[t]{0.11\columnwidth}\raggedright -3.01\strut -\end{minipage}\tabularnewline -\begin{minipage}[t]{0.08\columnwidth}\raggedright -0.14\strut -\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering -0.55\strut -\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering -0.12\strut -\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\centering -0.28\strut -\end{minipage} & \begin{minipage}[t]{0.18\columnwidth}\centering -0.05\strut -\end{minipage} & \begin{minipage}[t]{0.11\columnwidth}\raggedright -3.00\strut -\end{minipage}\tabularnewline -\begin{minipage}[t]{0.08\columnwidth}\raggedright -0.18\strut -\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering -0.39\strut -\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering -0.26\strut -\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\centering -0.21\strut -\end{minipage} & \begin{minipage}[t]{0.18\columnwidth}\centering -0.13\strut -\end{minipage} & \begin{minipage}[t]{0.11\columnwidth}\raggedright -3.01\strut -\end{minipage}\tabularnewline -\begin{minipage}[t]{0.08\columnwidth}\raggedright -0.21\strut -\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering -0.23\strut -\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering -0.42\strut -\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\centering -0.13\strut -\end{minipage} & \begin{minipage}[t]{0.18\columnwidth}\centering -0.23\strut -\end{minipage} & \begin{minipage}[t]{0.11\columnwidth}\raggedright -3.01\strut -\end{minipage}\tabularnewline -\begin{minipage}[t]{0.08\columnwidth}\raggedright -0.25\strut -\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering -0.10\strut -\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering -0.56\strut -\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\centering -0.05\strut -\end{minipage} & \begin{minipage}[t]{0.18\columnwidth}\centering -0.29\strut -\end{minipage} & \begin{minipage}[t]{0.11\columnwidth}\raggedright -3.02\strut -\end{minipage}\tabularnewline -\begin{minipage}[t]{0.08\columnwidth}\raggedright -0.28\strut -\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering -0.01\strut -\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering -0.65\strut -\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\centering -0.01\strut -\end{minipage} & \begin{minipage}[t]{0.18\columnwidth}\centering -0.33\strut -\end{minipage} & \begin{minipage}[t]{0.11\columnwidth}\raggedright -3.01\strut -\end{minipage}\tabularnewline -\bottomrule -\end{longtable} +\begin{table}[!h] -\begin{longtable}[]{@{}lccccl@{}} -\caption{\label{tab:rho-model-sel}Model selection for varying \(\rho\) -mixture parameters}\tabularnewline +\caption{\label{tab:tables}\label{tab:pi-model-sel}Model selection for varying $\pi$ mixture parameters} +\centering +\begin{tabular}[t]{lccccl} \toprule -\begin{minipage}[b]{0.09\columnwidth}\raggedright -\(\eps[\rho]\)\strut -\end{minipage} & \begin{minipage}[b]{0.15\columnwidth}\centering -\(iid\text{-}colBiSBM\)\strut -\end{minipage} & \begin{minipage}[b]{0.15\columnwidth}\centering -\(\pi\text{-}colBiSBM\)\strut -\end{minipage} & \begin{minipage}[b]{0.16\columnwidth}\centering -\(\rho\text{-}colBiSBM\)\strut -\end{minipage} & \begin{minipage}[b]{0.18\columnwidth}\centering -\(\pi\rho\text{-}colBiSBM\)\strut -\end{minipage} & \begin{minipage}[b]{0.11\columnwidth}\raggedright -Recovered \(Q_2\)\strut -\end{minipage}\tabularnewline +\multicolumn{1}{c}{ } & \multicolumn{4}{c}{Proportions of model selection} & \multicolumn{1}{c}{Blocks} \\ +\cmidrule(l{3pt}r{3pt}){2-5} \cmidrule(l{3pt}r{3pt}){6-6} +$\eps[\pi]$ & $iid\text{-}colBiSBM$ & $\pi\text{-}colBiSBM$ & $\rho\text{-}colBiSBM$ & $\pi\rho\text{-}colBiSBM$ & Recovered $Q_1$\\ \midrule -\endfirsthead -\toprule -\begin{minipage}[b]{0.09\columnwidth}\raggedright -\(\eps[\rho]\)\strut -\end{minipage} & \begin{minipage}[b]{0.15\columnwidth}\centering -\(iid\text{-}colBiSBM\)\strut -\end{minipage} & \begin{minipage}[b]{0.15\columnwidth}\centering -\(\pi\text{-}colBiSBM\)\strut -\end{minipage} & \begin{minipage}[b]{0.16\columnwidth}\centering -\(\rho\text{-}colBiSBM\)\strut -\end{minipage} & \begin{minipage}[b]{0.18\columnwidth}\centering -\(\pi\rho\text{-}colBiSBM\)\strut -\end{minipage} & \begin{minipage}[b]{0.11\columnwidth}\raggedright -Recovered \(Q_2\)\strut -\end{minipage}\tabularnewline -\midrule -\endhead -\begin{minipage}[t]{0.09\columnwidth}\raggedright -0.00\strut -\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering -0.63\strut -\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering -0.37\strut -\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\centering -0.00\strut -\end{minipage} & \begin{minipage}[t]{0.18\columnwidth}\centering -0.00\strut -\end{minipage} & \begin{minipage}[t]{0.11\columnwidth}\raggedright -3.00\strut -\end{minipage}\tabularnewline -\begin{minipage}[t]{0.09\columnwidth}\raggedright -0.04\strut -\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering -0.65\strut -\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering -0.34\strut -\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\centering -0.00\strut -\end{minipage} & \begin{minipage}[t]{0.18\columnwidth}\centering -0.01\strut -\end{minipage} & \begin{minipage}[t]{0.11\columnwidth}\raggedright -3.00\strut -\end{minipage}\tabularnewline -\begin{minipage}[t]{0.09\columnwidth}\raggedright -0.07\strut -\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering -0.64\strut -\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering -0.33\strut -\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\centering -0.01\strut -\end{minipage} & \begin{minipage}[t]{0.18\columnwidth}\centering -0.01\strut -\end{minipage} & \begin{minipage}[t]{0.11\columnwidth}\raggedright -3.00\strut -\end{minipage}\tabularnewline -\begin{minipage}[t]{0.09\columnwidth}\raggedright -0.11\strut -\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering -0.64\strut -\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering -0.31\strut -\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\centering -0.03\strut -\end{minipage} & \begin{minipage}[t]{0.18\columnwidth}\centering -0.02\strut -\end{minipage} & \begin{minipage}[t]{0.11\columnwidth}\raggedright -3.00\strut -\end{minipage}\tabularnewline -\begin{minipage}[t]{0.09\columnwidth}\raggedright -0.14\strut -\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering -0.53\strut -\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering -0.29\strut -\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\centering -0.11\strut -\end{minipage} & \begin{minipage}[t]{0.18\columnwidth}\centering -0.06\strut -\end{minipage} & \begin{minipage}[t]{0.11\columnwidth}\raggedright -3.00\strut -\end{minipage}\tabularnewline -\begin{minipage}[t]{0.09\columnwidth}\raggedright -0.18\strut -\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering -0.42\strut -\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering -0.20\strut -\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\centering -0.24\strut -\end{minipage} & \begin{minipage}[t]{0.18\columnwidth}\centering -0.14\strut -\end{minipage} & \begin{minipage}[t]{0.11\columnwidth}\raggedright -3.01\strut -\end{minipage}\tabularnewline -\begin{minipage}[t]{0.09\columnwidth}\raggedright -0.21\strut -\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering -0.25\strut -\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering -0.12\strut -\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\centering -0.40\strut -\end{minipage} & \begin{minipage}[t]{0.18\columnwidth}\centering -0.22\strut -\end{minipage} & \begin{minipage}[t]{0.11\columnwidth}\raggedright -3.01\strut -\end{minipage}\tabularnewline -\begin{minipage}[t]{0.09\columnwidth}\raggedright -0.25\strut -\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering -0.08\strut -\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering -0.06\strut -\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\centering -0.58\strut -\end{minipage} & \begin{minipage}[t]{0.18\columnwidth}\centering -0.29\strut -\end{minipage} & \begin{minipage}[t]{0.11\columnwidth}\raggedright -3.01\strut -\end{minipage}\tabularnewline -\begin{minipage}[t]{0.09\columnwidth}\raggedright -0.28\strut -\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering -0.01\strut -\end{minipage} & \begin{minipage}[t]{0.15\columnwidth}\centering -0.01\strut -\end{minipage} & \begin{minipage}[t]{0.16\columnwidth}\centering -0.65\strut -\end{minipage} & \begin{minipage}[t]{0.18\columnwidth}\centering -0.32\strut -\end{minipage} & \begin{minipage}[t]{0.11\columnwidth}\raggedright -3.00\strut -\end{minipage}\tabularnewline +0.00 & 0.65 & 0.00 & 0.35 & 0.00 & 3.00\\ +0.04 & 0.66 & 0.00 & 0.34 & 0.00 & 3.00\\ +0.07 & 0.64 & 0.01 & 0.34 & 0.01 & 3.01\\ +0.11 & 0.63 & 0.03 & 0.31 & 0.03 & 3.01\\ +0.14 & 0.55 & 0.12 & 0.28 & 0.05 & 3.00\\ +\addlinespace +0.18 & 0.39 & 0.26 & 0.21 & 0.13 & 3.01\\ +0.21 & 0.23 & 0.42 & 0.13 & 0.23 & 3.01\\ +0.25 & 0.10 & 0.56 & 0.05 & 0.29 & 3.02\\ +0.28 & 0.01 & 0.65 & 0.01 & 0.33 & 3.01\\ \bottomrule -\end{longtable} +\end{tabular} +\end{table} + +\begin{table}[!h] + +\caption{\label{tab:tables}\label{tab:rho-model-sel}Model selection for varying $\rho$ mixture parameters} +\centering +\begin{tabular}[t]{lccccl} +\toprule +\multicolumn{1}{c}{ } & \multicolumn{4}{c}{Proportions of model selection} & \multicolumn{1}{c}{Blocks} \\ +\cmidrule(l{3pt}r{3pt}){2-5} \cmidrule(l{3pt}r{3pt}){6-6} +$\eps[\rho]$ & $iid\text{-}colBiSBM$ & $\pi\text{-}colBiSBM$ & $\rho\text{-}colBiSBM$ & $\pi\rho\text{-}colBiSBM$ & Recovered $Q_2$\\ +\midrule +0.00 & 0.63 & 0.37 & 0.00 & 0.00 & 3.00\\ +0.04 & 0.65 & 0.34 & 0.00 & 0.01 & 3.00\\ +0.07 & 0.64 & 0.33 & 0.01 & 0.01 & 3.00\\ +0.11 & 0.64 & 0.31 & 0.03 & 0.02 & 3.00\\ +0.14 & 0.53 & 0.29 & 0.11 & 0.06 & 3.00\\ +\addlinespace +0.18 & 0.42 & 0.20 & 0.24 & 0.14 & 3.01\\ +0.21 & 0.25 & 0.12 & 0.40 & 0.22 & 3.01\\ +0.25 & 0.08 & 0.06 & 0.58 & 0.29 & 3.01\\ +0.28 & 0.01 & 0.01 & 0.65 & 0.32 & 3.00\\ +\bottomrule +\end{tabular} +\end{table} \begin{figure}[H] \includegraphics{./Rcodes/simulation/img/plot_model_function_eps.png} @@ -365,6 +103,8 @@ Recovered \(Q_2\)\strut \label{fig:pref_model_func_eps} \end{figure} +\paragraph{Results:} + On the figure \ref{fig:pref_model_func_eps} and tables \ref{tab:pi-model-sel} and \ref{tab:rho-model-sel}, one can see that there is a turning point around \(\eps[\pi] = 0.2\) (resp. @@ -375,5 +115,7 @@ most of the times and after \(0.2\) the \(\pi\text{-}colBiSBM\) (resp. more selected, highlighting our capacity to recover the simulated structure. +\paragraph*{Remark:} + Please note that when ``Recovered \(Q_1\)(or \(Q_2\))'' is not an integer it's because some procedures returned a value other than 3. diff --git a/Rcodes/simulation/netclustering_analyze.R b/Rcodes/simulation/netclustering_analyze.R index 70638a9..645df0e 100644 --- a/Rcodes/simulation/netclustering_analyze.R +++ b/Rcodes/simulation/netclustering_analyze.R @@ -1,9 +1,8 @@ require("ggplot2") require("tictoc") +require("colSBM") -devtools::load_all("R/") - -result_clustering <- readRDS("simulation/data/simulated_collection_clustering_rho_10-05-23-14:40:46.Rds") +result_clustering <- readRDS("./Rcodes/simulation/data/simulated") list_clustering <- lapply( seq_along(result_clustering), function(s) result_clustering[[s]]$list_of_clusterings @@ -13,7 +12,7 @@ list_best_partition <- lapply( seq_along(list_clustering), function(s) { list( epsilon = result_clustering[[s]]$epsilon, - best_partition = extract_bipartite_best_partition(list_clustering[[s]]) + best_partition = unlist(extract_best_bipartite_partition(list_clustering[[s]])) ) } ) diff --git a/Rcodes/simulation/netclustering_analyze.Rmd b/Rcodes/simulation/netclustering_analyze.Rmd new file mode 100644 index 0000000..3e5f15b --- /dev/null +++ b/Rcodes/simulation/netclustering_analyze.Rmd @@ -0,0 +1,19 @@ +```{r libraries, echo = FALSE, include = FALSE} +require("ggplot2") +require("tidyr") +require("dplyr") +require("patchwork") +require("latex2exp") +``` + +\section{Network clustering of simulated networks}\label{sec:network-clustering-of-simulated-networks} + +```{r impoting-data, echo = FALSE} +filenames <- list.files( + path = "./data/", + pattern = "simulated_collection_clustering_*", + full.names = TRUE +) +# data_list <- lapply(filenames, function(file) lapply(readRDS(file), function(model) model$list_clustering)) +data_list <- lapply(filenames, readRDS) +``` \ No newline at end of file diff --git a/Rcodes/simulation/netclustering_analyze.tex b/Rcodes/simulation/netclustering_analyze.tex new file mode 100644 index 0000000..290de08 --- /dev/null +++ b/Rcodes/simulation/netclustering_analyze.tex @@ -0,0 +1 @@ +\section{Network clustering of simulated networks}\label{sec:network-clustering-of-simulated-networks} diff --git a/Rmd2Latex-fragment.R b/Rmd2Latex-fragment.R index ed044e9..ac13366 100644 --- a/Rmd2Latex-fragment.R +++ b/Rmd2Latex-fragment.R @@ -1,11 +1,14 @@ -#!/usr/bin/env Rscript -require("knitr") +#!/usr/bin/Rscript + +print(getwd()) + +options(knitr.table.format = "latex") create_latex <- function(f) { knitr::knit(f, "/tmp/tmp-outputfile.md") newname <- 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De plus j'ai beaucoup progressé dans les domaines abordés pendant mon stage, et cela m'a rendu confiant dans le choix de faire le master \emph{MathSV} pour l'année scolaire 2023-2024. Ce stage a donc été -déterminant et confirme l'orientation de mon parcours professionnel. \ No newline at end of file +déterminant et confirme l'orientation de mon parcours professionnel. + +\paragraph*{Note} La suite de ce rapport a été rédigée en anglais. \ No newline at end of file diff --git a/rapport.pdf b/rapport.pdf index 14d70667b35a91d1e8389a5bfc602da09e15f920..7b4f9db09c0b051b7010e631dc5f3a3a8e738841 100644 GIT binary patch delta 147564 zcmZtsQ*bV96Ez6Owr$(mv2EM7eaAL;Y}>YN+qRRPWS)1v`v01mnuETotNP&TK3R>m zI!;(42iWQ*A%IzukwK^dp^5`hgG@+0Z?vba(Ce-&QrdjCL6cEIu18X@ij_KGN)6uk zcOIiq1iYSqIT;zflGD)|^tI1F;R--QF1CKqn~YIFkTM&KfgTXWSCQ0_=5f%>KyB1) zsxncBq|VTm6E{8zUBcDv{yL!EFgjQJz%;Ho;ipkVBEzsveoRCMFc z{&6~n6JRMcTj$KAaa-zhQkTt!yo!Aymoml;8%+-8eV9=W#cTS(zmxeef#UYuTC6fTWGJ3QiG|p29_*3$}OS=j^ zB^`X0v9QQ@T1c#a1?BJTFNXX3=g%g7S=UyL#9tU-VTA-=9%x7`}kJG@y7713OVA3&0vwBl5yiiAe z1jGX7=ushn(czyBbQSo?e?U5Gs%hwD@(=hbt+g6{)}mFY^l<|;1rBIa($z}HB<)Px 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