From 3b4128877cf2a3f6ab48ddab390e7a64b971537e Mon Sep 17 00:00:00 2001 From: Louis Lacoste Date: Fri, 16 Aug 2024 18:03:59 +0200 Subject: [PATCH] rapport : raccourcissement taille page --- .../chapter4-simulations/na-robustness.tex | 12 +++---- .../network-clustering.tex | 32 ++++++++++-------- rapport/rapport.pdf | Bin 2452622 -> 2470349 bytes 3 files changed, 23 insertions(+), 21 deletions(-) diff --git a/rapport/chapter4-simulations/na-robustness.tex b/rapport/chapter4-simulations/na-robustness.tex index 9562bd3..1115cff 100644 --- a/rapport/chapter4-simulations/na-robustness.tex +++ b/rapport/chapter4-simulations/na-robustness.tex @@ -6,13 +6,13 @@ For this purpose we generate collections of networks with the following parameters: \begin{align*} \bm{\pi}^m = \begin{cases} - \bm{\pi} = \left( 0.5, 0.3, 0.2 \right) & \text{for } iid\text{-colBiSBM} \\ - \sigma_1^m(\bm{\pi}) & \text{for } \pi\text{-colBiSBM} \text{ and } \pi\rho\text{-colBiSBM} - \end{cases} \\ + \bm{\pi} = \left( 0.5, 0.3, 0.2 \right) & \text{for } iid \\ + \sigma_1^m(\bm{\pi}) & \text{for } \pi \text{ and } \pi\rho + \end{cases}, & \bm{\rho}^m = \begin{cases} - \bm{\rho} = \left( 0.5, 0.3, 0.2 \right) & \text{for } iid\text{-colBiSBM} \\ - \sigma_2^m(\bm{\rho}) & \text{for } \rho\text{-colBiSBM} \text{ and } \pi\rho\text{-colBiSBM}, + \bm{\rho} = \left( 0.5, 0.3, 0.2 \right) & \text{for } iid \\ + \sigma_2^m(\bm{\rho}) & \text{for } \rho \text{ and } \pi\rho, \end{cases} \end{align*} for the block proportions, and two different structures with the corresponding @@ -105,5 +105,5 @@ $\pi\rho$ present smaller values and larger variances. An explanation for the cases in which our models return lower values than expected could be to look for in our simulation parameters. They may, combined with the $\rho$ model be a difficult case for the estimation. -As we currently do not have identifiability results this is just and +As we currently do not have identifiability results this is just an hypothesis. \ No newline at end of file diff --git a/rapport/chapter4-simulations/network-clustering.tex b/rapport/chapter4-simulations/network-clustering.tex index e52562d..8c70fb2 100644 --- a/rapport/chapter4-simulations/network-clustering.tex +++ b/rapport/chapter4-simulations/network-clustering.tex @@ -10,13 +10,13 @@ $\bm{\pi}^1 = \left( 0.2, 0.3, 0.5 \right), ~\bm{\rho}^1 = \left( 0.2, 0.3, 0.5 \right)$ and for all $m = 2,\dots,9$ \begin{align*} \bm{\pi}^m = \begin{cases} - \bm{\pi}^1 & \text{for } iid\text{-colBiSBM} \\ - \sigma_1^m(\bm{\pi}^1) & \text{for } \pi\text{-colBiSBM} \text{ and } \pi\rho\text{-colBiSBM} - \end{cases} \\ + \bm{\pi}^1 & \text{for } iid \\ + \sigma_1^m(\bm{\pi}^1) & \text{for } \pi \text{ and } \pi\rho + \end{cases},~ & \bm{\rho}^m = \begin{cases} - \bm{\rho}^1 & \text{for } iid\text{-colBiSBM} \\ - \sigma_2^m(\bm{\rho}^1) & \text{for } \rho\text{-colBiSBM} \text{ and } \pi\rho\text{-colBiSBM} + \bm{\rho}^1 & \text{for } iid \\ + \sigma_2^m(\bm{\rho}^1) & \text{for } \rho \text{ and } \pi\rho \end{cases} \end{align*} where $\sigma_1^m$ and $\sigma_2^m$ are permutations of \{1, 2, 3\} proper to network $m$ and @@ -35,7 +35,7 @@ parameters as follows: - \frac{\epsilon}{2} & \epsilon & \epsilon \\ \epsilon & - \frac{\epsilon}{2} & \epsilon \\ \epsilon & \epsilon & - \frac{\epsilon}{2} - \end{pmatrix}, \\ + \end{pmatrix}, & \bm{\alpha}^{cp} = .3 + \begin{pmatrix} \frac{3 \epsilon}{2} & \epsilon & \frac{\epsilon}{2} \\ \epsilon & \frac{\epsilon}{2} & 0 \\ @@ -51,17 +51,19 @@ connections between blocks than within blocks. If $\epsilon = 0$, the three matrices are equal and the 9 networks have the same connection structure. Increasing $\epsilon$ differentiates the 3 sub-collections of networks. -% ARI boxplot -\begin{figure}[!ht] - \centering - \includestandalone{tikz/simulations/clustering/ari-clustering.tex} - \caption{ARI obtained for the clustering with the different models in - function of $\epsilon$} - \label{fig:ari-clustering-boxplot} -\end{figure} \paragraph{Results} The evaluation of our method involves a comparison between the resulting partition of the network collection and the simulated partition using the ARI index. As the value of $\epsilon$ increases, our ability to distinguish between the networks improves, and this distinction becomes nearly -perfect in all setups of the colBiSBM. \ No newline at end of file +perfect in all setups of the colBiSBM. + + +% ARI boxplot +\begin{figure}[!hb] + \centering + \includestandalone[height=0.25\textheight]{tikz/simulations/clustering/ari-clustering.tex} + \caption{ARI obtained for the clustering with the different models in + function of $\epsilon$} + \label{fig:ari-clustering-boxplot} +\end{figure} \ No newline at end of file diff --git a/rapport/rapport.pdf b/rapport/rapport.pdf index ab130a62958060835d178da1eb30e745d0e53e1d..9b3cbaacd292c40440c539cefd8b8c99b7cb040e 100644 GIT binary patch delta 69814 zcmX_{V{j(H`nQuO8{4*RZftX7+x7-eY}>YN+uqo=t^Myg=dJg{HB~d!clDR4p8NWB zPs~~}==4Dfs9z9h5FiMw=|`Ck@PSV^@UktW5dQb>?ChLH!!MHxs$K1jsEzB+S^oKP zq)h`c)pj^fl@}AKGkNY+nsPp5A(hD_HV=y!T;8;jt9}li%4L<^PL*XN2mjD?34~|M 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