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baldock : ajout fig, interp à faire

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rapport/chapter5-applications/baldock.tex
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@ -3,31 +3,44 @@
\cite{baldockSystemsApproachReveals2019a} study the diversity, robustness and \cite{baldockSystemsApproachReveals2019a} study the diversity, robustness and
impact of the type of environment on the ecological aspect of plant-pollinator impact of the type of environment on the ecological aspect of plant-pollinator
networks in four major english cities. networks in four major english cities. The networks are presented in
figures~\ref{subfig:baldock-english-network-bristol} to~\ref{subfig:baldock-english-network-reading}
\cite{baldockDailyTemporalStructure2011} \cite{baldockDailyTemporalStructure2011} aim to study the daily temporal
structure in a savanna pollination network. The data was collected in 2004
and in two sites, \emph{Turkana Boma} (TB) and \emph{Junction} (JN) in Kenya.
We will not look for a temporal structure but only use the full networks merged
in one
due to their small sizes. The network obtained is presented in
figure~\ref{fig:baldock-african-networks}.
\emph{Note:} those networks were extracted from a bigger dataset
from~\cite{doreRelativeEffectsAnthropogenic2021}. The full dataset was also
clusterized but issues arose that are discussed in
sub-section~\ref{ssec:difficulties-encountered}.
\begin{figure}[ht] \begin{figure}[ht]
\centering \centering
\begin{subfigure}[htb]{0.47\textwidth} \begin{subfigure}[htb]{0.47\textwidth}
\includestandalone{tikz/applications/baldock/graph-Baldock2019_Bristol} \includestandalone[width=0.86\textwidth]{tikz/applications/baldock/graph-Baldock2019_Bristol}
\caption{Bristol} \caption{Bristol}
\label{subfig:baldock-english-network-bristol}
\end{subfigure} \end{subfigure}
\hfill \hfill
\begin{subfigure}[htb]{0.47\textwidth} \begin{subfigure}[htb]{0.47\textwidth}
\includestandalone{tikz/applications/baldock/graph-Baldock2019_Edinburgh} \includestandalone[width=0.86\textwidth]{tikz/applications/baldock/graph-Baldock2019_Edinburgh}
\caption{Edinburgh} \caption{Edinburgh}
\end{subfigure} \end{subfigure}
\newline \newline
\begin{subfigure}[htb]{0.47\textwidth} \begin{subfigure}[htb]{0.47\textwidth}
\includestandalone{tikz/applications/baldock/graph-Baldock2019_Leeds} \includestandalone[width=0.86\textwidth]{tikz/applications/baldock/graph-Baldock2019_Leeds}
\caption{Leeds} \caption{Leeds}
\end{subfigure} \end{subfigure}
\hfill \hfill
\begin{subfigure}[htb]{0.47\textwidth} \begin{subfigure}[htb]{0.47\textwidth}
\includestandalone{tikz/applications/baldock/graph-Baldock2019_Reading} \includestandalone[width=0.86\textwidth]{tikz/applications/baldock/graph-Baldock2019_Reading}
\caption{Reading} \caption{Reading}
\label{subfig:baldock-english-network-reading}
\end{subfigure} \end{subfigure}
\caption{English networks from~\cite{baldockSystemsApproachReveals2019a}} \caption{English networks from~\cite{baldockSystemsApproachReveals2019a}}
\label{fig:baldock-english-networks} \label{fig:baldock-english-networks}
@ -35,7 +48,51 @@ networks in four major english cities.
\begin{figure}[ht] \begin{figure}[ht]
\centering \centering
\includestandalone{tikz/applications/baldock/graph-Baldock2011_TB+Baldock2011_JN} \includestandalone[width=0.43\textwidth]{tikz/applications/baldock/graph-Baldock2011_TB+Baldock2011_JN}
\caption{South African network from~\cite{baldockDailyTemporalStructure2011}} \caption{African network from~\cite{baldockDailyTemporalStructure2011}}
\label{fig:baldock-south-african-networks} \label{fig:baldock-african-networks}
\end{figure} \end{figure}
We applied our clustering method on those 6 networks, using the four models.
Interesting results arose from \emph{iid} and $\pi\rho$ models, which are
presented below in figures~\ref{fig:baldock-clust-iid}
and~\ref{fig:baldock-clust-pirho}.
\begin{figure}
\begin{minipage}{.5\textwidth}
\begin{subfigure}[htb]{\textwidth}
\includestandalone{tikz/applications/baldock/iid-clust-struct}
\caption{$\bm{\alpha}$ structures of the\newline
collections identified}
\label{subfig:baldock-clust-iid-struct}
\end{subfigure}
\newline
\begin{subfigure}[htb]{\textwidth}
\includestandalone{tikz/applications/baldock/iid-clust-tree}
\caption{Tree of splits}
\label{subfig:baldock-clust-iid-split}
\end{subfigure}
\captionof{figure}{Results for \emph{iid} clustering}
\label{fig:baldock-clust-iid}
\end{minipage}%
\begin{minipage}{.5\textwidth}
\begin{subfigure}[htb]{\textwidth}
\includestandalone{tikz/applications/baldock/pirho-clust-struct}
\caption{$\bm{\alpha}$ structure of the\newline
collection identified}
\label{subfig:baldock-clust-pirho-struct}
\end{subfigure}
\newline
\begin{subfigure}[htb]{\textwidth}
\includestandalone[width=0.86\textwidth]{tikz/applications/baldock/pirho-clust-tree}
\caption{Tree of splits}
\label{subfig:baldock-clust-pirho-split}
\end{subfigure}
\captionof{figure}{Results for $\pi\rho$ clustering}
\label{fig:baldock-clust-pirho}
\end{minipage}
\end{figure}
\paragraph{Results} The main thing one can see when comparing the two
clusterings is that while \emph{iid} do not find a common structure, $\pi\rho$
manage to find one.