98 lines
No EOL
4 KiB
TeX
98 lines
No EOL
4 KiB
TeX
\section{Clustering
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of~\cite{baldockSystemsApproachReveals2019a,baldockDailyTemporalStructure2011}}
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\cite{baldockSystemsApproachReveals2019a} study the diversity, robustness and
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impact of the type of environment on the ecological aspect of plant-pollinator
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networks in four major english cities. The networks are presented in
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figures~\ref{subfig:baldock-english-network-bristol} to~\ref{subfig:baldock-english-network-reading}
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\cite{baldockDailyTemporalStructure2011} aim to study the daily temporal
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structure in a savanna pollination network. The data was collected in 2004
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and in two sites, \emph{Turkana Boma} (TB) and \emph{Junction} (JN) in Kenya.
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We will not look for a temporal structure but only use the full networks merged
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in one
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due to their small sizes. The network obtained is presented in
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figure~\ref{fig:baldock-african-networks}.
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\emph{Note:} those networks were extracted from a bigger dataset
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from~\cite{doreRelativeEffectsAnthropogenic2021}. The full dataset was also
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clusterized but issues arose that are discussed in
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sub-section~\ref{ssec:difficulties-encountered}.
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\begin{figure}[ht]
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\centering
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\begin{subfigure}[htb]{0.47\textwidth}
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\includestandalone[width=0.86\textwidth]{tikz/applications/baldock/graph-Baldock2019_Bristol}
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\caption{Bristol}
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\label{subfig:baldock-english-network-bristol}
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\end{subfigure}
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\hfill
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\begin{subfigure}[htb]{0.47\textwidth}
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\includestandalone[width=0.86\textwidth]{tikz/applications/baldock/graph-Baldock2019_Edinburgh}
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\caption{Edinburgh}
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\end{subfigure}
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\newline
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\begin{subfigure}[htb]{0.47\textwidth}
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\includestandalone[width=0.86\textwidth]{tikz/applications/baldock/graph-Baldock2019_Leeds}
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\caption{Leeds}
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\end{subfigure}
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\hfill
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\begin{subfigure}[htb]{0.47\textwidth}
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\includestandalone[width=0.86\textwidth]{tikz/applications/baldock/graph-Baldock2019_Reading}
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\caption{Reading}
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\label{subfig:baldock-english-network-reading}
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\end{subfigure}
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\caption{English networks from~\cite{baldockSystemsApproachReveals2019a}}
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\label{fig:baldock-english-networks}
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\end{figure}
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\begin{figure}[ht]
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\centering
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\includestandalone[width=0.43\textwidth]{tikz/applications/baldock/graph-Baldock2011_TB+Baldock2011_JN}
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\caption{African network from~\cite{baldockDailyTemporalStructure2011}}
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\label{fig:baldock-african-networks}
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\end{figure}
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We applied our clustering method on those 6 networks, using the four models.
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Interesting results arose from \emph{iid} and $\pi\rho$ models, which are
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presented below in figures~\ref{fig:baldock-clust-iid}
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and~\ref{fig:baldock-clust-pirho}.
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\begin{figure}
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\begin{minipage}{.5\textwidth}
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\begin{subfigure}[htb]{\textwidth}
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\includestandalone{tikz/applications/baldock/iid-clust-struct}
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\caption{$\bm{\alpha}$ structures of the\newline
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collections identified}
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\label{subfig:baldock-clust-iid-struct}
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\end{subfigure}
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\newline
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\begin{subfigure}[htb]{\textwidth}
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\includestandalone{tikz/applications/baldock/iid-clust-tree}
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\caption{Tree of splits}
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\label{subfig:baldock-clust-iid-split}
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\end{subfigure}
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\captionof{figure}{Results for \emph{iid} clustering}
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\label{fig:baldock-clust-iid}
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\end{minipage}%
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\begin{minipage}{.5\textwidth}
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\begin{subfigure}[htb]{\textwidth}
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\includestandalone{tikz/applications/baldock/pirho-clust-struct}
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\caption{$\bm{\alpha}$ structure of the\newline
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collection identified}
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\label{subfig:baldock-clust-pirho-struct}
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\end{subfigure}
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\newline
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\begin{subfigure}[htb]{\textwidth}
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\includestandalone[width=0.86\textwidth]{tikz/applications/baldock/pirho-clust-tree}
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\caption{Tree of splits}
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\label{subfig:baldock-clust-pirho-split}
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\end{subfigure}
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\captionof{figure}{Results for $\pi\rho$ clustering}
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\label{fig:baldock-clust-pirho}
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\end{minipage}
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\end{figure}
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\paragraph{Results} The main thing one can see when comparing the two
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clusterings is that while \emph{iid} do not find a common structure, $\pi\rho$
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manage to find one. |