120 lines
No EOL
5.5 KiB
TeX
120 lines
No EOL
5.5 KiB
TeX
\section{Clustering
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of~\cite{baldockSystemsApproachReveals2019a,baldockDailyTemporalStructure2011}}
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\label{sec:baldock-clustering}
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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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In the following results, the row nodes represent the plants and the column
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nodes represent the pollinators (mostly insects in this case).
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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]{0.40\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]{0.40\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]{0.40\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]{0.40\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[width=0.86\textwidth]{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.
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When comparing figures~\ref{subfig:baldock-clust-iid-struct}
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and~\ref{subfig:baldock-clust-pirho-struct} and confirming with the
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figures~\ref{fig:struct-mixture-iid},~\ref{fig:struct-mixture-pirho}
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in appendix we can deduce the following differences between the two models.
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The TB+JN network doesn't have the \nth{3} column block and the first and second column blocks coincides with the English networks. But interestingly, the \nth{3} column block is the larger one in the English networks.
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For the row blocks, where with the \emph{iid} model only two groups where detected in the African network, it is refined with the $\pi\rho$ detecting 4 blocks in its row nodes. The African network does not have the first row block, a few row nodes in row blocks 2 and 3, more in the \nth{4} block and the majority in the \nth{5}.
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This contrasts, once again, with the English networks that have the majority of their row nodes in the \nth{4} block.
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Two interesting points can be made with those results, firstly the $\pi\rho$
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collection model allowed the detection of a finer structure in the African
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network regarding the row block memberships. And secondly, whereas the English
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networks are really similar, the African network while presenting the same
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blocks fills them differently.
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Those observations invite us to look at the species that are in those different
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groups. |