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\begin{document}

\maketitle
\begin{abstract}
Evaluating the performance of clustering models is a challenging task where the outcome depends on the definition of what constitutes a cluster. Due to this design, current existing metrics rarely handle multiple clustering models with diverse cluster definitions, nor do they comply with the integration of constraints when available. In this work, we take inspiration from consensus clustering and assume that a set of clustering models is able to uncover hidden structures in the data. We propose to construct a discriminative ordering through ensemble consensus based on the distance between the connectivity of a clustering model and the consensus matrix. We first validate the proposed method with synthetic scenarios, highlighting that the proposed score ranks the models that best match the consensus first. We then show that this simple ranking score significantly outperforms other scoring methods when comparing sets of different clustering algorithms that are not restricted to a fixed number of clusters and is compatible with clustering constraints.
\end{abstract}

\section{Introduction}
\label{sec:introduction}

\input{sections/1_introduction}

\section{Related works}
\label{sec:related_works}
\input{sections/2_related_works}

\section{The DISCOTEC}
\label{sec:method}
\input{sections/3_method}


\section{Experiments}
\label{sec:experiment}
\input{sections/4_experiment}


\section{Conclusion}
\label{sec:conclusion}
\input{sections/5_conclusion}

\begin{acknowledgements}
This research is financially supported by the Swedish Research Council via projects 2020-04122 and 2024-05011, the Knut and Alice Wallenberg Foundation via project KAW 2020.0033 and the Wallenberg AI, Autonomous Systems and Software Program (WASP), and the Excellence Center at Linköping--Lund in Information Technology (ELLIIT).
\end{acknowledgements}

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\title{Discriminative ordering through ensemble consensus\\(Supplementary Material)}
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\appendix

\section{Supplementary details for experiments}
\label{app:benchmark_details}
\input{appendix/benchmark_details}

\section{Scaling with the number of models under synthetic scenarios}
\label{app:scaling}
\input{appendix/scaling_experiment}

\section{Consensus matrix visualisation}
\label{app:consensus_visualisation}
\input{appendix/consensus_visualisation}

\section{Extended benchmark results}
\label{app:extended_benchmark}
\input{appendix/extended_benchmark}

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