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\title{Modeling high dimensional point clouds with the spherical cluster model}


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\author{
Fr\'ed\'eric Cazals \email{Frederic.Cazals@inria.fr} \addr \ucainria\\
\AND
Antoine Commaret \email Antoine.Commaret@inria.fr \addr \ucainria\\
\AND
Louis Goldenberg \email{lf.goldenberg@gmail.com} \addr Ecole Polytechnique, Department of Computer Science Palaiseau, France}



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\begin{document}

\maketitle

\input{clustermodel-abstract-v1.tex}
\bigskip

\noindent{\bf Keywords:}
subspace clustering, spherical clusters, centerpoints, medians,  non smooth optimization.


\clearpage

\input{clustermodel-main-v1.tex}








%% \clearpage
%% \section*{Impact statement}
%% %%i%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% This paper presents work whose goal is to advance the field
%% of Machine Learning. There are many potential societal
%% consequences of our work, none which we feel must be
%% specifically highlighted here. 


\subsubsection*{Acknowledgements}
%% All acknowledgments go at the end of the paper, including thanks to reviewers who gave useful comments, to colleagues who contributed to the ideas, and to funding agencies and corporate sponsors that provided financial support. 
%% To preserve the anonymity, please include acknowledgments \emph{only} in the camera-ready papers.

%%This work has been supported by the French government, through the 3IA C\^ote d’Azur Investments 
%%(ANR-19-P3IA-0002), and the ANR project Innuendo (ANR-23-CE45-0019).

% Acknowledgements and Disclosure of Funding should go at the end, before appendices and references
%\acks{Alessandra Carbone is  acknowledged for the ProteinHMM dataset. This work has been supported by the French government, through the 3IA C\^ote d’Azur Investments (ANR-23-IACL-0001), and the ANR project Innuendo (ANR-23-CE45-0019).}


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\newpage
\beginSI
\appendix


The supporting information is structured as follows:
\begin{itemize}
\item Section \ref{sec:alg-pro}: Algorithms and proofs
\item Section \ref{sec:exp}: Experiments
\end{itemize}

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\input{clustermodel-SI-exp-v1.tex}

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