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\begin{document}
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\title{Extracting latent variables from forecast ensembles and advancements in
similarity metric utilizing optimal transport}



\author[1]{Seiya Nishizawa}%
\affil[1]{RIKEN Center for Computational Science}%


\vspace{-1em}



  
  \date{May 06, 2026}


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\begin{abstract}
~This study presents a novel methodology for extracting latent variables
from high-dimensional sparse data, particularly emphasizing spatial
distributions such as precipitation distribution.~This approach utilizes
multidimensional scaling with a distance matrix derived from a new
similarity metric, the Unbalanced Optimal Transport Score (UOTS). UOTS
effectively captures discrepancies in spatial distributions while
preserving physical units. This is similar to mean absolute error,
however it considers location errors, providing a more robust measure
crucial for understanding differences between observations, forecasts,
and ensembles. Probability distribution estimation of these latent
variables enhances the analytical utility, quantifying ensemble
characteristics. The adaptability of the method to spatiotemporal data
and its ability to handle errors suggest its potential as a promising
tool for diverse research applications.%
\end{abstract}%



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