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This paper investigates a new Lie group regression model for input-output data belonging to Lie groups. The originality of the model lies in the fact that the unknown weights also lie in Lie groups and are learned using an intrinsic optimization algorithm based on maximum likelihood estimation. The model is validated through numerical simulations conducted using synthetic data belonging to the Lie group SO(3), which is commonly used in robotics to represent rotational observations.

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A New Geometric Regression with Inputs-Outputs on Matrix Lie Groups

  • 会议论文

  • 发表日期：

    2026年

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  • Serigne Daouda Pene,
  • Samy Labsir,
  • Julien Lesouple,
  • Jean-Yves Tourneret

摘要

This paper investigates a new Lie group regression model for input-output data belonging to Lie groups. The originality of the model lies in the fact that the unknown weights also lie in Lie groups and are learned using an intrinsic optimization algorithm based on maximum likelihood estimation. The model is validated through numerical simulations conducted using synthetic data belonging to the Lie group SO(3), which is commonly used in robotics to represent rotational observations.