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<p>Manifold-valued data analysis has led to generalizing statistical tools to the manifold setting. In this paper we introduce a simplified version of the weighted exponential mean and study its basic properties in the setting of Lie groups. We also calculate the exponential mean for some illustrative examples and derive some existence and uniqueness results.</p>

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The weighted exponential (Karcher) mean on Lie groups

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年7月3日

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  • Jimmie Lawson

摘要

Manifold-valued data analysis has led to generalizing statistical tools to the manifold setting. In this paper we introduce a simplified version of the weighted exponential mean and study its basic properties in the setting of Lie groups. We also calculate the exponential mean for some illustrative examples and derive some existence and uniqueness results.