In this paper, we address a fundamental limitation of the classical Wasserstein barycenter -- its sensitivity to outliers and its reliance on finite first/second moment assumptions. To overcome these issues, we propose the robust Wasserstein barycenter (RWB) based on a recent concept of the robust optimal transport. Theoretical guarantees, including existence and consistency, are established for the proposed RWB. Through extensive numerical experiments on both simulated and real-world data -- including image processing and financial time series analysis -- we demonstrate that the RWB exhibits superior robustness compared to the classical Wasserstein barycenter.

翻译：本文针对经典Wasserstein重心存在的两个根本性局限——对异常值的敏感性以及对有限一阶/二阶矩假设的依赖——提出了解决方案。为克服这些问题，我们基于近期提出的鲁棒最优传输概念，提出了鲁棒Wasserstein重心（RWB）。我们为所提出的RWB建立了包括存在性与一致性在内的理论保证。通过在模拟数据和真实世界数据（涵盖图像处理与金融时间序列分析）上进行的大量数值实验，我们证明相较于经典Wasserstein重心，RWB展现出更优越的鲁棒性。