证明了任意空间中广义中位数的抗异常值能力，突破了以往仅限特定空间的研究局限。
Robustness of Generalized Median Computation for Consensus Learning in Arbitrary Spaces
- 在任意度量空间中，广义中位数的崩溃点不低于0.5，即最多一半数据为异常值仍能保持稳定。
- 分析了不同来源异常值对计算结果的影响，揭示了其鲁棒性边界与行为特征。
- 拓展至加权和非度量距离场景，为实际应用提供理论依据和避坑指南。
异常值下的鲁棒性是机器学习与计算机视觉中的重要议题，已有大量研究。广义中位数是共识学习的一种特殊形式，常用于寻找原型。尽管其应用广泛，但目前对广义中位数的鲁棒性分析仅限于少数特定空间。本文首次在一般设定（任意空间）下给出鲁棒性刻画：对于度量距离函数，广义中位数的崩溃点≥0.5。此外，我们从多个角度分析了异常值存在时的行为表现，并给出了加权广义中位数及非度量距离函数下的鲁棒性结果。这些发现填补了文献空白，深化了对广义中位数的理解，为避免非鲁棒计算提供了实践指导。
原文摘要 · Abstract (English)
Robustness in terms of outliers is an important topic and has been formally studied for a variety of problems in machine learning and computer vision. Generalized median computation is a special instance of consensus learning and a common approach to finding prototypes. Related research can be found in numerous problem domains with a broad range of applications. So far, however, robustness of generalized median has only been studied in a few specific spaces. To our knowledge, there is no robustness characterization in a general setting, i.e. for arbitrary spaces. We address this open issue in our work. The breakdown point >=0.5 is proved for generalized median with metric distance functions in general. We also study the detailed behavior in case of outliers from different perspectives. In addition, we present robustness results for weighted generalized median computation and non-metric distance functions. Given the importance of robustness, our work contributes to closing a gap in the literature. The presented results have general impact and applicability, e.g. providing deeper understanding of generalized median computation and practical guidance to avoid non-robust computation.
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