提出通用方法计算鲁棒的持久性图加权平均，提升抗异常值能力。
Robust Barycenters of Persistence Diagrams
- 用固定点法替代传统匹配均值，适配任意运输成本
- 在 $q \in (1,2)$ 时对异常值更鲁棒，优于经典 $q=2$ 方法
- 适用于持久性图聚类与字典编码，适合拓扑数据分析者
本文提出一种通用方法，用于计算持久性图的鲁棒 Wasserstein 加权平均。经典方法依赖最优传输方案后取算术均值，仅适用于 $q=2$ 的 $q$-Wasserstein 距离。我们采用替代的固定点法，可推广至任意 $q>1$ 的运输成本，尤其在 $q \in (1,2)$ 时对异常值更具鲁棒性。我们在两个场景中验证有效性：(i) 在度量空间中对持久性图进行聚类；(ii) 对持久性图进行字典编码。实验表明，新框架显著提升了抗异常值能力。代码已开源：https://github.com/Keanu-Sisouk/RobustBarycenter。
原文摘要 · Abstract (English)
This short paper presents a general approach for computing robust Wasserstein barycenters of persistence diagrams. The classical method consists in computing assignment arithmetic means after finding the optimal transport plans between the barycenter and the persistence diagrams. However, this procedure only works for the transportation cost related to the $q$-Wasserstein distance $W_q$ when $q=2$. We adapt an alternative fixed-point method to compute a barycenter diagram for generic transportation costs ($q > 1$), in particular those robust to outliers, $q \in (1,2)$. We show the utility of our work in two applications: \emph{(i)} the clustering of persistence diagrams on their metric space and \emph{(ii)} the dictionary encoding of persistence diagrams. In both scenarios, we demonstrate the added robustness to outliers provided by our generalized framework. Our Python implementation is available at this address: https://github.com/Keanu-Sisouk/RobustBarycenter .
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。