This article studies the robust version of persistent homology based on trimming methodology to capture the geometric feature through support of the data in presence of outliers. Precisely speaking, the proposed methodology works when the outliers lie outside the main data cloud as well as inside the data cloud. In the course of theoretical study, it is established that the Bottleneck distance between the proposed robust version of persistent homology and its population analogue can be made arbitrary small with a certain rate for a sufficiently large sample size. The practicability of the methodology is shown for various simulated data and bench mark real data associated with cellular biology.

翻译：本文研究基于修剪方法的稳健持久同调，旨在通过数据支撑在存在异常值的情况下捕捉几何特征。具体而言，所提方法在异常值位于主数据云外部及内部时均适用。在理论研究过程中，我们证明了对于足够大的样本量，所提稳健持久同调与其总体对应之间的瓶颈距离可以按特定速率任意缩小。通过多种模拟数据及与细胞生物学相关的基准真实数据，验证了该方法的实用性。