论文标题
通过小组非扩张算子在拓扑数据分析中降低冲动性降噪的概率结果
A probabilistic result on impulsive noise reduction in Topological Data Analysis through Group Equivariant Non-Expansive Operators
论文作者
论文摘要
近年来，小组的非企业非企业运算符（Geneos）引起了拓扑数据分析和机器学习领域的关注。在本文中，我们展示了这些操作员在存在嘈杂数据的情况下如何使用这些操作员也可以使用脉冲噪声并提高TDA的稳定性。特别是，当数据由$ l $ -lipschitz函数从$ \ mathbb {r} $到$ \ mathbb {r} $表示时，我们证明基因诺可以控制由均匀分布的冲动噪声引起的持久图的预期值。
In recent years, group equivariant non-expansive operators (GENEOs) have attracted attention in the fields of Topological Data Analysis and Machine Learning. In this paper we show how these operators can be of use also for the removal of impulsive noise and to increase the stability of TDA in the presence of noisy data. In particular, we prove that GENEOs can control the expected value of the perturbation of persistence diagrams caused by uniformly distributed impulsive noise, when data are represented by $L$-Lipschitz functions from $\mathbb{R}$ to $\mathbb{R}$.
