论文标题
基于锤距的弦线相似性的度量
Measures of string similarities based on the Hamming distance
论文作者
论文摘要
在本文中，我们考虑了使用锤子距离和持久性同源性工具构建的两组字符串之间相似性的衡量标准。首先，我们描述了与字符串相邻的\ V CECH过滤的构造，持久模块对应于该过滤及其条形码结构。使用这些手段，我们基于对其相同维度的条形码内的条形码的比较，为两组字符串引入了一种新颖的相似性度量。我们的想法是寻找一种比较，该比较将不仅要考虑棒的重叠，而且还要确保观察到的条形在定性上匹配，从而代表了类似的同源特征。为了实现这个想法，我们开发了一种称为单纯射线半径技术分离的方法。
In this paper we consider measures of similarity between two sets of strings built up using the Hamming distance and tools of persistence homology as a basis. First we describe the construction of the \v Cech filtration adjoined to the set of strings, the persistence module corresponding to this filtration and its barcode structure. Using these means, we introduce a novel similarity measure for two sets of strings, based on a comparison of bars within their barcodes of the same dimension. Our idea is to look for a comparison that will take under consideration not only the overlap of bars, but also ensure that observed bars are qualitatively matched, in the sense that they represent similar homological features. To make this idea happen, we developed a method called the separation of simplex radii technique.
