Comparison of persistence diagrams
Comparison of persistence diagrams
复制标题
DOI：
10.1080/03610918.2021.1894335
复制
发表时间：
2021-02-24
影响因子：
0.9
通讯作者：
Agami, Sarit
中科院分区：
文献类型：
--
作者：
Agami, Sarit
拓扑数据分析（TDA）是一种通过研究其形状来处理大数据的方法。TDA的一个主要工具是持久性图，人们可以用它来比较数据集。学习两个持久性图之间的相似性的一种方法是使用瓶颈距离和Wasserstein距离。另一种方法是为每个图拟合参数模型，然后比较模型系数。我们研究了距离测度和双参数模型的行为。距离测度的理论行为很难得到发展，因此我们用数值方法研究了它们的行为。我们的结论是，在这个意义上，它可以给出一个明确的结论，两个持久性图之间的相似性的瓶颈和Wasserstein的距离，它具有优势。更重要的是，该算法的一个很大的优点是它能够区分两个几何上不同但拓扑上相同的数据集，这是两个距离度量不可能做到的。
Topological Data Analysis (TDA) is an approach to handle with big data by studying its shape. A main tool of TDA is the persistence diagram, and one can use it to compare data sets. One approach to learn on the similarity between two persistence diagrams is to use the Bottleneck and the Wasserstein distances. Another approach is to fit a parametric model for each diagram, and then to compare the model coefficients. We study the behavior of both distance measures and the RST parametric model. The theoretical behavior of the distance measures is difficult to be developed, and therefore we study their behavior numerically. We conclude that the RST model has an advantage over the Bottleneck and the Wasserstein distances in sense that it can give a definite conclusion regarding the similarity between two persistence diagrams. More of that, a great advantage of the RST is its ability to distinguish between two data sets that are geometrically different but topologically are the same, which is impossible to have by the two distance measures.