论文标题
持续图的比较
Comparison of Persistence Diagrams
论文作者
论文摘要
拓扑数据分析（TDA）是通过研究其形状来处理大数据的一种方法。 TDA的主要工具是持久图，并且可以使用它来比较数据集。学习两个持久图之间相似性的一种学习方法是使用瓶颈和瓦斯泰因距离。另一种方法是拟合每个图的参数模型，然后比较模型系数。我们研究距离度量和第一个参数模型的行为。距离措施的理论行为很难开发，因此我们在数值上研究了它们的行为。我们得出的结论是，第一个模型比瓶颈具有优势，而瓦斯坦斯坦的距离可以从两个持久图之间的相似性得出明确的结论。更重要的是，第一个的一个很大的优势是它可以区分几何不同但拓扑相同的两个数据集，这是两个距离测量的不可能。
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 behaviour of both distance measures and the RST parametric model. The theoretical behaviour of the distance measures is difficult to be developed, and therefore we study their behaviour 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.
