论文标题
互连矢量：持续同源性的有限维矢量表示
The Interconnectivity Vector: A Finite-Dimensional Vector Representation of Persistent Homology
论文作者
论文摘要
持续的同源性（PH）是研究数据集的基础结构的有用工具。持久图（PDS）是点的2D多组，是研究数据集的pH值发现的信息。但是，PD难以将其纳入典型的机器学习工作流程中。为此，已经开发了表示代表PD的两种主要方法：内核方法和矢量化方法。在本文中，我们提出了一个新的有限维矢量，称为互连矢量，是根据词袋（BOON）改编的PD的代表。构建了这种新表示形式，以证明数据集的同源特征之间的连接。互连向量的最初定义被证明是不稳定的，但是我们引入了矢量的稳定版本，并证明了其相对于输入中的小扰动的稳定性。我们在几个数据集上评估了两个版本的矢量化，并显示了它们的高歧视能力。
Persistent Homology (PH) is a useful tool to study the underlying structure of a data set. Persistence Diagrams (PDs), which are 2D multisets of points, are a concise summary of the information found by studying the PH of a data set. However, PDs are difficult to incorporate into a typical machine learning workflow. To that end, two main methods for representing PDs have been developed: kernel methods and vectorization methods. In this paper we propose a new finite-dimensional vector, called the interconnectivity vector, representation of a PD adapted from Bag-of-Words (BoW). This new representation is constructed to demonstrate the connections between the homological features of a data set. This initial definition of the interconnectivity vector proves to be unstable, but we introduce a stabilized version of the vector and prove its stability with respect to small perturbations in the inputs. We evaluate both versions of the presented vectorization on several data sets and show their high discriminative power.
