论文标题
树状图及其稳定性的合并图
The mergegram of a dendrogram and its stability
论文作者
论文摘要
本文将持久性的关键概念扩展在拓扑数据分析（TDA）中，朝着新的方向扩展。 TDA量化了隐藏在无组织数据中的拓扑形状，例如无序点的云。在0维情况下，基于距离的持久性是由公制空间中有限设置的单个链接（SL）聚类确定的。同等地，0D持久性仅捕获最小跨越树（MST）的边缘长度。在点的扰动下，SL模拟图和MST都是不稳定的。我们定义了新的稳定噪声合并，它在persay对点云的分类上胜过先前的等轴测图。
This paper extends the key concept of persistence within Topological Data Analysis (TDA) in a new direction. TDA quantifies topological shapes hidden in unorganized data such as clouds of unordered points. In the 0-dimensional case the distance-based persistence is determined by a single-linkage (SL) clustering of a finite set in a metric space. Equivalently, the 0D persistence captures only edge-lengths of a Minimum Spanning Tree (MST). Both SL dendrogram and MST are unstable under perturbations of points. We define the new stable-under-noise mergegram, which outperforms previous isometry invariants on a classification of point clouds by PersLay.
