论文标题
数据的几何形状
Geometry of Data
论文作者
论文摘要
拓扑数据分析询问何时在度量空间中$（x，d）$相交。几何数据分析询问必须扩大多少球才能相交。我们将这一原理与传统的曲率核心几何概念联系起来。这使我们一方面能够重新概念化曲率并将其链接到超概率的几何概念。另一方面，我们还可以从几何学角度理解拓扑数据分析的方法。
Topological data analysis asks when balls in a metric space $(X,d)$ intersect. Geometric data analysis asks how much balls have to be enlarged to intersect. We connect this principle to the traditional core geometric concept of curvature. This enables us, on one hand, to reconceptualize curvature and link it to the geometric notion of hyperconvexity. On the other hand, we can then also understand methods of topological data analysis from a geometric perspective.
