论文标题
连接点：发现数据的“形状”
Connecting the Dots: Discovering the "Shape" of Data
论文作者
论文摘要
科学家使用名为“拓扑”的数学主题来研究对象的形状。拓扑的一个重要部分是计算对象中的碎片和孔的数量，人们使用此信息将对象分组为不同类型。例如，甜甜圈具有相同数量的孔和与一个手柄的茶杯相同数量的碎片，但与球不同。在类似于“连接点”之类的活动的研究中，科学家使用拓扑的思想来研究数据的形状。数据可以采取许多可能的形式：由点制成的图片，科学实验中的大量数字或其他类似数字。这些研究中的方法称为“拓扑数据分析”，它被用来研究叶片中静脉的分支结构，人们如何在选举中投票，鸟类植物模型中的飞行模式等等。科学家可以获取叶子分支上的静脉分支的数据，并使用拓扑数据分析将叶子分为不同的群体，并发现可能很难找到的模式。
Scientists use a mathematical subject called 'topology' to study the shapes of objects. An important part of topology is counting the numbers of pieces and holes in objects, and people use this information to group objects into different types. For example, a doughnut has the same number of holes and the same number of pieces as a teacup with one handle, but it is different from a ball. In studies that resemble activities like "connect the dots", scientists use ideas from topology to study the shape of data. Data can take many possible forms: a picture made of dots, a large collection of numbers from a scientific experiment, or something else. The approach in these studies is called 'topological data analysis', and it has been used to study the branching structures of veins in leaves, how people vote in elections, flight patterns in models of bird flocking, and more. Scientists can take data on the way veins branch on leaves and use topological data analysis to divide the leaves into different groups and discover patterns that may otherwise be hard to find.
