The analysis of large and complex data sets is one of the most important problems facing the scientific community, and physics in particular. One response to this challenge has been the development of topological data analysis (TDA), which models data by graphs or networks rather than by linear algebraic (matrix) methods or cluster analysis. TDA represents the shape of the data (suitably defined) in a combinatorial fashion. Methods for measuring shape have been developed within mathematics, providing a toolkit referred to as homology. In working with data, one can use this kind of modelling to obtain an understanding of the overall structure of the data set. There is a suite of methods for constructing vector representations of various kinds of unstructured data. In this Review, we sketch the basics of TDA and provide examples where this kind of analysis has been carried out.

大型和复杂数据集的分析是科学界尤其是物理界面临的最重要问题之一。对这一挑战的一种应对方法是开发了拓扑数据分析（TDA），它可以通过图形或网络而不是通过线性代数（矩阵）方法或聚类分析来对数据进行建模。TDA以组合方式表示数据的形状（适当定义）。在数学中已经开发了用于测量形状的方法，提供了称为同源性的工具包。在处理数据时，可以使用这种建模来了解数据集的整体结构。有一套用于构造各种非结构化数据的矢量表示的方法。在这篇评论中，