A primary hypothesis that drives scientific and engineering studies is that data has structure. The dominant paradigms for describing such structure are statistics (e.g., moments, correlation functions) and signal processing (e.g., convolutional neural nets, Fourier series). Topological Data Analysis (TDA) is a field of mathematics that analyzes data from a fundamentally different perspective. TDA represents datasets as geometric objects and provides dimensionality reduction techniques that project such objects onto low-dimensional descriptors. The key properties of these descriptors (also known as topological features) are that they provide multiscale information and that they are stable under perturbations (e.g., noise, translation, and rotation). In this work, we review the key mathematical concepts and methods of TDA and present different applications in chemical engineering.

驱动科学和工程研究的主要假设是数据具有结构。描述这种结构的主要范例是统计量（例如矩，相关函数）和信号处理（例如卷积神经网络，傅立叶级数）。拓扑数据分析（TDA）是一个数学领域，它从根本上不同的角度分析数据。TDA将数据集表示为几何对象，并提供将这些对象投影到低维描述符上的降维技术。这些描述符的关键特性（也称为拓扑特征）是它们提供多尺度信息，并且在扰动（例如，噪声，平移和旋转）下保持稳定。在这项工作中