论文标题
拓扑数据分析：化学工程中的概念，计算和应用
Topological Data Analysis: Concepts, Computation, and Applications in Chemical Engineering
论文作者
论文摘要
推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（例如矩，相关函数）和信号处理（例如卷积神经网，傅立叶序列）。拓扑数据分析（TDA）是一个数学领域，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，并提供降低降低技术，这些技术将这些对象投射到由基本几何对象组成的低维空间上。这些基本对象的关键特性（也称为拓扑特征）是它们持续在不同的尺度上，并且它们在扰动下（例如噪声，拉伸，扭曲和弯曲）稳定。在这项工作中，我们回顾了TDA的关键数学概念和方法，并在化学工程中提出了不同的应用。
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 spaces that are composed of elementary geometric objects. Key property of these elementary objects (also known as topological features) are that they persist at different scales and that they are stable under perturbations (e.g., noise, stretching, twisting, and bending). In this work, we review key mathematical concepts and methods of TDA and present different applications in chemical engineering.
