提供可直接用于机器学习的拓扑数据分析向量化工具
Vectorization of Persistence Diagrams for Topological Data Analysis in R and Python Using TDAvec Package
- 将拓扑数据的持久图转化为机器学习可用的向量表示
- 支持R和Python双语言，实现高效向量化处理
- 适合需要将拓扑特征融入模型的研究者使用
持久同调是拓扑数据分析（TDA）中广泛使用的工具，用于揭示复杂数据的内在形状。通过从数据点构建单纯复形的滤链，它能在多尺度下捕捉连通分量、环路和空洞等拓扑特征，并以持久图（PDs）形式编码。然而，持久图所在空间不具备希尔伯特性质，难以直接用于机器学习。为此，核方法与向量化技术被提出，将持久图转换为机器学习兼容格式。本文介绍一个新软件包TDAvec，旨在简化持久图的向量化流程，提供直观的工作流与高级功能。通过实际案例展示其必要性，并深入讨论其在应用拓扑数据分析中的贡献。包内所有向量化方法的定义均附于附录。
原文摘要 · Abstract (English)
Persistent homology is a widely-used tool in topological data analysis (TDA) for understanding the underlying shape of complex data. By constructing a filtration of simplicial complexes from data points, it captures topological features such as connected components, loops, and voids across multiple scales. These features are encoded in persistence diagrams (PDs), which provide a concise summary of the data's topological structure. However, the non-Hilbert nature of the space of PDs poses challenges for their direct use in machine learning applications. To address this, kernel methods and vectorization techniques have been developed to transform PDs into machine-learning-compatible formats. In this paper, we introduce a new software package designed to streamline the vectorization of PDs, offering an intuitive workflow and advanced functionalities. We demonstrate the necessity of the package through practical examples and provide a detailed discussion on its contributions to applied TDA. Definitions of all vectorization summaries used in the package are included in the appendix.
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