标题： 食谱空间的拓扑分析 显示英文标题

标题： A topological analysis of the space of recipes

摘要： 近年来，数据驱动的方法为理解烹饪配方背后的潜在模式和原理提供了见解。 在这项探索性工作中，我们引入了使用拓扑数据分析（尤其是持久同调）来研究烹饪配方空间的方法。 特别是，持久同调分析提供了一组围绕现有配方空间中多尺度“孔洞”的配方。 然后，我们提出了一种方法，利用这种拓扑信息上的组合优化来生成新的成分组合。 我们用这些新的成分组合制作了饼干，并通过感官评估研究确认它们是可以接受的。 我们的研究结果表明，拓扑数据分析有潜力为烹饪配方的研究提供新的工具和见解。 显示英文摘要

摘要： In recent years, the use of data-driven methods has provided insights into underlying patterns and principles behind culinary recipes. In this exploratory work, we introduce the use of topological data analysis, especially persistent homology, in order to study the space of culinary recipes. In particular, persistent homology analysis provides a set of recipes surrounding the multiscale "holes" in the space of existing recipes. We then propose a method to generate novel ingredient combinations using combinatorial optimization on this topological information. We made biscuits using the novel ingredient combinations, which were confirmed to be acceptable enough by a sensory evaluation study. Our findings indicate that topological data analysis has the potential for providing new tools and insights in the study of culinary recipes.