Topological Data Analysis - Nerves and Towers · Around abouts
▻https://sauln.github.io/pages/towers
The field of algebraic topology supplies a few tools to help answer this question. We can ask topological questions about the data, such as how many clusters or connected components are there? or are there gaps, holes, or voids in the data?. These question can be easy to answer if the shape is well defined, but in practice, we instead have data sampled from that shape. If we can construct a nerve from the shape, maybe we can estimate these properties instead. These questions and methods to answer them are central to the field of #Topological_Data_Analysis (TDA).