Čech Complex

A Čech complex is a mathematical tool used to analyze the shape and features of data points in space. Imagine placing a small sphere around each data point; the Čech complex captures how these spheres overlap. When multiple spheres intersect, it indicates the presence of a higher-dimensional feature, like a loop or void, in the data. This method is useful in topological data analysis to identify connected regions, holes, and structures within complex datasets by translating spatial relationships into a combinatorial framework.