Persistent Betti number

Persistent Betti numbers are a concept from the field of topological data analysis (TDA), a branch of mathematics that studies the shape and structure of data. They provide a way to quantify the topology of data at multiple scales. In topological data analysis, one often examines a point cloud (a collection of points in a metric space) to understand its shape. This is done using concepts from algebraic topology, where one associates simplicial complexes to the data.