What is persistence diagram?

The persistence diagram of a real-valued function on a topological space is a multiset of points in the extended plane. We prove that under mild assumptions on the function, the persistence diagram is stable: small changes in the function imply only small changes in the diagram.

How do you draw a persistence diagram?

Video quote: Ones called in the literature called persistence diagrams. Simply says there is a multi set of points. In them B it is denotes the birth and B denotes the death and well from this persistence diagram.

What is persistent homology used for?

Persistent homology (PH) is a method used in topological data analysis (TDA) to study qualitative features of data that persist across multiple scales. It is robust to perturbations of input data, independent of dimensions and coordinates, and provides a compact representation of the qualitative features of the input.

Who invented persistent homology?

Computation

Is topological data analysis useful?

Topological data analysis, or TDA, is a set of approaches providing additional insight into datasets. It augments other forms of analysis, like statistical and geometric approaches, and is useful to any data scientist that wants a more complete understanding of their data.