Persistence Curves: A canonical framework for summarizing persistence diagrams

Persistence diagrams are one of the main tools in field Topological Data Analysis (TDA). They contain fruitful information about shape data. The use machine learning algorithms on space persistence proves to be challenging as lacks an inner product. For that reason, transforming these a way is compatible with important topic currently researched TDA. In this paper, our contribution consists three components. First, we develop general and unifying framework vectorizing call Curves (PCs), show several well-known summaries, such Landscapes, fall under PC framework. Second, propose new summaries based provide theoretical foundation for their stability analysis. Finally, apply proposed PCs two applications—texture classification determining parameters discrete dynamical system; performances competitive other TDA methods.