Graded Persistence Diagrams and Persistence Landscapes

We introduce a refinement of the persistence diagram, graded diagram. It is Möbius inversion rank function, which obtained from function using unary numeral system. Both diagrams and are integer-valued functions on Cartesian plane. Whereas diagram takes non-negative values, values 0, 1, or $$-1$$ . The sum show that positive negative points in kth correspond to local maxima minima, respectively, landscape. prove stability theorem for diagrams: 1-Wasserstein distance between bounded by twice corresponding diagrams, this bound attained. In other direction, lower distances diagrams. fact, more discriminative than