Before revision:  We discuss two example realizationsof these functions : tent functions and Chybeyshev interpolating polynomials. Both of these functions are defined on a grid superposed on the birth-lifetime plane. We then combine the resulting features with machine learning algorithms to perform supervised classification and regression on several example data sets, including manifold data, shape data , and an embedded time series from a Rossler system.
After revision:  We discuss two example realizationsof these functions : tent functions , which emphasize the local contributions of points in a persistence diagram, and interpolating polynomials, which capture global pairwise interactions. We combine the resulting features with machine learning algorithms to perform supervised classification and regression on several example data sets, including manifold data, shape data , and an embedded time series from a Rossler system.