I love persistent homology; it's such a weirdo bit of maths that topologists keep trying to make useful. Similarly its bigger cousin, Topological Data Analysis, which as far as I can tell is used by people who love weirdo maths but also want to be paid.
I don't see how much good the persistent topology adds here, though. Why bother to do the abstract birth-death diagram and measure the variance in lifetime of these simplices, when the variance and median of the areas in the Voronoi diagram will give you a much easier and more interpretable result?
I don't see how much good the persistent topology adds here, though. Why bother to do the abstract birth-death diagram and measure the variance in lifetime of these simplices, when the variance and median of the areas in the Voronoi diagram will give you a much easier and more interpretable result?