Yeah that looks like a step in the right direction, but the use of purely synthetic examples leaves me a little sceptical it will work in practice. I don't have

Yeah that looks like a step in the right direction, but the use of purely synthetic examples leaves me a little sceptical it will work in practice. I don't have time to try every papers algorithms out. If they don;t put in real examples I think perhaps they tried it on real data but it still did not work. Persistent Homology is in its infancy, its developed by pure mathematicians who are a bit innocent to the horrors of real data (or willfully ignore pragmatic trivialities in preference to interesting theoretical results).