Though my understanding is this is used in interp, not so much because people necessarily expect deep connections to homology, but because its just another way to look for structure in your data.
As someone who does both data analysis and algebraic topology, my take is that TDA showed promise but ultimately there’s something missing such that it’s not at full capacity. Either the formalism isn’t developed enough or it’s being consistently used on the wrong kinds of datasets. Which is kind of a shame, because it’s the kind of thing that should work beautifully and in some cases even does!
Topological data analysis comes closest, and there are some people who try to use it for ML, eg.
Though my understanding is this is used in interp, not so much because people necessarily expect deep connections to homology, but because its just another way to look for structure in your data.
TDA itself is also a relatively shallow tool too.
As someone who does both data analysis and algebraic topology, my take is that TDA showed promise but ultimately there’s something missing such that it’s not at full capacity. Either the formalism isn’t developed enough or it’s being consistently used on the wrong kinds of datasets. Which is kind of a shame, because it’s the kind of thing that should work beautifully and in some cases even does!