There have been many comments that have pointed out the poverty of real ML applications that ride on algebraic topology. The problem is this -- topological spa

There have been many comments that have pointed out the poverty of real ML applications that ride on algebraic topology. The problem is this -- topological spaces on their own have a lot less structure than say a vector space or a metric space. Most of the real world data that ML applications deal with today have more structure and are thus handled using vector space methods or metric space methods or manifold methods. It is also the right thing to do. When you have structure you shoukd use it. TDA would be useful for data sets where the members have no clear analogue of a distance, or the distances cannot be trusted, or where vector embeddings do not make sense.