I've read the topology and data paper; it lays down motivations for TDA, but it doesn't quite connect it to existing literature on dimensionality reduction and manifold learning and explain -- "Here's something you can learn by using tools from TDA, but not existing methods." The best I could see was that it produces results similar to existing methods.
I've read the topology and data paper; it lays down motivations for TDA, but it doesn't quite connect it to existing literature on dimensionality reduction and manifold learning and explain -- "Here's something you can learn by using tools from TDA, but not existing methods." The best I could see was that it produces results similar to existing methods.