Thanks for references.<p>I&#x27;ve read the topology and data paper; it lays down motivations for TDA, but it doesn&#x27;t quite connect it to existing literature on dimensionality reduction and manifold learning and explain -- &quot;Here&#x27;s something you can learn by using tools from TDA, but not existing methods.&quot;  The best I could see was that it produces results similar to existing methods.