These are notes from a talk given at the Stanford applied topology seminar by Gunnar Carlsson from 9 Oct 2009. The main function of this blog post is to get me an easily accessible point of access for the ideas in that talk.
First off, a few words on what we mean by coordinatization: as in algebraic geometry, we say that a coordinate function is some or possibly some , with all the niceness properties we’d expect to see in the context we’re working.
A particularly good example is Principal Component Analysis which yields a split linear automorphism on the ambient space that maximizes spread of the data points in the initial coordinates.
The core question we’re working with right now is this:
Given a space (point cloud) X, and a (persistent) view of , can we use some map to generate a map inducing that map?