| If what you're asking about is the math, the steps are (essentially) as follows: 1. A Riemannian manifold is constructed from the dataset. 2. The manifold is approximately mapped to an n-dimensional topological structure. 3. The reduced embedding is an (n - k)-dimensional projection equivalent to the initial topological structure, where k is the number of dimensions you'd like to reduce by. I don't know how well that answers your question because it's difficult to simplify the math beyond that. But you can also check out the paper on arXiv. [1] The underlying idea is to transform the data into a topological representation, analyze its structure, then find a much smaller (dimensionally speaking) topological structure which is either the same thing ("equivalent") or very close to it. You get most of the way there by thinking about how two things which look very different can be topologically the same based on their properties. A pretty accessible demonstration of that idea is the classical donut <-> coffee mug example on the Wikipedia page for homeomorphisms. [2] __________________ 1. https://arxiv.org/pdf/1802.03426.pdf 2. https://en.wikipedia.org/wiki/Homeomorphism |