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>In the last 15 years or so, researchers have created a number of tools to probe the geometry of these hidden structures. For example, you might build a model of the surface by first zooming in at many different points. At each point, you would place a drop of virtual ink on the surface and watch how it spread out.

It sounds to me like this 'ink drop' is a metaphor to explain some state-of-the-art dimensionality reduction technique. Does anyone know the common name of this technique?

There are diffusion based methods for unsupervised learning based on the graph laplacian, or heat kernel [0]. Maybe this is what she was referring to? I would guess so, because Coifman (who is also closely tied to wavelets [1]) introduced the diffusion maps [2] method. On the other hand, I have not seen any unsupervised method based on say, Navier-Stokes, which is the only other thing that comes to mind for regarding ink drops diffusing.

[0]: http://www.mit.edu/~9.520/spring11/slides/class20_misha.pdf

[1]: https://en.wikipedia.org/wiki/Coiflet

[2]: https://en.wikipedia.org/wiki/Diffusion_map

This reminded me of this paper on using deep autoencoders as a generative model: http://papers.nips.cc/paper/5023-generalized-denoising-auto-... I don't think it's exactly a right analogy, but there's something there about the local flow of MCMC locally describing the manifold structure, and thus generating it globally.

I thought it just simply had something to do with gradient descent.

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