|
Most ML papers I read assume that the data domain is a high-dimensional Euclidean space. But a lot of interesting / profitable datasets have a different topology. Where can I read about learning on a cylinder, 2-torus, graph, or even just on a formerly Euclidean space with a few points identified? (This question was partially inspired by the following blog post: http://cs.unm.edu/~terran/academic_blog/?p=11) |
|
Although a little dated, the best introduction to this topic is the AAAI 2007 tutorial by Sridhar Mahadevan. http://www.cs.umass.edu/~mahadeva/aaai07-tutorial/aaai07-tutorial.pdf In addition, you might be interested in following the Computational Topology literature here: http://www.stanford.edu/~henrya/CTRG.html |
|
You can learn about manifold learning here: http://scikit-learn.org/stable/modules/manifold.html Also look at the work of Robert Ghrist, who works in applied topology: I've seen Ghrist's work but it's not obvious to me how to apply it to ML.
(Nov 26 '11 at 18:35)
isomorphisms
@isomorphisms What about something like http://www.math.upenn.edu/~ghrist/preprints/barcodes.pdf
(Nov 27 '11 at 11:34)
Alejandro
|
|
I VERY highly recommend this survey by Gunnar Carlsson: http://www.ams.org/journals/bull/2009-46-02/S0273-0979-09-01249-X/S0273-0979-09-01249-X.pdf This should also point out many great references. Good one! Gunnar Carlsson's group at Stanford has some well cited literature on this topic. The reading group link I suggested is from that group.
(Nov 27 '11 at 12:50)
Delip Rao
|
|
Take a look at the Generative Topology mapping. A lot of info can be found and several nice packages. |
