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I'm a computer science graduate student. I recently discovered manifold learning. I think I understand the very basic, high-level concept of nonlinear dimensionality reduction, but I'd like a stronger background. I majored in applied mathematics as an undergraduate, but did not take abstract algebra or topology.

Do I need to read up on algebra and topology to understand/effectively use manifold learning? Regardless, does anyone have any references for a beginner?

Thanks in advance.

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  • $\begingroup$ Did you take any differential geometry? That's primarily where you will find manifolds. $\endgroup$ – fhyve Jul 13 '13 at 19:08
  • $\begingroup$ @fhyve No. I've pretty much have just taken (multiple levels of) calculus, linear algebra, diffeq, number theory, probability, statistics, optimization, and a bunch of CS-related math courses. Nothing on analysis, abstract algebra, topology or differential geometry. $\endgroup$ – Steve P. Jul 13 '13 at 19:10
  • $\begingroup$ @fhyve any recommendations for someone with my background? ie, a good introductory text to differential geometry? Will I be able to understand it without knowing topology? On that note, can I understand topology without knowing abstract algebra? I want to learn whatever I have to... $\endgroup$ – Steve P. Jul 13 '13 at 19:12
  • $\begingroup$ You can understand topology without algebra, since I don't think you will need any algebraic topology (though you would need that if you did topological data analysis which is super cool). Some topology will be helpful though I think you can get by without it. You will need a strong grasp of linear algebra, which might start getting into abstract algebra. I am not sure exactly what you will need for manifold learning, so I can't exactly recommend a text, but this might be helpful: mathoverflow.net/questions/7834/… $\endgroup$ – fhyve Jul 13 '13 at 19:22
  • $\begingroup$ @fhyve Okay, thanks for the response. $\endgroup$ – Steve P. Jul 13 '13 at 19:22
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Of course, i think Loring W. Tu

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    $\begingroup$ Thank you for the recommendation. $\endgroup$ – Steve P. Jul 14 '13 at 17:02
  • $\begingroup$ You're welcome. $\endgroup$ – B11b Jul 14 '13 at 17:20

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