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I am not a mathematician but I need mathematicians' general knowledge and that is why I chose this community to ask my question from.

As a student/researcher in Data Mining, with background in Pure Math, every time that I see a topic that used to be existing only in the realm of Pure Mathematics and suddenly finds its way to the realm of big data, I get super excited. For instance, when in our community (DM/ML), the curse of dimensionality was considered a real threat (explained well here) by several people. Or when topology came to help people understand the strange behavior of the networks (as in social media). Or the use of Fractals to extract features, such as Fractal Dimension, from images when there are too many of them to be processed.

You may know plenty of other good examples which are already employed. But I was wondering if you guys have come across a topic in mathematics that made you think it can be used to tweak the data so that it make more sense, to mine the data more efficiently, or simply make it possible to look at the data from a different angle.

Of course, every single machine learning algorithm/approach is directly rooted in Math and Statistics. I understand that. But I am asking about intuitive concepts that could potentially make the data more understandable.

Any suggestions, direction, or hint is very much appreciated.

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    $\begingroup$ See: stats385.github.io $\endgroup$
    – Bombyx mori
    Apr 19, 2018 at 4:33
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    $\begingroup$ Well, I guess concentration of measure is a direct example. $\endgroup$
    – usul
    Apr 19, 2018 at 6:11
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    $\begingroup$ Johnson-Lindenstrauss dimensionality reduction. Also PCA. $\endgroup$
    – Aryeh Kontorovich
    Apr 19, 2018 at 8:29
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    $\begingroup$ Also, all of these: Top 10 algorithms in data mining link.springer.com/article/10.1007/s10115-007-0114-2 $\endgroup$
    – Aryeh Kontorovich
    Apr 19, 2018 at 8:30
  • $\begingroup$ I really appreciate your comments. I am aware of the existing mathematical concepts in machine learning. I would like to know more about those which are not yet used but you believe they are worth a shot. $\endgroup$
    – Azim
    Apr 20, 2018 at 13:45

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