4 ms·
Glad to hear that the URL was helpful to someone :) Are you studying Morse & Morse-Smale complexes for data-mining purposes? Just curious.
by Rod 17y ago
Glad to hear that the URL was helpful to someone :) Are you studying Morse & Morse-Smale complexes for data-mining purposes? Just curious.
- slackenerny 17y agoYes exactly, but I don't have anything to say about specifics yet. This was on my radar from few years now, but slacking off as usual I got wakened only by recent buzzing around. In fact I'm still slacking off, being nowhere exceptional programmer, my motivation slightly diminished when everyone and their pets started digging into this too. Speaking for myself, this is one of the rare applications of mathematics to DM that is proper and doesn't outright stink.
- Rod 17y agoI have read about Smale's work on data mining, and I was immediately intrigued by it. It's not everyday that one sees a world class mathematician doing such "dirty" applied research ;-) BTW, I would like to start doing some reading on this. Any books / papers you would recommend?
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- slackenerny 17y agoYou may find the book "Computational Homology" by Mrozek and Kaczynski interesting (though not obviously useful). Available in the usual places. Years back I had a chance to finish a course by the author, but being a confused physicist, I switched. Now I rediscover obvious references via HN :/
- Rod 17y agoI have just discovered Prof. Ghrist's work: http://www.math.uiuc.edu/~ghrist/index_files/research.htm http://www.math.uiuc.edu/~ghrist/index_files/research.htm I am profoundly enchanted by this stuff ;-)
- slackenerny 17y agoGhrist has one nice overview article, another one comes from Gunnar Carlsson and his group at Stanford, http://comptop.stanford.edu/preprints/topologyAndData.pdf http://comptop.stanford.edu/preprints/topologyAndData.pdf (and a toy: http://www.stanford.edu/~gurjeet/mapper.html http://www.stanford.edu/~gurjeet/mapper.html), but you surely know that already. Sorry for I won't attempt to survey literature as this area is new for me too, and I don't want to confuse you, or embarass myself =) I was sure you will find these anyway. I just began dusting off my Morse theory and handful of other mathematics and I am not yet paying much attention to what present developments are directed at. One unfortnate aspect of strictly applied part of this field is that most of results and a leading conference are funded by DARPA, which leads to publications I would consider mostly recruiting material than a scientific communication. My background and goals are anyways disparate to most of the approaches so I took only cursory look.
- Rod 17y agoThanks for the info. My fields are Signal Processing and Control Theory, and I am years away from being able to contribute anything remotely interesting to this nascent field of Computational Topology. Maybe after my PhD. And, indeed, I tend to dislike DARPA-funded stuff for the same exact reasons...