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... for someone with, say, graduate level math skills? EDIT: I left this question intentionally open, since I'm actually looking for both theoretical (proof-based) and applied books. |
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RMT is a pretty large domain indeed. Some connections with compressed sensing can be found here: http://nuit-blanche.blogspot.com/2010/04/cs-random-matrix-theory-and-compressive.html or more generally: http://nuit-blanche.blogspot.com/search?q="random+matrix+theory" On the applied side you might want to read the introduction of this paper: http://arxiv.org/PS_cache/arxiv/pdf/0910/0910.1205v1.pdf (appied to finance) or those of Raj Nadakuditi http://www.eecs.umich.edu/~rajnrao/publications.html |
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This is a tough one, since random matrix theory is huge and different people are interested in very different kinds of questions. So the answer may be very different depending on where you want to go with it. But one good place to start is Terry Tao's recent lecture notes. Another is this new book by Anderson, Guionnet, and Zeitouni. |
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A simple readable introduction for NLP applications of random projections is Sahlgren (2005), "An Introduction to Random Indexing". That paper assumes you want to use random projections for NLP, and aren't interested in the proofs. |
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Just started reading this: http://web.mit.edu/18.338/www/Acta05rmt.pdf Not sure if it helps. |
What kind of treatment are you looking for? Theoretical? Or application-based?
I intentionally left the question open-ended because (from an intellectual point of view) I'd like a theoretical reference, but (from an applied POV) I wouldn't mind a more application-focused treatment.