I have asked myself many times about Quantization Numerical Methods, is anyone here familiar with the subject and could give a reasonable insight of what Quantization concepts are about, and what are the underlying principles that make it work ?
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3$\begingroup$ No idea, but this looks interesting if you haven't seen it: "Optimal quantization methods and applications to numerical problems in finance": proba.jussieu.fr/mathdoc/textes/PMA-813.pdf $\endgroup$– PeteFeb 11, 2011 at 3:11
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$\begingroup$ This is typically what I was curious about, but with some explanations of the underlying principles and main points, rather than an ultra- technical one. $\endgroup$– TheBridgeFeb 15, 2011 at 9:55
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$\begingroup$ Is there some parallel to the term "Quantization" in Physics? $\endgroup$– PhilipFeb 16, 2011 at 21:54
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2 Answers
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Here is a website devoted to optimal quantization methods for numerical probability and mathematical finance specifically:
http://www.quantize.maths-fi.com
You can find a wide bibliography on the subject on the web site, as well as a database of pre-computed quantization grids.
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Centroidal Voronoi methods you mean? i.e. approximating a continous space with discrete points (generators) and for the sake of modeling evaluate the neighborhood around each generator as having the same value?
Example. Here is a guy who encodes images with unicode in twitter. He is quantizing in both the spacial and color spaces.
http://www.flickr.com/photos/quasimondo/3518306770/in/photostream/
Here is a paper I wrote about it in 2001. You can use them to cluster the behavior of time series data. Useful for both portfolio diversification and so you can make fine models for each cluster of time series data.
http://orion.math.iastate.edu:80/reu/2001/voronoi_paper/voronoi.pdf
