Quantization with Voronoi Grids for Numerical Finance

Summary

The discussion introduces quantization as a way to approximate a continuous space with a finite set of representative points. In the response, this idea is associated with centroidal Voronoi methods: each generator represents a neighborhood, allowing a continuous input or state space to be modeled through discrete values. An image-encoding example illustrates that discretization can apply across more than one dimension.

For quantitative work, the post suggests using quantization grids to cluster time-series behavior, support portfolio diversification, and build finer models for individual clusters. It points readers to material on optimal quantization in numerical probability and mathematical finance, including references to bibliographies and precomputed grids. The exchange is introductory rather than technical: it gives no construction algorithm, error measure, or empirical trading results, so it does not establish how well the proposed applications perform or how grids should be selected.

Key ideas

• Quantization approximates a continuous space with a finite set of representative points.
• Centroidal Voronoi methods associate nearby inputs with a representative generator.
• Quantization grids can be used to cluster time-series behavior and inform portfolio diversification.
• The discussion is introductory and provides no algorithm or evidence about trading performance.

Tags

# What is Quantization?


# What is Quantization?












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 ?

## Answer by Quant (score 4, accepted)

https://quant.stackexchange.com/a/1190

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.

## Answer by Chad Brewbaker (score 9)

https://quant.stackexchange.com/a/513

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

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