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Concept
Vector quantization
Summary
Vector quantization (VQ) is a classical quantization technique from signal processing that allows the modeling of probability density functions by the distribution of prototype vectors. It was originally used for data compression. It works by dividing a large set of points (vectors) into groups having approximately the same number of points closest to them. Each group is represented by its centroid point, as in k-means and some other clustering algorithms.
The density matching property of vector quantization is powerful, especially for identifying the density of large and high-dimensional data. Since data points are represented by the index of their closest centroid, commonly occurring data have low error, and rare data high error. This is why VQ is suitable for lossy data compression. It can also be used for lossy data correction and density estimation.
Vector quantization is based on the competitive learning paradigm, so it is closely related to the self-organizing map model and to sparse coding models used in deep learning algorithms such as autoencoder.
The simplest training algorithm for vector quantization is:
Pick a sample point at random
Move the nearest quantization vector centroid towards this sample point, by a small fraction of the distance
Repeat
A more sophisticated algorithm reduces the bias in the density matching estimation, and ensures that all points are used, by including an extra sensitivity parameter :
Increase each centroid's sensitivity by a small amount
Pick a sample point at random
For each quantization vector centroid , let denote the distance of and
Find the centroid for which is the smallest
Move towards by a small fraction of the distance
Set to zero
Repeat
It is desirable to use a cooling schedule to produce convergence: see Simulated annealing. Another (simpler) method is LBG which is based on K-Means.
The algorithm can be iteratively updated with 'live' data, rather than by picking random points from a data set, but this will introduce some bias if the data are temporally correlated over many samples.
Official source
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