VECTOR QUANTIZATION USING NEURAL NETWORKS

Vector quantization is a classical quantization technique from signal processing which 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-dimensioned data. Since data points are represented by the index of their closest centroid, commonly occurring data have low error, and rare data high error. 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.

A simple training algorithm for vector quantization is:

1. Pick a sample point at random

2. Move the nearest quantization vector centroid towards this sample point, by a small fraction of the distance

3. 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:

1. Increase each centroid's sensitivity by a small amount

2. Pick a sample point at random

3. Find the quantization vector centroid with the smallest

1. Move the chosen centroid toward the sample point by a small fraction of the distance

2. Set the chosen centroid's sensitivity to zero

4. Repeat

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 is temporally correlated over many samples. 

APPLICATIONS: 

Vector quantization is used for lossy data compression, lossy data correction and density estimation. Lossy data correction, or prediction, is used to recover data missing from some dimensions. It is done by finding the nearest group with the data dimensions available, then predicting the result based on the values for the missing dimensions, assuming that they will have the same value as the group's centroid. For density estimation, the area/volume that is closer to a particular centroid than to any other is inversely proportional to the density