Vector Quantization - Training

Training

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

It is desirable to use a cooling schedule to produce convergence: see Simulated annealing.

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. A vector is represented either geometrically by an arrow whose length corresponds to its magnitude and points in an appropriate direction, or by two or three numbers representing the magnitude of its components.