The difference between a cluster of K-environments and vector quantization?

Question

What is the difference between K-Mans clusters and vector quantization? They seem to be very similar.

I deal with hidden Markov models , and I need to extract characters from object vectors.

To extract characters, do I do vector quantization or clustering Kmeans?

Answer 1

The way I understand it, K-means one type of vector quantization.

Answer 2

K-means algorithms are a specialization of the famous Lloyd I quantization algorithm for the case of empirical distributions. (see Lloyd)

It is proved that Lloyd's algorithm I gives a sequence of quantizers with decreasing quadratic distortion. However, with the exception of the special case of one-dimensional log-concave distributions, it does not always converge to a quadratic optimal quantizer. (For quantization errors, there are local minima, especially when working with an empirical distribution, i.e., for the clustering problem.)

A method that converges (always) to an optimal quantizer is the so-called CLVQ algorithms, which also generalize to the problem of more general quantization L ^ p. This is a kind of stochastic gradient method. (see Pagès)

There are also some approaches based on genetic algorithms. (see Hamida et al.) and / or classical optimization procedures for the one-dimensional case, which converges faster (Pagès, Printems).