Setting Vector Quantizer Resolution via Density Estimation Theory

We introduce a framework for selecting the number of codebook vectors in a vector quantizer based on local characteristics of the data density, the degree to which the process of VQ distorts the representation of this density, and the theoretical efficiency of estimators of these densities. In our analysis, \(L^2\) theory from kernel density estimation relates the number of VQ prototypes to observed sample size, dimension, and complexity, all of which intuitively influence codebook sizing.