Training ratio and comparison of trained vector quantizers

The vector quantizer (VQ) codebook is usually designed by clustering a training sequence (TS) drawn from the underlying distribution function. In order to cluster a TS, we may use the K-means algorithm (generalized Lloyd algorithm) or the self-organizing map algorithm. In this paper, a survey of trained VQ performance is conducted to study the effect of the training ratio on training quantizers. The training ratio, which is defined by the ratio of the TS size to the codebook size, is dependent on theVQ structure. Hence, different VQs may show different training properties, even though the VQs are designed for the same TS. A numerical comparison of trained VQs is then conducted in conjunction with deriving their training ratios. Through the comparison, it is shown that structured VQs can achieve better performance than the full-search scheme if the codebooks are trained by a finite TS. Further, we can derive a design or comparison guideline that maintains equal training ratios in training different VQs.