Relation between fractal dimension and performance of vector quantization

Abstract

This paper shows that the performance of a vector quantizer is related to the intrinsic ("fractal") dimension of the data set for a perfectly self-similar object. Experiments are performed to confirm the result on synthetic and real data sets. Further to verify the result, we computed the slope and compared it to the estimate of the fractal dimension obtained using the correlation integral. However, the computation of the correlation fractal dimension is linear on the number of data points and significantly faster than vector quantization.