centroid calculation for weighted Euclidian distance

Started by Biundo Giuseppina June 7, 2001
Dear all,

I would like to train a dictionary for vector quantization of LSFs for
speech coding.

At every iteration, the new centroid is calculated as the arithmetic
mean of all the vectors allocated to one cell, if we use Eucledian
distance as distortion measure. In the case we use weighted euclidean
distance as distortion measure, and the weights are constant, it is
easily proved that the centroid is still the arithmetic mean.

My question is: what happens when the weights are not constant, but a
function of the vector to be quantized? It should be done by minimizing
the distortion with respect to the centroid (derivate, equate to zero
and solve). Has anybody done the calculation already?

Thanks a lot for your help,