A frequent goal is the minimization of the *expected quantization
(or distortion) error*. In the case of a continuous input signal
distribution this amounts to finding values for the
reference vectors such that the error

is minimized ( is the Voronoi region of unit *c*).

Correspondingly, in the case of a finite data set the error

has to be minimized with being the Voronoi set of the unit *c*.

A typical application where error minimization is important is *
vector quantization* (Gray, 1984; Linde et al., 1980). In vector quantization
data is transmitted over limited bandwidth communication channels by
transmitting for each data vector only the *index* of the nearest
reference vector. The set of reference vectors (which is called *
codebook* in this context) is assumed to be known both to sender and
receiver. Therefore, the receiver can use the transmitted indexes to
retrieve the corresponding reference vector. There is an information
loss in this case which is equal to the distance of current data
vector and nearest reference vector. The expectation value of this
error is described by equations (3.1) and
(3.2). In particular if the data distribution is
clustered (contains subregions of high probability density), dramatic
compression rates can be achieved with vector quantization with
relatively little distortion.

Sat Apr 5 18:17:58 MET DST 1997