
THE CANONICAL DISTORTION MEASURE FOR VECTOR QUANTIZATION AND FUNCTION APPROXIMATION
by Jonathan Baxter
To measure the quality of a set of vector quantization points a means
of measuring the distance between a random point and its quantization
is required. Common metrics such as the Hamming and Euclidean metrics,
while mathematically simple, are inappropriate for comparing natural
signals such as speech or images. In this paper it is shown how an
environment of functions on an input space X induces a canonical
distortion measure (CDM) on X. The depiction "canonical" is justified
because it is shown that optimizing the reconstruction error of X with
respect to the CDM gives rise to optimal piecewise constant
approximations of the functions in the environment. The CDM is
calculated in closed form for several different function classes. An
algorithm for training neural networks to implement the CDM is
presented along with some encouraging experimental results.
