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NeuroCOLT
Technical Report NC-TR-95-047
The
Canonical Metric for Vector Quantization
Jonathan
Baxter
Royal Hollloway, University of London
Abstract
To measure the quality of a set of vector quantization points a means
of measuring the distance between two points is required. Common metrics
such as the Hamming and Euclidean metrics, while
mathematically simple, are inappropriate for comparing speech signals
or images. In this paper it is argued that there often exists a natural
environment of functions to the quantization process (for
example, the word classifiers in speech recognition and the character
classifiers in character recognition) and that such an enviroment
induces a canonical metric on the space being quantized.
It is proved that optimizing the reconstruction error with
respect to the canonical metric gives rise to optimal approximations
of the functions in the environment, so that the canonical metric
can be viewed as embodying all the essential information relevant
to learning the functions in the environment. Techniques for learning
the canonical metric are discussed, in particular the relationship
between learning the canonical metric and internal representation
learning.
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Postscript
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