TR announcement: Adaptive Distance Measures

[Gabriele Scheler]

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Pattern Classification with Adaptive Distance Measures
Gabriele Scheler
Technische Universit"at M"unchen
(25 pages)

also available as Report FKI-188-94 from
Institut f"ur Informatik
TU M"unchen
D 80290 M"unchen

ftp-host: flop.informatik.tu-muenchen.de
ftp-file: pub/fki/fki-188-94.ps.gz

ABSTRACT:


In this paper, we want to explore the notion of learning the classification
of patterns from examples by synthesizing distance functions.

A working implementation of a distance classifier is presented.
Its operation is illustrated with the problem of classification according
to parity (highly non-linear) and a classification of feature vectors which
involves dimension reduction (a linear problem). A solution to these
problems is sought in two steps: (a) a parametrized distance function (called
a `distance function scheme') is chosen, (b) setting parameters to values
according to the classification of training patterns results in a specific
distance function. This induces a classification on all remaining
patterns.

The general idea of this approach is to find restricted functional shapes
in order to model certain cognitive functions of classification exactly,
i.e. performing classifications that occur as well as excluding classifications
that do not naturally occur and may even be experimentally proven to be 
excluded from learnability by a living organism.
 
There are also certain technical advantages in using restricted function
shapes and simple learning rules, such as reducing learning time, generating
training sets and individual patterns to set certain parameters, determining
the learnability of a specific problem with a given function scheme or 
providing additions to functions for individual exceptions, while retaining 
the general shape for generalization.