It can happen that the variability that makes it difficult to distinguish
patterns is due to complexity rather than noise. For example,
it would make no sense to try to use a nearest-distance clasifier to detect
syntactic errors in expressions in a programming language.
Similar problems arise in classifying sensory data. Whenever the patterns
can be subject to well-defined transformations such as translation or rotation,
there is a danger of introducing a large amount of complexity into a primitive
feature space. In general, one should employ features that are invariant
to such transformations, rather than forcing the classifier to
handle them.
In human communication, larger patterns are frequently composed of smaller
paterns, which in turn are composed of smaller patterns. For example, sentences
are made up of words which are made up of letters which are made up of strokes.
Designing classifiers to cope with this level of complexity is definitely
beyond the scope of these notes.
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