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.