Hi all,

in the past I came across of feature based algorithms and techniques.

The trick is usually to reduce the representation of a complex

function/signal/geometric or real object by a relative small number of

feature vectors. This reduces the complexity of tasks like pattern

matching, speech recognition etc. Especially in neural-nets this

technique seems to be often used (see e.g. SOM).

The only question that is not addressed in the papers I have read so

far, is the question about the _number_ of these feature vectors.

Usually the authors come up with a certain number of vectors used for

the represention, without explaining how they got this number. I guess

they simple chose the number by looking at their object/function and

estimating how many features they have to represent. A simple

geometric object (line, cube) can get described by a less number of

vectors compared e.g. to a human face. Usually one would like to get s

small number of vectors to reduce the complexity of the task, but at

the same time the objects have to be discribed sufficiently to avoid

errors.

So I am still wondering: Isn't there a mathematical way to describe

this, so that one could justify the number of chosen vectors or

perhaps come up with a function/algorithm that calculates

automatically the number of vectors that is neccessary to represent a

certain object or function. I know this of course also depends on the

concrete application, but still there has to by a kind of general

approach.

It would be great if you could point me to a paper or mathematical

field that addresses these kind of problems.

Btw.: I am mostly interested in pattern matching (2D/3D).

Thanks a lot,

Steve

Google w.r.t. "principal component analysis" and/or "PCA".

Hope this helps.

Greg

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