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From: saswss@hotellng.unx.sas.com (Warren Sarle)
Subject: Re: Fuzzy Clustering
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Date: Wed, 19 Jun 1996 00:34:01 GMT
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In article <4pmbec$qk7@news.Informatik.Uni-Oldenburg.DE>, "Thomas Mantay" <Thomas.Mantay@Informatik.Uni-Oldenburg.DE> writes:
|> I have a question concerning fuzzy-clustering of feature-vectors of
|> different lengths. Consider you have two vectors v=(v1,...,vn) and
|> w=(w1,...,wm) with m < n, that is, w is shorter than v. Ordinary fuzzy-
|> clustering-algorithms like the FCM require the vectors to be of equal
|> lengths, so what possibilities do you have to equal their lengths? One
|> way is to enlengthen w to w'=(w1,...,wm,wm+1,...,wn), but will this
|> really give the a reasonable result? Another possibility would be to 
|> apply a dynamic length normalization to both vectors in the sense of
|> minimizing a criteria by a dynamic programming procedure according to 
|> Belman.
...
|> The vectors are feature vectors extracted from a speech signal. To be
|> more exact they represent utterances of spoken words. Every 10 ms that
|> vector is extended by (in my model) 20 components. And now it becomes
|> clear, why they're not of equal length: Words of different lengths produce
|> vectors of different length, so there is a need to align the vectors
|> adequately. BTW this even holds for two utterances of the same word.
|> 
|> The purpose of the analysis is to find out the spoken word from a given
|> vector, a fuzzy-classification-method for automatic speech recognition, that
|> is.

Simply padding out the shorter vector will not work with Euclidean
distance or any other simple dissimilarity measure. I'm not sure what
"dynamic length normalization" means, but there are time-warping
algorithms that are relevant (Sankoff and Kruskal 1983). If you compute
a dissimilarity matrix via time-warping or some such thing, you can use
the fuzzy clustering algorithm in Kaufmann and Rousseeuw (1990)--fuzzy
c-means cannot be used.

There is a large literature on speech recognition (e.g. Bourlard
and Morgan 1994) with which I am not very familiar. There does
not seem to be a comp.ai.* group for speech recognition, but
maybe the miscellaneeous group comp.ai has some readers who
know more than I.

   Bourlard, H.A., and Morgan, N. (1994), Connectionist Speech
   Recognition: A Hybrid Approach, Boston: Kluwer Academic
   Publishers.

   Kaufmann, L. and Rousseeuw, P.J. (1990), Finding Groups in Data,
   New York: John Wiley & Sons, Inc.

   Sankoff, D. and Kruskal, J.B. (1983), Time Warps, String Edits,
   And Macromolecules: The Theory And Practice of Sequence Comparison,
   Reading, MA: Addison-Wesley, ISBN 0-201-07809-0.


-- 

Warren S. Sarle       SAS Institute Inc.   The opinions expressed here
saswss@unx.sas.com    SAS Campus Drive     are mine and not necessarily
(919) 677-8000        Cary, NC 27513, USA  those of SAS Institute.
