[Fwd: Fuzzines index m in Fuzzy C-Means]

Catherine DANG AN NINH (c.dangan@essaim.univ-mulhouse.fr)
Tue, 14 Jul 1998 02:09:28 +0200 (MET DST)

Vincent BARRA wrote:

> -----Message d'origine-----
> De : Sebastian Lozano <slozano@cica.es>
> Groupes de discussion : comp.ai.fuzzy
> Date : lundi 29 juin 1998 16:45
> Objet : Fuzzines index m in Fuzzy C-Means
>
> >Hi,
> >
> >Is there any preference for choosing the value of the fuzziness index m
> >in Fuzzy C-Means. I have seen that many people use the value m=2 but
> >without giving any reason. They say it can be chosen arbitrarily in the
> >interval (1, infinite).
> >
> >--
> >Sebastian Lozano
> >Escuela Superior de Ingenieros
> >University of Seville, Spain
>
> hi
> the fuzziness index m solely depends on your application. there is no way to
> optimize it theorically. when m is close to 1, the partition is almost
> crisp. when m tends to infinite, the partition follows a uniform law (i.e
> the degrees of membership of all vectors are equal to 1/c, where c is the
> number of classes). it is generally accepted that a value between 1.5 and
> 2.5 suits to the majority of problems, and a value of 2 is convenient
> because it reduces the computation time (the power functions are replaced by
> squares)
>
>

Hi,
As you have said, the choice of the parameter m who contols the amount if
fuzziness in u is still largely heuristic but several studies
have attempted to find a good way to choose m :
1/ Choe, H and Jordan, J . On the optimal choice of parameters in fuzzy c means
algorithms
Proc. first IEEE Conf. on fuzzy systems, sans diego, 1992.
2/ McBratney, A.B and Moore, A.W. Apllication of fuzzy sets to climatic
classification
Ag. & Forest meteor 35, 165-185, 1985

catherine.

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