Re: Fuzzines index m in Fuzzy C-Means

Vincent BARRA (vincent.barra@u-clermont1.fr)
Wed, 8 Jul 1998 02:53:00 +0200 (MET DST)

-----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).
>
>Thank you in advance
>--
>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)

for further reference, see for example
[1] BEZDEK J.C. (1981): Pattern Recognition with Fuzzy Objective Function
Algorithms, New-York : Plenum Press.

[6] KRISHNAPURAM R., KELLER J.M. (1993): a possibilistic approach to
clustering. IEEE Transactions on Fuzzy Systems, 1, 98-110.

hope this helps.

Vincent BARRA
ERIM - Faculté de Médecine
BP 38
63001 CLERMONT FERRAND Cedex (FRANCE)
Tel/Fax : (33) 4 73 60 80 00 poste 2206
vincent.barra@u-clermont1.fr
http://www.u-clermont1.fr/erim

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