State of the Art and Development Trend - Computational Intelligence in Time Series Forecasting - page 344

where t is the iteration number.

Step 4:

x Test for the terminating condition, i.e . calculate

2

Evt vt 1 ,

t g g

if

E d or,

tT t

max

then stop
else go to step 2.

It is to be noted that very often a termination tolerance H = 0.001 is selected, even
though H = 0.01 works well in most cases. In the above algorithm, the weight
vector v g of the winning unit is closest to the input vector z s . During the learning,
the weight vector corresponding to the winning unit is adjusted so as to move
further closer to the input vector. Most importantly, for a fixed value of m , the
FKCN updates the weight vectors, using the conditions that are necessary for FCM
and, in fact, with a fixed value of fuzziness exponent m , Bezdek et al. (1992)
showed that the FKCN is equivalent to the fuzzy c -means clustering algorithm.
However, particularly for m = 1, the FKCN behaves as a hard c -means clustering.
As an illustration, they used an FKCN for clustering of iris data.

10.5.2 Entropy-based Fuzzy Clustering

The fuzzy c -means clustering methods, proposed by Bezdek (1974), and it's
variant, the Gustafson-Kessel clustering algorithms (Babuška, 2002), based on an
adaptive distance metric, although being very popular and powerful, both had to
undergo some modifications (Yuan et al. , 1995; Medasani et al. , 1995; Babuška et
al. , 2002), particularly the improvement of their performance and the reduction of
their computational complexities.
One of the most important issues here is the determination of the number and
initial location of cluster centres. In the original versions of both the above
approaches the initial locations are selected randomly. Setnes and Kaymak (1998)
in their extended version of both approaches have advocated selecting a large
number of clusters initially and by compatible cluster merging reducing their
number. Babuška (1996) and Setnes (2000) have suggested using a cluster validity
measure, such as Xie and Benie's index , to select the optimum number of clusters.
Yager and Filev (1994) and Chiu (1994) proposed methods that automatically
determine the number of clusters and locations of cluster centres. Chiu's method is
a modification of Yager and Filev's mountain method, in which the potential of
each data point is determined based on it's distance from other data. A data point is
considered to have a high potential if it has many data points nearby and the data
point having the highest potential is selected as the first cluster centre. Thereafter,
the potentials of all other data points are recalculated according to their distance