State of the Art and Development Trend - Computational Intelligence in Time Series Forecasting - page 343

the three conditions (see Section 4.7.1.3). Here, represents the degree

of membership of data object z s in the cluster group g . Based on the above
representation of data and membership degree, the following steps implement the
FKCN algorithm.

PP z

gs g s

Step 1:

x Initialize the constants c, m and H, where c represents the number of
clusters sought in the data, m is the fuzziness exponent and H is the
termination tolerance, such that

1
1

dd
ddf
!

cN
m

H 0

x Initialize the cluster centre vectors

n

Vv ª , v , " , v º , v \

¬ ¼

0 1,0 2,0 c ,0 g ,0

g v represents the prototype vector for cluster group g .
x Select the fuzziness exponent m > 1, and m is usually set to 2. Select also
T max , the number of maximum allowed iterations.

where

,0

Repeat for iteration t = 1, 2, 3, ..., T max ;

Step 2:

x Compute all learning rates using

1

§

2 m 1

·

§ ·

zv

m

¨

c

¸

s g

¨ ¸

D P , where P ,1 d d g c , 1 d d h c ,

¦

gs gs gs

¨ ¸

¨ ¸

zv

¨ ¸

h 1

© ¹

s h

© ¹

where D is the learning rate, P are the membership values and c is the
number of clusters.

Step 3:

x Update the weight vectors with

N N

vt vt 1

¦

D z vt 1

¦

D

g g gs s g gs

s 1 s 1