PWARX Model Identification Based on Clustering Approach - Complex System Modelling and Control Through Intelligent Soft Computations - page 168

4.1 The Chiu s Clustering Technique

'

The Chiu ed form of the Mountain method for

cluster estimation (Chiu 1994 ). Each data point is considered as a potential cluster
center instead of considering it as a grid point. This method is very advantageous
compared with the Mountain method:

' is clustering method is a modi

The number of points to be evaluated is equal to the number of data points.

￿

It does not need to specify a grid solution which trades off between the accuracy
and the computational complexity.

￿

It improves the computational ef ciency and robustness of the original method.

￿

cation method consists in computing a potential value for each point
of the data set based on its distances to the other data points and consider each data
point as a potential cluster center. The point having the highest potential value is
chosen as the

Chiu s classi

'

rst
cluster center is chosen, the potential of all other points is reduced according to their
distance from the cluster center. All the points which are close to the

first cluster center. The key idea in this method is that once the

first cluster
center will have greatly reduced potentials. The next cluster center take then the
highest remaining potential value. The procedure for determining a new center and
updating other potentials is executed until a prede

ned condition is reached. This
condition depends on the minimum value of the potentials or the required number
of clusters which are reached.
This method consists

in computing a potential value for each point

( N), based on its distances to the other data points and consider each

data point as a potential cluster center. The potential is computed using the fol-
lowing expression:

h i ; i ¼ 1 ; ...;

X

N

2

kk

4
r a h i h j

e

P i ¼ : ð 9 Þ

j¼1

The potential of each local parameter is a function of the distance from this
parameter to all the other local parameters. Thus, a local parameter with many
neighboring local parameters will have the highest potential value. The constant r a
is the radius de

ning the neighborhood which can be determined by the following

expression:

n q
j¼1 h i h j

r a ¼ N X

N

X

:

1
n q

ð 10 Þ

i¼1

a

\ a \

where can be chosen as follows 0 1.