௡ୀଵ

௞ୀଵ

erivative of this quadratic error function leads to the direction of

nimisation or the update of cluster centres. The K-means centre

ule is thus derived and is shown below, where

f data points clustered into the k^th cluster,

ܰ௞ൌ∑݂௡௞ is the

࢛௞ൌ¹

ܰ௞

෍

ܠ௡

௙೙ೖୀଵ

(2.22)

a data set composed of seven data points (Figure 2.22) was used

strate how the K-means algorithm works. In this example, seven

ts marked by a, b, c, d, e, f and g were assumed to belong to two

which were marked by A and B. Figure 2.22(a) shows two initial

entres, which were denoted by ࢛ۯ

଴ and ࢛۰

଴. They were random

this stage. These two initial cluster centres (࢛ۯ

଴ and ࢛۰

଴) were

very different from the true cluster centres. However, they will

uring a learning process.

of seven data points was assigned a membership function value

luster to which the distance between them was the least and zeros

e. A membership function value one was thus assigned between

because they had the least distance, so did between b and A. A

hip function value one was assigned between c and B, d and B, e

and B as well as g and B. All other membership function values

gned zeros. This is shown as the arrows in Figure 2.22(b) and the

med by Step 1 in Table 2.7.