(a) (b)

A simple example for showing how the K-means algorithm works. (a) Seven

(marked by a, b, c, d, e, f and g) and two hypothesised (initialised) cluster

arked by A and B). (b) The assignments of membership function values to the

points. If a data point belongs to a cluster, an arrow acting as a unit membership

therwise nothing.

wards, the cluster centres were updated using the following

, where the new centre of cluster A was the mean of two data

and b and the new centre of cluster B was the mean of the rest five

ts,

࢛ۯ

ଵൌ¹

2 ^{ሺܽ൅ܾሻ}

࢛۰

ଵൌ¹

5 ^{ሺܿ൅݀൅݁൅݂൅݃ሻ}

the update, two cluster centres moved away from their initial

(࢛ۯ

଴ and ࢛۰

଴) towards new positions (࢛ۯ

ଵ and ࢛۰

ଵ). Figure 2.23(a)

e new centres of these two clusters (open dots) based on the

new memberships were derived as shown in Figure 2.23(b). In

three data points (a, b, c) were assigned to the cluster A and four

ts (d, e, f, g) were assigned to the cluster B. The panel named by

Table 2.7 shows new membership function values for these seven

nts. Afterwards, the cluster centres were updated again using

g equations,

࢛ۯ

ଶൌ¹

3 ^{ሺܽ൅ܾ൅ܿሻ}

࢛۰

ଶൌ¹

4 ^{ሺ݀൅݁൅݂൅݃ሻ}