ܠ௡|࢛௞, Σ௞ሻ

1

2ߨሻ^ௗ/ଶඥ|Σ௞|

exp ቆെ^{ሺܠ௡െ࢛௞ሻ௧Σ௞}

ିଵሺܠ௡െ࢛௞ሻ

2

ቇ

(2.27)

use of the use of this membership function, especially the use of

nce matrix, the cluster boundaries of a cluster model constructed

xture model algorithm will be different from that constructed by

ans algorithm and the fuzzy C-means algorithm. The clustering

es of a cluster model constructed by the mixture model algorithm

iptic in addition to spheric. The latter is used in both the K-means

m and the fuzzy C-means algorithm.

(a) (b)

The comparison between a K-means model and a model constructed by the

del algorithm for clustering a data set with elliptic cluster boundaries. There are

es of data points. Their classifications using the K-means and mixture model

algorithms are labelled using three colours. (a) The k-means model. (b) The

tructed by the mixture model algorithm.

e 2.34 shows a comparison between the K-means model (a) and

l constructed by the mixture model algorithm (b) for a data set

e clusters, in which the cluster boundaries were designed as

t can be seen that the K-means model did not work well for this

because it employs the spherical cluster boundaries. When this

is violated such as the cluster structure shown in Figure 2.34, a

model may not be useful for interpretation. However, in the

onstructed by the mixture model algorithm, this phenomenon