Databases Reference
In-Depth Information
where,
U
ij
is between 0 and 1;
c
i
is the centroids of cluster
i
;
d
ij
is the
Euclidean distance between
i
th centroids
c
i
and
j
th data point.
m
]
is a weighting exponent. There is no prescribed manner for choosing the
exponent parameter,
m
. In practice,
m
= 2 is common choice, which is
equivalent to normalizing the coecients linearly to make their sum equal
to 1. When
m
is close to 1, then the cluster centre closest to the point
is given much larger weight than the others and the algorithm is similar
to
k
-means. To reach a minimum of dissimilarity function there are two
conditions. These are given in (6.4) and (6.5).
c
i
=
j
=1
∈
[1
,
∞
u
ij
x
j
j
=1
,
(6.6)
u
ij
1
u
ij
=
.
(6.7)
d
ij
d
kj
m
−
1
k
=1
This algorithm determines the following steps in Fig. 6.11. By
iteratively updating the cluster centers and the membership grades for each
Fig. 6.11.
Fuzzy
c
-Means Clustering Algorithm.
