Biomedical Engineering Reference
In-Depth Information
c
i
centroid of cluster i;
d
ij
Euclidian distance between ith centroid (ci) and jth data point
m
] is a weighting exponent.
To attain minimum dissimilarity function, there exist two conditions which are
given in Eqs. (
3
) and (
4
).
[1,
є
∞
P
j
¼
1
u
ij
x
j
P
j
¼
1
u
ij
c
i
¼
ð
3
Þ
1
u
ij
¼
ð
4
Þ
d
kj
2
=ð
m
1
Þ
P
k
¼
1
d
ij
This algorithm ascertains the following steps.
Step-1: Randomly initializing the membership matrix (U) which has constraints in
Eq. (
1
).
Step-2: Calculating centroids (ci) by using Eq. (
3
).
Step-3: Computing dissimilarity between the data points and the centroids using
Eq. (
2
).
If the threshold value is below the previous iteration, then stop the pro-
cess, else continue.
Step-4: Compute the new
U
using Eq. (
4
) and go to Step 2.
“
”
On iteratively updating the membership grades and the cluster centers for each
data point, Fuzzy C-Means iteratively moves cluster centers to the
location
within the dataset. Fuzzy C-Means shall not ensure that it converges to optimal
solution for the reason being the cluster centers (centroids) are initialized using
right
“
”
U
“
”
which are randomly initialized (Eq.
3
).
The Performance of algorithm depends on initial centroids. There are two ways
for robust approach viz.,
1. Determining all the centroids by using algorithm.
2. Execute FCM iteratively starting with initial centroids.
However, as the canopy clustering technique is utilized as a pre-processing step
for Fuzzy C-Means algorithm, the results obtained by the application of FCM has
converged to an optimal solution.
5 Results and Discussions
The experimentation has been performed on FOUR (04) nodes with 1-master node
and 3-slave nodes. The con
guration of the master node is Intel Core2 Duo with 2 GB
RAM and the slave nodes with con
guration as Intel Core2 Duo with 1 GB RAM.
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