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274 CHAPTER 11 KIDNEY-INSPIRED ALGORITHM AND FUZZY CLUSTERING

11.5 PROPOSED MODEL
This proposed model for biomedical data analysis makes use of KA (Section 11.3) and FCM clustering
(Section 11.5.1).

11.5.1 FUZZY C-MEANS ALGORITHM
This algorithm allows belongingness of one piece of data to several clusters. It is a partitional algorithm
based on the minimization of one objective function (Eq. 11.3) [34] with regards to the partition matrix.
C N
XX

2
JU, VÞ ¼ u ij m
x j v i
(11.3)
ð
i¼1 j¼1
where “x j ” and “v i ” indicates the jth cluster point and ith cluster center respectively. u i, j indicates the
membership value of jth cluster point with regards to cluster “i.” “m” is the fuzzy controlling factor. It
may result in hard partition when setting the value as “1” and complete fuzziness when setting the value
as “∞.” kk is the norm function. The FCM algorithm works with three main factors [35]: fuzzy mem-
bership function, partitional matrix, and objective function.
m
u ij is calculated as described in Eq. (11.4) and the cluster center as in Eq. (11.5).
"

! # 1
c
X

2
x j v i
U ij ¼

m 1 (11.4)

x j v k
k¼1
N
X
m ,
u ij x j
v i ¼ j¼1 wherei 1,i c (11.5)
N
X
m
u ij
j¼1
m
This method is almost equivalent to the K-means algorithm except for the factor u ij (fuzziness factor).
The fuzziness factor determines the level of fuzziness for the clusters. The results of FCM depends on
the initial choice of values for the clusters, which is one of the disadvantages of this system. The de-
tailed algorithm steps of FCM are described in [36].
11.5.2 PROPOSED KA-BASED APPROACH FOR BIOMEDICAL DATA ANALYSIS
In this section, a metaheuristics approach based on the KA and FCM (KA-FCM) has been developed
for cluster analysis in biomedical data. Existing biomedical data are usually nonlinear and complex in
nature, which contains many clusters in data while applying FCM clustering [37]. Although FCM has
been found to be successful in biomedical data clustering, there is always a chance of further improve-
ments due to the randomness in initial cluster center selection (Eq. 11.4). This proposed work has been
carried with the objective to help the FCM in cluster analysis on biomedical data by making available
optimal cluster centers, which enable the FCM to have initial optimal clusters rather than random clus-
ters. This proposed approach has been observed as efficient not only in faster convergence but also in
forming qualitative clusters. The synthesized working schema of this projected method is demonstrated
in Fig. 11.1, which has two major phases, i.e., phase 1 is the process of obtaining optimal cluster centers
using KA (Section 11.5.2.1) and phase 2 is the method for cluster analysis using optimal cluster centers
(Section 11.5.2.2).