Intuitionistic Fuzzy Clustering Algorithms - Intuitionistic Fuzzy Aggregation and Clustering - page 220

Table 2.11 The results derived by Algorithm 2.7 with different cluster numbers on the simulated
data set
c 2 3 4 5 6 7 8 9 10

Obj 76.760 7.087 5.853 5.389 3.543 3.138 2.743 2.536 2.161

V PC 0.744 0.949 0.779 0.710 0.475 0.420 0.367 0.338 0.289

V CE 0.582 0.198 0.563 0.809 1.198 1.404 1.598 1.749 1.927

Note :(1)“ Obj ” is the objective function value after the convergence of Algorithm 2.7
(2) The optimal values of the measures are highlighted in bold and italic fonts

Fig. 2.4 Comparison of Obj and V PC given different c values

a data set with a large sample size, say, 1,000,000, Algorithm-IFSC may encounter
some computational troubles.
In summary, while Algorithm 2.2 has some unique merits such as simplicity
and flexibility, it cannot provide the information about the membership degree of
the samples to all the clusters, and has a relatively high computational complexity,
which indeed motivates Algorithm 2.7.
In this part, we compare the performances of Algorithm 2.7 with the traditional
FCM algorithm. We first exploit Algorithm 2.7 on the simulated data set. In this
experiment, we set a series of c values in the range of 2 to 10, and compute the V PC
and V CE measures for each clustering result. The results can be found in Table 2.11
(Xu and Wu 2010).
As can be seen in Table 2.11 , when c 3, V PC reaches its optimal (maximum)

value 0.949, and V CE also reaches its optimal (minimum) value 0.198. This implies
that both V PC and V CE are capable of finding the optimal number of clusters, i.e.,
c . The objective function value, however, is not the case. Let us look at Fig. 2.4 (Xu
and Wu 2010).
As the increase of the number of clusters, Obj decreases continuously and finally
reaches 2.161 when c

=

10. This just illustrates why we employ V PC and V CE to
evaluate the clustering results produced by Algorithm 2.7.

=