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2. Probability and Random Process 81

2
2 2
M 45 = 1/ [((vector 4-c5) / (vector4 –c1) ) +
2
2 2
((vector 4-c5) / (vector4–c2 ) +
2
2 2
((vector 4-c5) / (vector4 –c3 ) +
2
2 2
((vector 4-c5) / (vector4 –c4 ) +
2 2
2
((vector 4-c5) / (vector4 –c5 ) +
2 2
2
((vector 4-c5) / (vector4 –c6 ) ]

Similarly other membership values are computed.

Step 4: Compute the sum of the squared difference between the previous
membership value and the current membership value. If the computed
value is not less than the threshold value go to step 2 to compute the
next set of centroids and followed by next set of membership values. If
the threshold value is less than the threshold value, stop the iteration.
Thus the centroids are obtained using fuzzy k-means algorithm. Using
the computed centroids, clustering can be obtained as described in the
section 3.
4.2 Example
The particular sets of marks (data) are subjected to Fuzzy k-means
algorithm. Final clusters along with clusters obtained at every iteration are
displayed below.

Figure 2-4. Illustration of Fuzzy K-means algorithm