Question

Consider a dataset of six points given in the following table, each of which has two features f1 and f2 . Assuming the values of the parameters c and m as 2 and the initial cluster centers v1 = (5,5 ) and v2 (10 ,10, ) , apply FCm algorithm to find the new cluster center after one iteration.

 

f1

f 2

x1

3

11

x 2

3

10

x3

8

12

x 4

10

6

x5

13

6

x 6

13

5

06 Feb 2025
Answer :
Word Count : 126
Apply FCM with $m=2$. For two clusters the membership $u_{i1}=\dfrac{1}{1+(d_{i1}/d_{i2})^{2}}$ and $u_{i2}=1-u_{i1}$, where $d_{ik}=\|x_i-v_k\|$. Distances to $v_1=(5,5)$ and $v_2=(10,10)$: $x_1=(3,11):\ d_{1,1}=\sqrt{40}\approx6.3249,\ ______ _______ _____ _____ _______ _________.
_____ _______ ____ ________ __________ _____ _____ _______ __________.
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________ _________ __________ ___ _______ __________.
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______ _____ _____ _______ _______ ______ ___ _________ __________ _____ __________ ________.
__________ ________ _____ _____ _________ _______ ________ ____ ____ __________.
____ ________ __________ ______ _______ ____ ___ _________.
_________ ____ _________ ____ _____.
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_________ ______ _________.
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