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I figured that this doubt next can interest another students like me and help others also that are trying to understand mathematically the fuzzy c-means mathematical mechanism already that some books can't explain well and kinds of questions like this are very requested in some exams, and i have searched in books, articles and videos but they have only equations in theoretical form and no done examples about how to calculate step by step. I am stuck trying to know how could i calculate the Fuzzy C-Means to the points 1 = (0,10), 2 = (2,10), 3 = (8,0) and 4 = (10,0) with centroids located in V1 = (4,5) and V2 = (6,5) through the (Dunn 1973, Bezdek 1981) method by hand:

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For that it shows here the algorithm steps are:

1-Select the starting centers: in this case there are the two ones: V1 = (4,5) and V2 = (6,5)

2-Calculate μ_ij:

In this moment i can't able to understand if i consider x_j as two dimensional object(x,y) or as one dimensional here and about the difference between v_i and v_l as like how these iterations are performed step by step

3-Update centers:

again how these iterations are done

4-Stop in convergence case or back to step 2

So the doubts are: In step 2 it should be considered x_j as two-dimensional object(x,y) or as being an one-dimensional one? about the difference between v_i and v_l as well as like how these iterations are performed step by step, in step 3 how these interactions are made and how to know if the convergence was done or not? And in which part i use the objective function J? In overview it was easy to understand but mathematically the name of each variable and each iteraction that made me confused and how could i develop it

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  • $\begingroup$ If you study the EM algorithm for Gaussian Mixture Modeling (which is the much better approach than fuzzy-c-means anyway) this should become clear. $\endgroup$ – Anony-Mousse Sep 13 at 10:36

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