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Hello I am looking for help on understanding the maths of Fuzzy C Means as explained here: Fuzzy C Means I was hoping for a broken down explantion of the actual math. I have tryed googling for tutorials but it has came up empty. I understand clustering and fuzzy c means and I know how to implement it but I still lack the understanding of the math.

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closed as not a real question by Nate Eldredge, Lord_Farin, Ittay Weiss, azimut, Start wearing purple May 25 '13 at 8:22

It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.

I believe it is a version of an EM algorithm like a usual $k$-means algorithm; only that in this case each $x_i$ is allowed to belong to many clusters at the same time. If my intuition is right, you essentially try to maximize the log-likelihood function $\ell(c) = \log P(x|c)$. The EM proof should carry over to show that you can instead optimize $\ell(u, c) = \log P(x|u, c)$ in $u$, then in $c$, and repeat.

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Hi thanks for the answer but this wasnt really what I was looking for, my maths is alot more basic in what I am looking to understand. For instance a question I asked on cross validated shows a good answer and is really what I am looking for here link – Garrith Graham Sep 13 '12 at 14:57
I thought you were looking for a way to derive the algorithm since you said you understand clustering and fuzzy C means. I will try to give you a more detailed answer when I have time then. In the meantime, if you know about maximum likelihood estimation, you should study EM algorithm for unsupervised learning. (One popular use of EM is k-means algorithm.) – Tunococ Sep 13 '12 at 20:25

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