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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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1 Answer 1

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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