fuzzy k-mode clustering membership value calculation

Question

I was searching for a clustering algorithm to fuzzy cluster categorical attributes and I found the k-modes algorithm I've got the way it works but I'm not understanding if the membership or belonging matrix is calculated the same way as this matrix in fuzzy c-means algorithm? in the "no" case would you mind to clarify the way it's calculated?

thank you in advance for your help

Answer 1

Using the notation of the cited paper, the question is
is the W matrix for k-Mode calculated in the same fashion as for k-Mean ?

The answer is YES, there should be no differences at all, and of course all the constraints on W remain the same; particularly that its transpose be stochastic (*).

The main difference between k-Mean and k-Mode is with regards to the computation of Z, and of course with the distance function. I'd have to re-read the paper with a fresh mind, as ATM the details about Z are a bit fuzzy (pun intended) for me, for both k-Mode algorithms, the hard and the fuzzy one.

(*) Said less pedantically: for each object, the sum of its coefficients w for all k clusters should be 1 and all all these coefficients w must be positive (and hence in the [0,1] range).