Fuzzy K-modes clustering how to find the cluster centers

Question

I'm trying to understand fuzzy k-modes algorithm (look mainly at page 3) in order to implement it. I'm stuck at the calculation of cluster centers they said as shown in the pic

I need to know whether the following is true or false and please correct me

In order to get the center of a cluster we need to:

1. for each category in a variable calculate the sum of membership value for all the point, that the category belongs to, to this cluster
2. the highest obtained value to be set as the category of the center

Answer 1

I've got to admit, interpreting that cryptic text is difficult and the first step you should take is finding some more reference material.

There's quite a lot of such material available on the web, here is one such page: http://home.dei.polimi.it/matteucc/Clustering/tutorial_html/cmeans.html

The calculation of the cluster centres is simply a weighted mean using the membership values.