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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 pics
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:
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I guess I found the answer that's mean that for the set of points in the cluster we do the sum of membership value for similar attributes domain for those points , the one which has the highest result is taken to be the attribute of the cluster center |
To summarize; I need to understand how to find the cluster centers that satisfies the algorithm conditions, as I couldn't understand clearly what does the above mathematical expression means.Please help me :)
It looks like you pick the most popular value for each attribute. Does this make sense?
Wl-i is the membership value of the point i to the cluster l. points will have this structure A(1000,001011,000000001) 1000 means the first variable of A has the first category on ... B(0110,100000,101010000). suppose we're working on the 1st cluster so and we knew that W1-A=0.7 and W1-B=0.6 So will we take for each category the membership of the whole point? and make the sum for each point and chose the highest???
@Alexandre Passos any help?
This really looks like it's setting the value for each attribute in each cluster to the most popular value among all items assigned to that cluster. At least that's what eq (9) seems to be saying: this value has the highest sum among all other values.
Does this make sense with the rest of the paper?
@Alexandre Passos what do u mean by popular ? the one which's the most frequent or having the highest membership to the cluster ?
I didn't follow all of it but if I remember correctly fuzzy clustering mean assigning each variable some degree of membership to every cluster ( as opposed to hard clustering, which assign each object to a specific cluster). I think the algorithm first assign to each variable some degree of membership, and then determine the cluster center according to equation 9. ( the most popular value among all items)