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In Fuzzy c-means, we have to put how many centers(centroids) in the code. I am wondering how many centroids are suitbale ?

How to define a suitbale number of centroids for fuzzy c-means?

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You can try the exact same heuristics you would use for k-means.

But usually, you would do this:

  1. try some parameters by experience
  2. run the algorithm
  3. carefully inspect the result
  4. go back to 1 and try other parameters until you have found something interesting or are tired of trying

There is no "correct" solution in clustering.

It's about discovering some new pattern and you cannot out the "new" into an optimization equation. The point is to try, and try again. It is not a drop-in replacement for classification.

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You have two areas to satisfy:

  1. Your business need (how many cluster you want to have).
  2. The nature of the data (how dividable it is).

For the second point, you can notice when using random seeds that being away from the optimal c number, will lead to "more" differences in the results for each run.

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