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Fuzzy c-means clustering will use Euclidean distance and the mean square error, or Manhattan distance and the mean absolute error. Which of those distance measures you should use for fuzzy c-means, and why?

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  • $\begingroup$ I can't understand your question. Are you asking which of those distance measures you should use for fuzzy c-means? Or are you asking why those are the possibilities? Or something else? $\endgroup$ Feb 21, 2016 at 16:27
  • $\begingroup$ which of those distance measures you should use for fuzzy c-means? $\endgroup$ Feb 21, 2016 at 17:22

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Like k-means, the use of any other distance than squared Euclidean (except for a few Bregman divergences) is questionable.

The mean does not minimize arbitrary distance functions. It does minimize squared errors, thus squared Euclidean (= sum of squared errors) is consistent with this step.

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