whats is the difference between “k means” and “fuzzy c means” objective functions?

Question

I am trying to see if the performance of both can be compared based on the objective functions they work on?

Answer 1

K-Means clustering and Fuzzy-C Means Clustering are very similar in approaches. The main difference is that, in Fuzzy-C Means clustering, each point has a weighting associated with a particular cluster, so a point doesn't sit "in a cluster" as much as has a weak or strong association to the cluster, which is determined by the inverse distance to the center of the cluster.

Fuzzy-C means will tend to run slower than K means, since it's actually doing more work. Each point is evaluated with each cluster, and more operations are involved in each evaluation. K-Means just needs to do a distance calculation, whereas fuzzy c means needs to do a full inverse-distance weighting.