This is taken from Tom. Mitche Material as Old-Exam.
I think the (2) is true and not (3). Who can verify me?
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1 Answer
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(3) is correct. In k-means, the distance is computed independently of the cluster with the same function for all clusters. Thus, if a datapoint x is equally distant to two centers, it probability to belonging to either cluster is 0.5
Yet, if you are using - as explained in (2) - a different covariance matrix for each cluster, the probability for the datapoint x is higher to belong to the cluster with the higher $r_i$ (a bigger covariance matrix).
Further great input and explanation can be found in the answers to this question: How to understand the drawbacks of K-means
