Model based clustering equivalent to K means?

Question

Is it OK to say something like this: "A model-based clustering with a hard threshold is equivalent to a k means clustering"? One of my instructors stated this in his slides, I kind of doubt this.

(For model-based clustering I mean the one based on a mixture of multivariate gaussian distributions, with totally flexible covariance matrix) I guess this statement only holds when identity covariance matrix is assumed?

Answer 1

Not only do you need identical covariance matrices, you need them to be spherical. Otherwise "model-based clustering with a hard threshold" isn't a precise definition, and I'd for sure not say it this way even with the correct covariance matrix assumption, although I wouldn't say it's wrong, rather somewhat unclear.