This is why the author of this post is wrong. The answer is that there is no known efficient algorithm to ensure you get to a maximum of the k-Means objective (

This is why the author of this post is wrong. The answer is that there is no known efficient algorithm to ensure you get to a maximum of the k-Means objective (and there is unlikely to be one), even if you fix the dimension of the vectors to two. Also, nobody knows how to pick K.