Can a k-tool fall into an infinite loop?

Question

I have studied the k-means algorithm and I know how it works.

Just curious if there is a situation when this algorithm goes into an infinite loop, say, if we have some bad choices for the starting points of the center of gravity? I could only imagine a situation where k-means reached a local minimum with poor initial choices.

Answer 1

No. A k-means has an upper bound O (n ^kd ) in a d-dimensional space.