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To be fair, you haven't explained at all clearly why you don't think k-means adheres to Knuth's notion of an algorithm.

Your objection seems to be

> You can find pathological cases for k-means such that it will never converge on anything useful

As has been pointed out more than once, a good implementation of k-means is guaranteed to terminate in a finite time. And whatever you mean by "useful" doesn't seem to appear in Knuth's definition of an algorithm.

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