Github user srowen commented on the issue:
@sethah I agree that when there are lots of unique points (>> k) then this
is almost certain to not happen, and that's most real-world use cases, but the
question indeed is what should happen when this is not the case. In that sense,
this change only affects corner cases so isn't really a big deal either way.
Yes the one case is clear: sampling with replacement when the data set has
< k (unique) points. It will always return k centroids, so must return
duplicates. In this case, every point will be at distance 0 from some centroid
and so I don't think the centroids can move apart. It stops in 1 iteration with
the degenerate solution, with some centroids assigned 0 points. Not the end of
the world but not exactly meaningful.
The more interesting case is k-means ||. Of course, again, if there are < k
unique points to start, in this case as well, returning k centroids means
returning duplicates. Same argument there -- seems to be no value in returning
This is really the sum of the argument to me, regardless of what Derrick's
A twist: it's possible, but quite improbable, for k-means || to choose
fewer than k unique centroids, when there are >= k distinct points. This is
most likely when there are barely more than k distinct points. In that case
it's possible that duplicated centroids do get pulled apart and do end up doing
something meaningful. I am arguing this case is not worth dealing with because
it's rare and it doesn't meaningfully harm the quality of the resulting
clustering, but, that point is arguable.
I am about 7/10 in favor of the change, certainly the bit about sampling
without replacement, but the rest I could drop if there's any significant
objection to it.
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