Nice one. K-Means is one of those neat little powertools that once you get the hang of it you find more and more applications for, but it can be a bit slow for larger data sets. So this is very nice to have, thank you matt_d for posting.
Do they mean deterministic k-means, k-means++ ... ? Global optimal k-means is NP-Hard, so linear speedups aren't terribly helpful. It's nice, until you add more input. Standard k-means would be nice, or the k-means++ seed algorithm.
Also analogous to flash attention, a linear speedup in big O sense based on the typical algorithmoc complexity computing model can be a polynomial speedup in measured wall clock time due to memory hierarchy differences.
Still small compared to exponential differences, but for an NP-Hard problem, a linear 100x speedup is the difference between practically computable vs. not. There are a ton of things I'd wait 2 hours for that I wouldn't wait a week for.
The abstract suggests they're proposing speed-up techniques for the assignment and centroid update stages of the classic k-means algorithm. Which would therefore also apply to k-means++.
Does this have corresponding speed ups or memory gains for normal CPUs too? Just thinking about all the cups of coffee that have been made and drunk while scikit-learn kmeans chugs through a notebook :)
For CPU with bigger K you would put the centroids in a search tree, so take advantage of the sparsity, while a GPU would calculate the full NxK distance matrix. So from my understanding the bottleneck they are fixing doesn't show up on CPU.
Most data I've used is for geospatial with D<=4 (xyzt) so for me search trees worked great. But for things like descriptor or embedding clustering yes, trees wouldn't be useful.
http://arxiv.org/pdf/2505.18875
Also analogous to flash attention, a linear speedup in big O sense based on the typical algorithmoc complexity computing model can be a polynomial speedup in measured wall clock time due to memory hierarchy differences.
Still small compared to exponential differences, but for an NP-Hard problem, a linear 100x speedup is the difference between practically computable vs. not. There are a ton of things I'd wait 2 hours for that I wouldn't wait a week for.
from what I've seen I had the impression that Yinyang k-means was the best way to take advantage of the sparsity.