zhengruifeng opened a new pull request #27758: [SPARK-31007][ML] KMeans optimization based on triangle-inequality URL: https://github.com/apache/spark/pull/27758 ### What changes were proposed in this pull request? apply Lemma 1 in [Using the Triangle Inequality to Accelerate K-Means](https://www.aaai.org/Papers/ICML/2003/ICML03-022.pdf): > Let x be a point, and let b and c be centers. If d(b,c)>=2d(x,b) then d(x,c) >= d(x,b); It can be directly applied in EuclideanDistance, but not in CosineDistance. However, luckily for CosineDistance we can get a variant in the space of radian/angle. ### Why are the changes needed? It help improving the performance of prediction ### Does this PR introduce any user-facing change? No ### How was this patch tested? existing testsuites
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