srowen commented on a change in pull request #27758: [SPARK-31007][ML] KMeans 
optimization based on triangle-inequality
URL: https://github.com/apache/spark/pull/27758#discussion_r386450041
 
 

 ##########
 File path: 
mllib/src/main/scala/org/apache/spark/mllib/clustering/DistanceMeasure.scala
 ##########
 @@ -24,16 +24,60 @@ import org.apache.spark.mllib.util.MLUtils
 
 private[spark] abstract class DistanceMeasure extends Serializable {
 
+  /**
+   * Radii of centers used in triangle inequality to obtain useful bounds to 
find
+   * closest centers.
+   *
+   * @see <a 
href="https://www.aaai.org/Papers/ICML/2003/ICML03-022.pdf";>Charles Elkan,
+   *      Using the Triangle Inequality to Accelerate k-Means</a>
+   *
+   * @return Radii of centers. If distance between point x and center c is 
less than
+   *         the radius of center c, then center c is the closest center to 
point x.
+   */
+  def computeRadii(centers: Array[VectorWithNorm]): Array[Double] = {
 
 Review comment:
   Is there any value in this default impl? it's overridden in both subclasses. 
Or is it to support future impls that may not be able to use this optimization?

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