[GitHub] [spark] srowen commented on a change in pull request #27758: [SPARK-31007][ML] KMeans optimization based on triangle-inequality

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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_r386456920
 
 

 ##########
 File path: mllib/src/main/scala/org/apache/spark/mllib/clustering/DistanceMeasure.scala
 ##########
 @@ -154,22 +198,86 @@ object DistanceMeasure {
 }
 
 private[spark] class EuclideanDistanceMeasure extends DistanceMeasure {
+
+  /**
+   * @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.
+   *         For Euclidean distance, radius of center c is half of the distance between
+   *         center c and its closest center.
+   */
+  override def computeRadii(centers: Array[VectorWithNorm]): Array[Double] = {
+    val k = centers.length
+    if (k == 1) {
+      Array(Double.NaN)
+    } else {
+      val distances = Array.fill(k)(Double.PositiveInfinity)
+      var i = 0
+      while (i < k) {
+        var j = i + 1
+        while (j < k) {
+          val d = distance(centers(i), centers(j))
+          if (d < distances(i)) distances(i) = d
+          if (d < distances(j)) distances(j) = d
+          j += 1
+        }
+        i += 1
+      }
+
+      distances.map(_ / 2)
+    }
+  }
+
+  /**
+   * @return the index of the closest center to the given point, as well as the cost.
+   */
+  override def findClosest(
+      centers: Array[VectorWithNorm],
+      radii: Array[Double],
+      point: VectorWithNorm): (Int, Double) = {
+    var bestDistance = Double.PositiveInfinity
+    var bestIndex = 0
+    var i = 0
+    var found = false
+    while (i < centers.length && !found) {
+      val center = centers(i)
+      // Since `\|a - b\| \geq |\|a\| - \|b\||`, we can use this lower bound to avoid unnecessary
+      // distance computation.
+      var lowerBoundOfSqDist = center.norm - point.norm
+      lowerBoundOfSqDist = lowerBoundOfSqDist * lowerBoundOfSqDist
+      if (lowerBoundOfSqDist < bestDistance) {
+        val d = EuclideanDistanceMeasure.fastSquaredDistance(center, point)
+        val r = radii(i)
+        if (d < r * r) {
+          bestDistance = d
+          bestIndex = i
+          found = true
 
 Review comment:
   Same, just return?

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