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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