huaxingao commented on a change in pull request #26415: [SPARK-18409][ML] LSH 
approxNearestNeighbors should use approxQuantile instead of sort
URL: https://github.com/apache/spark/pull/26415#discussion_r346986229
 
 

 ##########
 File path: mllib/src/main/scala/org/apache/spark/ml/feature/LSH.scala
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 @@ -137,14 +139,23 @@ private[ml] abstract class LSHModel[T <: LSHModel[T]]
       val hashDistUDF = udf((x: Seq[Vector]) => hashDistance(x, keyHash), 
DataTypes.DoubleType)
       val hashDistCol = hashDistUDF(col($(outputCol)))
 
-      // Compute threshold to get exact k elements.
-      // TODO: SPARK-18409: Use approxQuantile to get the threshold
-      val modelDatasetSortedByHash = 
modelDataset.sort(hashDistCol).limit(numNearestNeighbors)
-      val thresholdDataset = modelDatasetSortedByHash.select(max(hashDistCol))
-      val hashThreshold = thresholdDataset.take(1).head.getDouble(0)
-
-      // Filter the dataset where the hash value is less than the threshold.
-      modelDataset.filter(hashDistCol <= hashThreshold)
+      val modelDatasetWithDist = modelDataset.withColumn(distCol, hashDistCol)
+      var filtered: DataFrame = null
+      var requestedNum = numNearestNeighbors
+      do {
+        requestedNum *= 2
+        if (requestedNum > modelDataset.count()) {
+          requestedNum = modelDataset.count().toInt
+        }
+        var quantile = requestedNum.toDouble / modelDataset.count()
+        var hashThreshold = modelDatasetWithDist.stat
+          .approxQuantile(distCol, Array(quantile), 0.001)
+
+        // Filter the dataset where the hash value is less than the threshold.
+        filtered = modelDatasetWithDist.filter(hashDistCol <= hashThreshold(0))
 
 Review comment:
   Seems to me that I have to filter out to find out if I can get enough number 
of the nearest neighbors. If not, I go back to the loop to double the quantile. 
   
   I am debating if I should continue this PR. The purpose of this PR is to 
improve performance. If the first round of the loop doesn't get enough number 
of the nearest neighbors and we have to go into the loop multiple times, the 
performance could be worse than the original code. 
   
   In the doc of ```approxNearestNeighbors```, it says ```Given a large dataset 
and an item, approximately find at most k items which have the closest distance 
to the item. ``` If this is true, then I guess we can just  use a quantile that 
should yield 2x the number of results. If we get less than k elements, that's 
OK. However, the original implementation returns exact k elements. I am not 
sure if we can change the original behavior. 

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