[SPARK-17595][MLLIB] Use a bounded priority queue to find synonyms in Word2VecModel

## What changes were proposed in this pull request?

The code in `Word2VecModel.findSynonyms` to choose the vocabulary elements with the highest similarity to the query vector currently sorts the collection of similarities for every vocabulary element. This involves making multiple copies of the collection of similarities while doing a (relatively) expensive sort. It would be more efficient to find the best matches by maintaining a bounded priority queue and populating it with a single pass over the vocabulary, and that is exactly what this patch does.

## How was this patch tested?

This patch adds no user-visible functionality and its correctness should be exercised by existing tests.  To ensure that this approach is actually faster, I made a microbenchmark for `findSynonyms`:

```
object W2VTiming {
  import org.apache.spark.{SparkContext, SparkConf}
  import org.apache.spark.mllib.feature.Word2VecModel
  def run(modelPath: String, scOpt: Option[SparkContext] = None) {
    val sc = scOpt.getOrElse(new SparkContext(new SparkConf(true).setMaster("local[*]").setAppName("test")))
    val model = Word2VecModel.load(sc, modelPath)
    val keys = model.getVectors.keys
    val start = System.currentTimeMillis
    for(key <- keys) {
      model.findSynonyms(key, 5)
      model.findSynonyms(key, 10)
      model.findSynonyms(key, 25)
      model.findSynonyms(key, 50)
    }
    val finish = System.currentTimeMillis
    println("run completed in " + (finish - start) + "ms")
  }
}
```

I ran this test on a model generated from the complete works of Jane Austen and found that the new approach was over 3x faster than the old approach.  (If the `num` argument to `findSynonyms` is very close to the vocabulary size, the new approach will have less of an advantage over the old one.)

Author: William Benton <willb@redhat.com>

Closes #15150 from willb/SPARK-17595.

1 files changed, 10 insertions, 3 deletions

diff --git a/mllib/src/main/scala/org/apache/spark/mllib/feature/Word2Vec.scala b/mllib/src/main/scala/org/apache/spark/mllib/feature/Word2Vec.scala
index 42ca9665e5..2364d43aaa 100644
--- a/mllib/src/main/scala/org/apache/spark/mllib/feature/Word2Vec.scala
+++ b/mllib/src/main/scala/org/apache/spark/mllib/feature/Word2Vec.scala
@@ -35,6 +35,7 @@ import org.apache.spark.mllib.linalg.{Vector, Vectors}
 import org.apache.spark.mllib.util.{Loader, Saveable}
 import org.apache.spark.rdd._
 import org.apache.spark.sql.SparkSession
+import org.apache.spark.util.BoundedPriorityQueue
 import org.apache.spark.util.Utils
 import org.apache.spark.util.random.XORShiftRandom
 
@@ -555,7 +556,7 @@ class Word2VecModel private[spark] (
       num: Int,
       wordOpt: Option[String]): Array[(String, Double)] = {
     require(num > 0, "Number of similar words should > 0")
-    // TODO: optimize top-k
+
     val fVector = vector.toArray.map(_.toFloat)
     val cosineVec = Array.fill[Float](numWords)(0)
     val alpha: Float = 1
@@ -580,10 +581,16 @@ class Word2VecModel private[spark] (
       ind += 1
     }
 
-    val scored = wordList.zip(cosVec).toSeq.sortBy(-_._2)
+    val pq = new BoundedPriorityQueue[(String, Double)](num + 1)(Ordering.by(_._2))
+
+    for(i <- cosVec.indices) {
+      pq += Tuple2(wordList(i), cosVec(i))
+    }
+
+    val scored = pq.toSeq.sortBy(-_._2)
 
     val filtered = wordOpt match {
-      case Some(w) => scored.take(num + 1).filter(tup => w != tup._1)
+      case Some(w) => scored.filter(tup => w != tup._1)
       case None => scored
     }