[SPARK-10809][MLLIB] Single-document topicDistributions method for LocalLDAModel

jira: https://issues.apache.org/jira/browse/SPARK-10809

We could provide a single-document topicDistributions method for LocalLDAModel to allow for quick queries which avoid RDD operations. Currently, the user must use an RDD of documents.

add some missing assert too.

Author: Yuhao Yang <hhbyyh@gmail.com>

Closes #9484 from hhbyyh/ldaTopicPre.

mllib/src/main/scala/org/apache/spark/mllib/clustering/LDAModel.scala

@@ -387,6 +387,32 @@ class LocalLDAModel private[spark] (
       }
   }
 
+  /**
+   * Predicts the topic mixture distribution for a document (often called "theta" in the
+   * literature).  Returns a vector of zeros for an empty document.
+   *
+   * Note this means to allow quick query for single document. For batch documents, please refer
+   * to [[topicDistributions()]] to avoid overhead.
+   *
+   * @param document document to predict topic mixture distributions for
+   * @return topic mixture distribution for the document
+   */
+  @Since("2.0.0")
+  def topicDistribution(document: Vector): Vector = {
+    val expElogbeta = exp(LDAUtils.dirichletExpectation(topicsMatrix.toBreeze.toDenseMatrix.t).t)
+    if (document.numNonzeros == 0) {
+      Vectors.zeros(this.k)
+    } else {
+      val (gamma, _) = OnlineLDAOptimizer.variationalTopicInference(
+        document,
+        expElogbeta,
+        this.docConcentration.toBreeze,
+        gammaShape,
+        this.k)
+      Vectors.dense(normalize(gamma, 1.0).toArray)
+    }
+  }
+
   /**
    * Java-friendly version of [[topicDistributions]]
    */

mllib/src/test/scala/org/apache/spark/mllib/clustering/LDASuite.scala

@@ -366,7 +366,8 @@ class LDASuite extends SparkFunSuite with MLlibTestSparkContext {
       (0, 0.99504), (1, 0.99504),
       (1, 0.99504), (1, 0.99504))
 
-    val actualPredictions = ldaModel.topicDistributions(docs).map { case (id, topics) =>
+    val actualPredictions = ldaModel.topicDistributions(docs).cache()
+    val topTopics = actualPredictions.map { case (id, topics) =>
         // convert results to expectedPredictions format, which only has highest probability topic
         val topicsBz = topics.toBreeze.toDenseVector
         (id, (argmax(topicsBz), max(topicsBz)))
@@ -374,9 +375,17 @@ class LDASuite extends SparkFunSuite with MLlibTestSparkContext {
       .values
       .collect()
 
-    expectedPredictions.zip(actualPredictions).forall { case (expected, actual) =>
-      expected._1 === actual._1 && (expected._2 ~== actual._2 relTol 1E-3D)
+    expectedPredictions.zip(topTopics).foreach { case (expected, actual) =>
+      assert(expected._1 === actual._1 && (expected._2 ~== actual._2 relTol 1E-3D))
     }
+
+    docs.collect()
+      .map(doc => ldaModel.topicDistribution(doc._2))
+      .zip(actualPredictions.map(_._2).collect())
+      .foreach { case (single, batch) =>
+        assert(single ~== batch relTol 1E-3D)
+      }
+    actualPredictions.unpersist()
   }
 
   test("OnlineLDAOptimizer with asymmetric prior") {