[SPARK-6258] [MLLIB] GaussianMixture Python API parity check

Implement Python API for major disparities of GaussianMixture cluster algorithm between Scala & Python
```scala
GaussianMixture
    setInitialModel
GaussianMixtureModel
    k
```

Author: Yanbo Liang <ybliang8@gmail.com>

Closes #6087 from yanboliang/spark-6258 and squashes the following commits:

b3af21c [Yanbo Liang] fix typo
2b645c1 [Yanbo Liang] fix doc
638b4b7 [Yanbo Liang] address comments
b5bcade [Yanbo Liang] GaussianMixture Python API parity check

2 files changed, 22 insertions, 11 deletions

diff --git a/mllib/src/main/scala/org/apache/spark/mllib/api/python/PythonMLLibAPI.scala b/mllib/src/main/scala/org/apache/spark/mllib/api/python/PythonMLLibAPI.scala
index f4c4775965..2fa54df6fc 100644
--- a/mllib/src/main/scala/org/apache/spark/mllib/api/python/PythonMLLibAPI.scala
+++ b/mllib/src/main/scala/org/apache/spark/mllib/api/python/PythonMLLibAPI.scala
@@ -345,28 +345,40 @@ private[python] class PythonMLLibAPI extends Serializable {
    * Returns a list containing weights, mean and covariance of each mixture component.
    */
   def trainGaussianMixture(
-      data: JavaRDD[Vector], 
-      k: Int, 
-      convergenceTol: Double, 
+      data: JavaRDD[Vector],
+      k: Int,
+      convergenceTol: Double,
       maxIterations: Int,
-      seed: java.lang.Long): JList[Object] = {
+      seed: java.lang.Long,
+      initialModelWeights: java.util.ArrayList[Double],
+      initialModelMu: java.util.ArrayList[Vector],
+      initialModelSigma: java.util.ArrayList[Matrix]): JList[Object] = {
     val gmmAlg = new GaussianMixture()
       .setK(k)
       .setConvergenceTol(convergenceTol)
       .setMaxIterations(maxIterations)
 
+    if (initialModelWeights != null && initialModelMu != null && initialModelSigma != null) {
+      val gaussians = initialModelMu.asScala.toSeq.zip(initialModelSigma.asScala.toSeq).map {
+        case (x, y) => new MultivariateGaussian(x.asInstanceOf[Vector], y.asInstanceOf[Matrix])
+      }
+      val initialModel = new GaussianMixtureModel(
+        initialModelWeights.asScala.toArray, gaussians.toArray)
+      gmmAlg.setInitialModel(initialModel)
+    }
+
     if (seed != null) gmmAlg.setSeed(seed)
 
     try {
       val model = gmmAlg.run(data.rdd.persist(StorageLevel.MEMORY_AND_DISK))
       var wt = ArrayBuffer.empty[Double]
-      var mu = ArrayBuffer.empty[Vector]      
+      var mu = ArrayBuffer.empty[Vector]
       var sigma = ArrayBuffer.empty[Matrix]
       for (i <- 0 until model.k) {
           wt += model.weights(i)
           mu += model.gaussians(i).mu
           sigma += model.gaussians(i).sigma
-      }    
+      }
       List(Vectors.dense(wt.toArray), mu.toArray, sigma.toArray).map(_.asInstanceOf[Object]).asJava
     } finally {
       data.rdd.unpersist(blocking = false)
diff --git a/mllib/src/main/scala/org/apache/spark/mllib/clustering/GaussianMixtureModel.scala b/mllib/src/main/scala/org/apache/spark/mllib/clustering/GaussianMixtureModel.scala
index ec65a3da68..c22862c130 100644
--- a/mllib/src/main/scala/org/apache/spark/mllib/clustering/GaussianMixtureModel.scala
+++ b/mllib/src/main/scala/org/apache/spark/mllib/clustering/GaussianMixtureModel.scala
@@ -38,11 +38,10 @@ import org.apache.spark.sql.{SQLContext, Row}
  * are drawn from each Gaussian i=1..k with probability w(i); mu(i) and sigma(i) are 
  * the respective mean and covariance for each Gaussian distribution i=1..k. 
  * 
- * @param weight Weights for each Gaussian distribution in the mixture, where weight(i) is
- *               the weight for Gaussian i, and weight.sum == 1
- * @param mu Means for each Gaussian in the mixture, where mu(i) is the mean for Gaussian i
- * @param sigma Covariance maxtrix for each Gaussian in the mixture, where sigma(i) is the
- *              covariance matrix for Gaussian i
+ * @param weights Weights for each Gaussian distribution in the mixture, where weights(i) is
+ *                the weight for Gaussian i, and weights.sum == 1
+ * @param gaussians Array of MultivariateGaussian where gaussians(i) represents
+ *                  the Multivariate Gaussian (Normal) Distribution for Gaussian i
  */
 @Experimental
 class GaussianMixtureModel(