[SPARK-5521] PCA wrapper for easy transform vectors

I implement a simple PCA wrapper for easy transform of vectors by PCA for example LabeledPoint or another complicated structure.

Example of usage:
```
  import org.apache.spark.mllib.regression.LinearRegressionWithSGD
  import org.apache.spark.mllib.regression.LabeledPoint
  import org.apache.spark.mllib.linalg.Vectors
  import org.apache.spark.mllib.feature.PCA

  val data = sc.textFile("data/mllib/ridge-data/lpsa.data").map { line =>
    val parts = line.split(',')
    LabeledPoint(parts(0).toDouble, Vectors.dense(parts(1).split(' ').map(_.toDouble)))
  }.cache()

  val splits = data.randomSplit(Array(0.6, 0.4), seed = 11L)
  val training = splits(0).cache()
  val test = splits(1)

  val pca = PCA.create(training.first().features.size/2, data.map(_.features))
  val training_pca = training.map(p => p.copy(features = pca.transform(p.features)))
  val test_pca = test.map(p => p.copy(features = pca.transform(p.features)))

  val numIterations = 100
  val model = LinearRegressionWithSGD.train(training, numIterations)
  val model_pca = LinearRegressionWithSGD.train(training_pca, numIterations)

  val valuesAndPreds = test.map { point =>
    val score = model.predict(point.features)
    (score, point.label)
  }

  val valuesAndPreds_pca = test_pca.map { point =>
    val score = model_pca.predict(point.features)
    (score, point.label)
  }

  val MSE = valuesAndPreds.map{case(v, p) => math.pow((v - p), 2)}.mean()
  val MSE_pca = valuesAndPreds_pca.map{case(v, p) => math.pow((v - p), 2)}.mean()

  println("Mean Squared Error = " + MSE)
  println("PCA Mean Squared Error = " + MSE_pca)
```

Author: Kirill A. Korinskiy <catap@catap.ru>
Author: Joseph K. Bradley <joseph@databricks.com>

Closes #4304 from catap/pca and squashes the following commits:

501bcd9 [Joseph K. Bradley] Small updates: removed k from Java-friendly PCA fit().  In PCASuite, converted results to set for comparison. Added an error message for bad k in PCA.
9dcc02b [Kirill A. Korinskiy] [SPARK-5521] fix scala style
1892a06 [Kirill A. Korinskiy] [SPARK-5521] PCA wrapper for easy transform vectors

1 files changed, 18 insertions, 1 deletions

diff --git a/docs/mllib-dimensionality-reduction.md b/docs/mllib-dimensionality-reduction.md
index 870fed6cc5..05f51168d8 100644
--- a/docs/mllib-dimensionality-reduction.md
+++ b/docs/mllib-dimensionality-reduction.md
@@ -137,7 +137,7 @@ statistical method to find a rotation such that the first coordinate has the lar
 possible, and each succeeding coordinate in turn has the largest variance possible. The columns of
 the rotation matrix are called principal components. PCA is used widely in dimensionality reduction.
 
-MLlib supports PCA for tall-and-skinny matrices stored in row-oriented format.
+MLlib supports PCA for tall-and-skinny matrices stored in row-oriented format and any Vectors.
 
 <div class="codetabs">
 <div data-lang="scala" markdown="1">
@@ -157,6 +157,23 @@ val pc: Matrix = mat.computePrincipalComponents(10) // Principal components are
 // Project the rows to the linear space spanned by the top 10 principal components.
 val projected: RowMatrix = mat.multiply(pc)
 {% endhighlight %}
+
+The following code demonstrates how to compute principal components on source vectors
+and use them to project the vectors into a low-dimensional space while keeping associated labels:
+
+{% highlight scala %}
+import org.apache.spark.mllib.regression.LabeledPoint
+import org.apache.spark.mllib.feature.PCA
+
+val data: RDD[LabeledPoint] = ...
+
+// Compute the top 10 principal components.
+val pca = new PCA(10).fit(data.map(_.features))
+
+// Project vectors to the linear space spanned by the top 10 principal components, keeping the label
+val projected = data.map(p => p.copy(features = pca.transform(p.features)))
+{% endhighlight %}
+
 </div>
 
 <div data-lang="java" markdown="1">