[SPARK-1945][MLLIB] Documentation Improvements for Spark 1.0

Standalone application examples are added to 'mllib-linear-methods.md' file written in Java.
This commit is related to the issue [Add full Java Examples in MLlib docs](https://issues.apache.org/jira/browse/SPARK-1945).
Also I changed the name of the sigmoid function from 'logit' to 'f'. This is because the logit function
is the inverse of sigmoid.

Thanks,
Michael

Author: Michael Giannakopoulos <miccagiann@gmail.com>

Closes #1311 from miccagiann/master and squashes the following commits:

8ffe5ab [Michael Giannakopoulos] Update code so as to comply with code standards.
f7ad5cc [Michael Giannakopoulos] Merge remote-tracking branch 'upstream/master'
38d92c7 [Michael Giannakopoulos] Adding PCA, SVD and LBFGS examples in Java. Performing minor updates in the already committed examples so as to eradicate the call of 'productElement' function whenever is possible.
cc0a089 [Michael Giannakopoulos] Modyfied Java examples so as to comply with coding standards.
b1141b2 [Michael Giannakopoulos] Added Java examples for Clustering and Collaborative Filtering [mllib-clustering.md & mllib-collaborative-filtering.md].
837f7a8 [Michael Giannakopoulos] Merge remote-tracking branch 'upstream/master'
15f0eb4 [Michael Giannakopoulos] Java examples included in 'mllib-linear-methods.md' file.

1 files changed, 95 insertions, 1 deletions

diff --git a/docs/mllib-optimization.md b/docs/mllib-optimization.md
index 651958c781..26ce5f3c50 100644
--- a/docs/mllib-optimization.md
+++ b/docs/mllib-optimization.md
@@ -207,6 +207,10 @@ the loss computed for every iteration.
 
 Here is an example to train binary logistic regression with L2 regularization using
 L-BFGS optimizer. 
+
+<div class="codetabs">
+
+<div data-lang="scala" markdown="1">
 {% highlight scala %}
 import org.apache.spark.SparkContext
 import org.apache.spark.mllib.evaluation.BinaryClassificationMetrics
@@ -263,7 +267,97 @@ println("Loss of each step in training process")
 loss.foreach(println)
 println("Area under ROC = " + auROC)
 {% endhighlight %}
-
+</div>
+
+<div data-lang="java" markdown="1">
+{% highlight java %}
+import java.util.Arrays;
+import java.util.Random;
+
+import scala.Tuple2;
+
+import org.apache.spark.api.java.*;
+import org.apache.spark.api.java.function.Function;
+import org.apache.spark.mllib.classification.LogisticRegressionModel;
+import org.apache.spark.mllib.evaluation.BinaryClassificationMetrics;
+import org.apache.spark.mllib.linalg.Vector;
+import org.apache.spark.mllib.linalg.Vectors;
+import org.apache.spark.mllib.optimization.*;
+import org.apache.spark.mllib.regression.LabeledPoint;
+import org.apache.spark.mllib.util.MLUtils;
+import org.apache.spark.SparkConf;
+import org.apache.spark.SparkContext;
+
+public class LBFGSExample {
+  public static void main(String[] args) {
+    SparkConf conf = new SparkConf().setAppName("L-BFGS Example");
+    SparkContext sc = new SparkContext(conf);
+    String path = "data/mllib/sample_libsvm_data.txt";
+    JavaRDD<LabeledPoint> data = MLUtils.loadLibSVMFile(sc, path).toJavaRDD();
+    int numFeatures = data.take(1).get(0).features().size();
+    
+    // Split initial RDD into two... [60% training data, 40% testing data].
+    JavaRDD<LabeledPoint> trainingInit = data.sample(false, 0.6, 11L);
+    JavaRDD<LabeledPoint> test = data.subtract(trainingInit);
+    
+    // Append 1 into the training data as intercept.
+    JavaRDD<Tuple2<Object, Vector>> training = data.map(
+      new Function<LabeledPoint, Tuple2<Object, Vector>>() {
+        public Tuple2<Object, Vector> call(LabeledPoint p) {
+          return new Tuple2<Object, Vector>(p.label(), MLUtils.appendBias(p.features()));
+        }
+      });
+    training.cache();
+
+    // Run training algorithm to build the model.
+    int numCorrections = 10;
+    double convergenceTol = 1e-4;
+    int maxNumIterations = 20;
+    double regParam = 0.1;
+    Vector initialWeightsWithIntercept = Vectors.dense(new double[numFeatures + 1]);
+
+    Tuple2<Vector, double[]> result = LBFGS.runLBFGS(
+      training.rdd(),
+      new LogisticGradient(),
+      new SquaredL2Updater(),
+      numCorrections,
+      convergenceTol,
+      maxNumIterations,
+      regParam,
+      initialWeightsWithIntercept);
+    Vector weightsWithIntercept = result._1();
+    double[] loss = result._2();
+
+    final LogisticRegressionModel model = new LogisticRegressionModel(
+      Vectors.dense(Arrays.copyOf(weightsWithIntercept.toArray(), weightsWithIntercept.size() - 1)),
+      (weightsWithIntercept.toArray())[weightsWithIntercept.size() - 1]);
+
+    // Clear the default threshold.
+    model.clearThreshold();
+
+    // Compute raw scores on the test set.
+    JavaRDD<Tuple2<Object, Object>> scoreAndLabels = test.map(
+      new Function<LabeledPoint, Tuple2<Object, Object>>() {
+      public Tuple2<Object, Object> call(LabeledPoint p) {
+        Double score = model.predict(p.features());
+        return new Tuple2<Object, Object>(score, p.label());
+      }
+    });
+
+    // Get evaluation metrics.
+    BinaryClassificationMetrics metrics = 
+      new BinaryClassificationMetrics(scoreAndLabels.rdd());
+    double auROC = metrics.areaUnderROC();
+     
+    System.out.println("Loss of each step in training process");
+    for (double l : loss)
+      System.out.println(l);
+    System.out.println("Area under ROC = " + auROC);
+  }
+}
+{% endhighlight %}
+</div>
+</div>
 #### Developer's note
 Since the Hessian is constructed approximately from previous gradient evaluations, 
 the objective function can not be changed during the optimization process.