[SPARK-5539][MLLIB] LDA guide

This is the LDA user guide from jkbradley with Java and Scala code example.

Author: Xiangrui Meng <meng@databricks.com>
Author: Joseph K. Bradley <joseph@databricks.com>

Closes #4465 from mengxr/lda-guide and squashes the following commits:

6dcb7d1 [Xiangrui Meng] update java example in the user guide
76169ff [Xiangrui Meng] update java example
36c3ae2 [Xiangrui Meng] Merge remote-tracking branch 'apache/master' into lda-guide
c2a1efe [Joseph K. Bradley] Added LDA programming guide, plus Java example (which is in the guide and probably should be removed).

1 files changed, 128 insertions, 1 deletions

diff --git a/docs/mllib-clustering.md b/docs/mllib-clustering.md
index 1e9ef345b7..99ed6b60e3 100644
--- a/docs/mllib-clustering.md
+++ b/docs/mllib-clustering.md
@@ -55,7 +55,7 @@ has the following parameters:
 
 Power iteration clustering is a scalable and efficient algorithm for clustering points given pointwise mutual affinity values.  Internally the algorithm:
 
-* accepts a [Graph](https://spark.apache.org/docs/0.9.2/api/graphx/index.html#org.apache.spark.graphx.Graph) that represents a  normalized pairwise affinity between all input points.
+* accepts a [Graph](api/graphx/index.html#org.apache.spark.graphx.Graph) that represents a  normalized pairwise affinity between all input points.
 * calculates the principal eigenvalue and eigenvector
 * Clusters each of the input points according to their principal eigenvector component value
 
@@ -71,6 +71,35 @@ Example outputs for a dataset inspired by the paper - but with five clusters ins
   <!-- Images are downsized intentionally to improve quality on retina displays -->
 </p>
 
+### Latent Dirichlet Allocation (LDA)
+
+[Latent Dirichlet Allocation (LDA)](http://en.wikipedia.org/wiki/Latent_Dirichlet_allocation)
+is a topic model which infers topics from a collection of text documents.
+LDA can be thought of as a clustering algorithm as follows:
+
+* Topics correspond to cluster centers, and documents correspond to examples (rows) in a dataset.
+* Topics and documents both exist in a feature space, where feature vectors are vectors of word counts.
+* Rather than estimating a clustering using a traditional distance, LDA uses a function based
+ on a statistical model of how text documents are generated.
+
+LDA takes in a collection of documents as vectors of word counts.
+It learns clustering using [expectation-maximization](http://en.wikipedia.org/wiki/Expectation%E2%80%93maximization_algorithm)
+on the likelihood function. After fitting on the documents, LDA provides:
+
+* Topics: Inferred topics, each of which is a probability distribution over terms (words).
+* Topic distributions for documents: For each document in the training set, LDA gives a probability distribution over topics.
+
+LDA takes the following parameters:
+
+* `k`: Number of topics (i.e., cluster centers)
+* `maxIterations`: Limit on the number of iterations of EM used for learning
+* `docConcentration`: Hyperparameter for prior over documents' distributions over topics. Currently must be > 1, where larger values encourage smoother inferred distributions.
+* `topicConcentration`: Hyperparameter for prior over topics' distributions over terms (words). Currently must be > 1, where larger values encourage smoother inferred distributions.
+* `checkpointInterval`: If using checkpointing (set in the Spark configuration), this parameter specifies the frequency with which checkpoints will be created.  If `maxIterations` is large, using checkpointing can help reduce shuffle file sizes on disk and help with failure recovery.
+
+*Note*: LDA is a new feature with some missing functionality.  In particular, it does not yet
+support prediction on new documents, and it does not have a Python API.  These will be added in the future.
+
 ### Examples
 
 #### k-means
@@ -293,6 +322,104 @@ for i in range(2):
 
 </div>
 
+#### Latent Dirichlet Allocation (LDA) Example
+
+In the following example, we load word count vectors representing a corpus of documents.
+We then use [LDA](api/scala/index.html#org.apache.spark.mllib.clustering.LDA)
+to infer three topics from the documents. The number of desired clusters is passed 
+to the algorithm. We then output the topics, represented as probability distributions over words.
+
+<div class="codetabs">
+<div data-lang="scala" markdown="1">
+
+{% highlight scala %}
+import org.apache.spark.mllib.clustering.LDA
+import org.apache.spark.mllib.linalg.Vectors
+
+// Load and parse the data
+val data = sc.textFile("data/mllib/sample_lda_data.txt")
+val parsedData = data.map(s => Vectors.dense(s.trim.split(' ').map(_.toDouble)))
+// Index documents with unique IDs
+val corpus = parsedData.zipWithIndex.map(_.swap).cache()
+
+// Cluster the documents into three topics using LDA
+val ldaModel = new LDA().setK(3).run(corpus)
+
+// Output topics. Each is a distribution over words (matching word count vectors)
+println("Learned topics (as distributions over vocab of " + ldaModel.vocabSize + " words):")
+val topics = ldaModel.topicsMatrix
+for (topic <- Range(0, 3)) {
+  print("Topic " + topic + ":")
+  for (word <- Range(0, ldaModel.vocabSize)) { print(" " + topics(word, topic)); }
+  println()
+}
+{% endhighlight %}
+</div>
+
+<div data-lang="java" markdown="1">
+{% highlight java %}
+import scala.Tuple2;
+
+import org.apache.spark.api.java.*;
+import org.apache.spark.api.java.function.Function;
+import org.apache.spark.mllib.clustering.DistributedLDAModel;
+import org.apache.spark.mllib.clustering.LDA;
+import org.apache.spark.mllib.linalg.Matrix;
+import org.apache.spark.mllib.linalg.Vector;
+import org.apache.spark.mllib.linalg.Vectors;
+import org.apache.spark.SparkConf;
+
+public class JavaLDAExample {
+  public static void main(String[] args) {
+    SparkConf conf = new SparkConf().setAppName("LDA Example");
+    JavaSparkContext sc = new JavaSparkContext(conf);
+
+    // Load and parse the data
+    String path = "data/mllib/sample_lda_data.txt";
+    JavaRDD<String> data = sc.textFile(path);
+    JavaRDD<Vector> parsedData = data.map(
+        new Function<String, Vector>() {
+          public Vector call(String s) {
+            String[] sarray = s.trim().split(" ");
+            double[] values = new double[sarray.length];
+            for (int i = 0; i < sarray.length; i++)
+              values[i] = Double.parseDouble(sarray[i]);
+            return Vectors.dense(values);
+          }
+        }
+    );
+    // Index documents with unique IDs
+    JavaPairRDD<Long, Vector> corpus = JavaPairRDD.fromJavaRDD(parsedData.zipWithIndex().map(
+        new Function<Tuple2<Vector, Long>, Tuple2<Long, Vector>>() {
+          public Tuple2<Long, Vector> call(Tuple2<Vector, Long> doc_id) {
+            return doc_id.swap();
+          }
+        }
+    ));
+    corpus.cache();
+
+    // Cluster the documents into three topics using LDA
+    DistributedLDAModel ldaModel = new LDA().setK(3).run(corpus);
+
+    // Output topics. Each is a distribution over words (matching word count vectors)
+    System.out.println("Learned topics (as distributions over vocab of " + ldaModel.vocabSize()
+        + " words):");
+    Matrix topics = ldaModel.topicsMatrix();
+    for (int topic = 0; topic < 3; topic++) {
+      System.out.print("Topic " + topic + ":");
+      for (int word = 0; word < ldaModel.vocabSize(); word++) {
+        System.out.print(" " + topics.apply(word, topic));
+      }
+      System.out.println();
+    }
+  }
+}
+{% endhighlight %}
+</div>
+
+</div>
+
+
 In order to run the above application, follow the instructions
 provided in the [Self-Contained Applications](quick-start.html#self-contained-applications)
 section of the Spark