Merge pull request #552 from martinjaggi/master. Closes #552.

tex formulas in the documentation

using mathjax.
and spliting the MLlib documentation by techniques

see jira
https://spark-project.atlassian.net/browse/MLLIB-19
and
https://github.com/shivaram/spark/compare/mathjax

Author: Martin Jaggi <m.jaggi@gmail.com>

== Merge branch commits ==

commit 0364bfabbfc347f917216057a20c39b631842481
Author: Martin Jaggi <m.jaggi@gmail.com>
Date:   Fri Feb 7 03:19:38 2014 +0100

    minor polishing, as suggested by @pwendell

commit dcd2142c164b2f602bf472bb152ad55bae82d31a
Author: Martin Jaggi <m.jaggi@gmail.com>
Date:   Thu Feb 6 18:04:26 2014 +0100

    enabling inline latex formulas with $.$

    same mathjax configuration as used in math.stackexchange.com

    sample usage in the linear algebra (SVD) documentation

commit bbafafd2b497a5acaa03a140bb9de1fbb7d67ffa
Author: Martin Jaggi <m.jaggi@gmail.com>
Date:   Thu Feb 6 17:31:29 2014 +0100

    split MLlib documentation by techniques

    and linked from the main mllib-guide.md site

commit d1c5212b93c67436543c2d8ddbbf610fdf0a26eb
Author: Martin Jaggi <m.jaggi@gmail.com>
Date:   Thu Feb 6 16:59:43 2014 +0100

    enable mathjax formula in the .md documentation files

    code by @shivaram

commit d73948db0d9bc36296054e79fec5b1a657b4eab4
Author: Martin Jaggi <m.jaggi@gmail.com>
Date:   Thu Feb 6 16:57:23 2014 +0100

    minor update on how to compile the documentation

1 files changed, 106 insertions, 0 deletions

diff --git a/docs/mllib-clustering.md b/docs/mllib-clustering.md
new file mode 100644
index 0000000000..65ed75b82e
--- /dev/null
+++ b/docs/mllib-clustering.md
@@ -0,0 +1,106 @@
+---
+layout: global
+title: MLlib - Clustering
+---
+
+* Table of contents
+{:toc}
+
+
+# Clustering
+
+Clustering is an unsupervised learning problem whereby we aim to group subsets
+of entities with one another based on some notion of similarity.  Clustering is
+often used for exploratory analysis and/or as a component of a hierarchical
+supervised learning pipeline (in which distinct classifiers or regression
+models are trained for each cluster). MLlib supports
+[k-means](http://en.wikipedia.org/wiki/K-means_clustering) clustering, one of
+the most commonly used clustering algorithms that clusters the data points into
+predfined number of clusters. The MLlib implementation includes a parallelized
+variant of the [k-means++](http://en.wikipedia.org/wiki/K-means%2B%2B) method
+called [kmeans||](http://theory.stanford.edu/~sergei/papers/vldb12-kmpar.pdf).
+The implementation in MLlib has the following parameters:  
+
+* *k* is the number of desired clusters.
+* *maxIterations* is the maximum number of iterations to run.
+* *initializationMode* specifies either random initialization or
+initialization via k-means\|\|.
+* *runs* is the number of times to run the k-means algorithm (k-means is not
+guaranteed to find a globally optimal solution, and when run multiple times on
+a given dataset, the algorithm returns the best clustering result).
+* *initializiationSteps* determines the number of steps in the k-means\|\| algorithm.
+* *epsilon* determines the distance threshold within which we consider k-means to have converged. 
+
+Available algorithms for clustering: 
+
+* [KMeans](api/mllib/index.html#org.apache.spark.mllib.clustering.KMeans)
+
+
+
+# Usage in Scala
+
+Following code snippets can be executed in `spark-shell`.
+
+In the following example after loading and parsing data, we use the KMeans object to cluster the data
+into two clusters. The number of desired clusters is passed to the algorithm. We then compute Within
+Set Sum of Squared Error (WSSSE). You can reduce this error measure by increasing *k*. In fact the
+optimal *k* is usually one where there is an "elbow" in the WSSSE graph.
+
+{% highlight scala %}
+import org.apache.spark.mllib.clustering.KMeans
+
+// Load and parse the data
+val data = sc.textFile("kmeans_data.txt")
+val parsedData = data.map( _.split(' ').map(_.toDouble))
+
+// Cluster the data into two classes using KMeans
+val numIterations = 20
+val numClusters = 2
+val clusters = KMeans.train(parsedData, numClusters, numIterations)
+
+// Evaluate clustering by computing Within Set Sum of Squared Errors
+val WSSSE = clusters.computeCost(parsedData)
+println("Within Set Sum of Squared Errors = " + WSSSE)
+{% endhighlight %}
+
+
+# Usage in Java
+
+All of MLlib's methods use Java-friendly types, so you can import and call them there the same
+way you do in Scala. The only caveat is that the methods take Scala RDD objects, while the
+Spark Java API uses a separate `JavaRDD` class. You can convert a Java RDD to a Scala one by
+calling `.rdd()` on your `JavaRDD` object.
+
+# Usage in Python
+Following examples can be tested in the PySpark shell.
+
+In the following example after loading and parsing data, we use the KMeans object to cluster the data
+into two clusters. The number of desired clusters is passed to the algorithm. We then compute Within
+Set Sum of Squared Error (WSSSE). You can reduce this error measure by increasing *k*. In fact the
+optimal *k* is usually one where there is an "elbow" in the WSSSE graph.
+
+{% highlight python %}
+from pyspark.mllib.clustering import KMeans
+from numpy import array
+from math import sqrt
+
+# Load and parse the data
+data = sc.textFile("kmeans_data.txt")
+parsedData = data.map(lambda line: array([float(x) for x in line.split(' ')]))
+
+# Build the model (cluster the data)
+clusters = KMeans.train(parsedData, 2, maxIterations=10,
+        runs=30, initialization_mode="random")
+
+# Evaluate clustering by computing Within Set Sum of Squared Errors
+def error(point):
+    center = clusters.centers[clusters.predict(point)]
+    return sqrt(sum([x**2 for x in (point - center)]))
+
+WSSSE = parsedData.map(lambda point: error(point)).reduce(lambda x, y: x + y)
+print("Within Set Sum of Squared Error = " + str(WSSSE))
+{% endhighlight %}
+
+Similarly you can use RidgeRegressionWithSGD and LassoWithSGD and compare training Mean Squared
+Errors.
+