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, 130 insertions, 0 deletions

diff --git a/docs/mllib-collaborative-filtering.md b/docs/mllib-collaborative-filtering.md
new file mode 100644
index 0000000000..aa22f67b30
--- /dev/null
+++ b/docs/mllib-collaborative-filtering.md
@@ -0,0 +1,130 @@
+---
+layout: global
+title: MLlib - Collaborative Filtering 
+---
+
+* Table of contents
+{:toc}
+
+# Collaborative Filtering 
+
+[Collaborative filtering](http://en.wikipedia.org/wiki/Recommender_system#Collaborative_filtering)
+is commonly used for recommender systems.  These techniques aim to fill in the
+missing entries of a user-item association matrix.  MLlib currently supports
+model-based collaborative filtering, in which users and products are described
+by a small set of latent factors that can be used to predict missing entries.
+In particular, we implement the [alternating least squares
+(ALS)](http://www2.research.att.com/~volinsky/papers/ieeecomputer.pdf)
+algorithm to learn these latent factors. The implementation in MLlib has the
+following parameters:
+
+* *numBlocks* is the number of blacks used to parallelize computation (set to -1 to auto-configure). 
+* *rank* is the number of latent factors in our model.
+* *iterations* is the number of iterations to run.
+* *lambda* specifies the regularization parameter in ALS.
+* *implicitPrefs* specifies whether to use the *explicit feedback* ALS variant or one adapted for *implicit feedback* data
+* *alpha* is a parameter applicable to the implicit feedback variant of ALS that governs the *baseline* confidence in preference observations
+
+## Explicit vs Implicit Feedback
+
+The standard approach to matrix factorization based collaborative filtering treats 
+the entries in the user-item matrix as *explicit* preferences given by the user to the item.
+
+It is common in many real-world use cases to only have access to *implicit feedback* 
+(e.g. views, clicks, purchases, likes, shares etc.). The approach used in MLlib to deal with 
+such data is taken from 
+[Collaborative Filtering for Implicit Feedback Datasets](http://www2.research.att.com/~yifanhu/PUB/cf.pdf).
+Essentially instead of trying to model the matrix of ratings directly, this approach treats the data as 
+a combination of binary preferences and *confidence values*. The ratings are then related 
+to the level of confidence in observed user preferences, rather than explicit ratings given to items. 
+The model then tries to find latent factors that can be used to predict the expected preference of a user
+for an item. 
+
+Available algorithms for collaborative filtering: 
+
+* [ALS](api/mllib/index.html#org.apache.spark.mllib.recommendation.ALS)
+
+
+# Usage in Scala
+
+Following code snippets can be executed in `spark-shell`.
+
+In the following example we load rating data. Each row consists of a user, a product and a rating.
+We use the default ALS.train() method which assumes ratings are explicit. We evaluate the recommendation
+model by measuring the Mean Squared Error of rating prediction.
+
+{% highlight scala %}
+import org.apache.spark.mllib.recommendation.ALS
+import org.apache.spark.mllib.recommendation.Rating
+
+// Load and parse the data
+val data = sc.textFile("mllib/data/als/test.data")
+val ratings = data.map(_.split(',') match {
+    case Array(user, item, rate) =>  Rating(user.toInt, item.toInt, rate.toDouble)
+})
+
+// Build the recommendation model using ALS
+val numIterations = 20
+val model = ALS.train(ratings, 1, 20, 0.01)
+
+// Evaluate the model on rating data
+val usersProducts = ratings.map{ case Rating(user, product, rate)  => (user, product)}
+val predictions = model.predict(usersProducts).map{
+    case Rating(user, product, rate) => ((user, product), rate)
+}
+val ratesAndPreds = ratings.map{
+    case Rating(user, product, rate) => ((user, product), rate)
+}.join(predictions)
+val MSE = ratesAndPreds.map{
+    case ((user, product), (r1, r2)) =>  math.pow((r1- r2), 2)
+}.reduce(_ + _)/ratesAndPreds.count
+println("Mean Squared Error = " + MSE)
+{% endhighlight %}
+
+If the rating matrix is derived from other source of information (i.e., it is inferred from
+other signals), you can use the trainImplicit method to get better results.
+
+{% highlight scala %}
+val model = ALS.trainImplicit(ratings, 1, 20, 0.01)
+{% 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 we load rating data. Each row consists of a user, a product and a rating.
+We use the default ALS.train() method which assumes ratings are explicit. We evaluate the
+recommendation by measuring the Mean Squared Error of rating prediction.
+
+{% highlight python %}
+from pyspark.mllib.recommendation import ALS
+from numpy import array
+
+# Load and parse the data
+data = sc.textFile("mllib/data/als/test.data")
+ratings = data.map(lambda line: array([float(x) for x in line.split(',')]))
+
+# Build the recommendation model using Alternating Least Squares
+model = ALS.train(ratings, 1, 20)
+
+# Evaluate the model on training data
+testdata = ratings.map(lambda p: (int(p[0]), int(p[1])))
+predictions = model.predictAll(testdata).map(lambda r: ((r[0], r[1]), r[2]))
+ratesAndPreds = ratings.map(lambda r: ((r[0], r[1]), r[2])).join(predictions)
+MSE = ratesAndPreds.map(lambda r: (r[1][0] - r[1][1])**2).reduce(lambda x, y: x + y)/ratesAndPreds.count()
+print("Mean Squared Error = " + str(MSE))
+{% endhighlight %}
+
+If the rating matrix is derived from other source of information (i.e., it is inferred from other
+signals), you can use the trainImplicit method to get better results.
+
+{% highlight python %}
+# Build the recommendation model using Alternating Least Squares based on implicit ratings
+model = ALS.trainImplicit(ratings, 1, 20)
+{% endhighlight %}