[WIP] SPARK-1430: Support sparse data in Python MLlib

This PR adds a SparseVector class in PySpark and updates all the regression, classification and clustering algorithms and models to support sparse data, similar to MLlib. I chose to add this class because SciPy is quite difficult to install in many environments (more so than NumPy), but I plan to add support for SciPy sparse vectors later too, and make the methods work transparently on objects of either type.

On the Scala side, we keep Python sparse vectors sparse and pass them to MLlib. We always return dense vectors from our models.

Some to-do items left:
- [x] Support SciPy's scipy.sparse matrix objects when SciPy is available. We can easily add a function to convert these to our own SparseVector.
- [x] MLlib currently uses a vector with one extra column on the left to represent what we call LabeledPoint in Scala. Do we really want this? It may get annoying once you deal with sparse data since you must add/subtract 1 to each feature index when training. We can remove this API in 1.0 and use tuples for labeling.
- [x] Explain how to use these in the Python MLlib docs.

CC @mengxr, @JoshRosen

Author: Matei Zaharia <matei@databricks.com>

Closes apache#341 from mateiz/py-ml-update and squashes the following commits:

d52e763 [Matei Zaharia] Remove no-longer-needed slice code and handle review comments
ea5a25a [Matei Zaharia] Fix remaining uses of copyto() after merge
b9f97a3 [Matei Zaharia] Fix test
1e1bd0f [Matei Zaharia] Add MLlib logistic regression example in Python
88bc01f [Matei Zaharia] Clean up inheritance of LinearModel in Python, and expose its parametrs
37ab747 [Matei Zaharia] Fix some examples and docs due to changes in MLlib API
da0f27e [Matei Zaharia] Added a MLlib K-means example and updated docs to discuss sparse data
c48e85a [Matei Zaharia] Added some tests for passing lists as input, and added mllib/tests.py to run-tests script.
a07ba10 [Matei Zaharia] Fix some typos and calculation of initial weights
74eefe7 [Matei Zaharia] Added LabeledPoint class in Python
889dde8 [Matei Zaharia] Support scipy.sparse matrices in all our algorithms and models
ab244d1 [Matei Zaharia] Allow SparseVectors to be initialized using a dict
a5d6426 [Matei Zaharia] Add linalg.py to run-tests script
0e7a3d8 [Matei Zaharia] Keep vectors sparse in Java when reading LabeledPoints
eaee759 [Matei Zaharia] Update regression, classification and clustering models for sparse data
2abbb44 [Matei Zaharia] Further work to get linear models working with sparse data
154f45d [Matei Zaharia] Update docs, name some magic values
881fef7 [Matei Zaharia] Added a sparse vector in Python and made Java-Python format more compact

docs/mllib-classification-regression.md

@@ -356,16 +356,17 @@ error.
 import org.apache.spark.SparkContext
 import org.apache.spark.mllib.classification.SVMWithSGD
 import org.apache.spark.mllib.regression.LabeledPoint
+import org.apache.spark.mllib.linalg.Vectors
 
 // Load and parse the data file
 val data = sc.textFile("mllib/data/sample_svm_data.txt")
 val parsedData = data.map { line =>
-  val parts = line.split(' ')
-  LabeledPoint(parts(0).toDouble, parts.tail.map(x => x.toDouble).toArray)
+  val parts = line.split(' ').map(_.toDouble)
+  LabeledPoint(parts(0), Vectors.dense(parts.tail))
 }
 
 // Run training algorithm to build the model
-val numIterations = 20
+val numIterations = 100
 val model = SVMWithSGD.train(parsedData, numIterations)
 
 // Evaluate model on training examples and compute training error
@@ -401,29 +402,30 @@ val modelL1 = svmAlg.run(parsedData)
 The following example demonstrate how to load training data, parse it as an RDD of LabeledPoint.
 The example then uses LinearRegressionWithSGD to build a simple linear model to predict label 
 values. We compute the Mean Squared Error at the end to evaluate
-[goodness of fit](http://en.wikipedia.org/wiki/Goodness_of_fit)
+[goodness of fit](http://en.wikipedia.org/wiki/Goodness_of_fit).
 
 {% highlight scala %}
 import org.apache.spark.mllib.regression.LinearRegressionWithSGD
 import org.apache.spark.mllib.regression.LabeledPoint
+import org.apache.spark.mllib.linalg.Vectors
 
 // Load and parse the data
 val data = sc.textFile("mllib/data/ridge-data/lpsa.data")
 val parsedData = data.map { line =>
   val parts = line.split(',')
-  LabeledPoint(parts(0).toDouble, parts(1).split(' ').map(x => x.toDouble).toArray)
+  LabeledPoint(parts(0).toDouble, Vectors.dense(parts(1).split(' ').map(_.toDouble)))
 }
 
 // Building the model
-val numIterations = 20
+val numIterations = 100
 val model = LinearRegressionWithSGD.train(parsedData, numIterations)
 
 // Evaluate model on training examples and compute training error
 val valuesAndPreds = parsedData.map { point =>
   val prediction = model.predict(point.features)
   (point.label, prediction)
 }
-val MSE = valuesAndPreds.map{ case(v, p) => math.pow((v - p), 2)}.reduce(_ + _)/valuesAndPreds.count
+val MSE = valuesAndPreds.map{case(v, p) => math.pow((v - p), 2)}.reduce(_ + _) / valuesAndPreds.count
 println("training Mean Squared Error = " + MSE)
 {% endhighlight %}
 
@@ -518,18 +520,22 @@ and make predictions with the resulting model to compute the training error.
 
 {% highlight python %}
 from pyspark.mllib.classification import LogisticRegressionWithSGD
+from pyspark.mllib.regression import LabeledPoint
 from numpy import array
 
 # Load and parse the data
+def parsePoint(line):
+    values = [float(x) for x in line.split(' ')]
+    return LabeledPoint(values[0], values[1:])
+
 data = sc.textFile("mllib/data/sample_svm_data.txt")
-parsedData = data.map(lambda line: array([float(x) for x in line.split(' ')]))
-model = LogisticRegressionWithSGD.train(parsedData)
+parsedData = data.map(parsePoint)
 
 # Build the model
-labelsAndPreds = parsedData.map(lambda point: (int(point.item(0)),
-        model.predict(point.take(range(1, point.size)))))
+model = LogisticRegressionWithSGD.train(parsedData)
 
 # Evaluating the model on training data
+labelsAndPreds = parsedData.map(lambda p: (p.label, model.predict(p.features)))
 trainErr = labelsAndPreds.filter(lambda (v, p): v != p).count() / float(parsedData.count())
 print("Training Error = " + str(trainErr))
 {% endhighlight %}
@@ -538,22 +544,25 @@ print("Training Error = " + str(trainErr))
 The following example demonstrate how to load training data, parse it as an RDD of LabeledPoint.
 The example then uses LinearRegressionWithSGD to build a simple linear model to predict label 
 values. We compute the Mean Squared Error at the end to evaluate
-[goodness of fit](http://en.wikipedia.org/wiki/Goodness_of_fit)
+[goodness of fit](http://en.wikipedia.org/wiki/Goodness_of_fit).
 
 {% highlight python %}
-from pyspark.mllib.regression import LinearRegressionWithSGD
+from pyspark.mllib.regression import LabeledPoint, LinearRegressionWithSGD
 from numpy import array
 
 # Load and parse the data
+def parsePoint(line):
+    values = [float(x) for x in line.replace(',', ' ').split(' ')]
+    return LabeledPoint(values[0], values[1:])
+
 data = sc.textFile("mllib/data/ridge-data/lpsa.data")
-parsedData = data.map(lambda line: array([float(x) for x in line.replace(',', ' ').split(' ')]))
+parsedData = data.map(parsePoint)
 
 # Build the model
 model = LinearRegressionWithSGD.train(parsedData)
 
 # Evaluate the model on training data
-valuesAndPreds = parsedData.map(lambda point: (point.item(0),
-        model.predict(point.take(range(1, point.size)))))
-MSE = valuesAndPreds.map(lambda (v, p): (v - p)**2).reduce(lambda x, y: x + y)/valuesAndPreds.count()
+valuesAndPreds = parsedData.map(lambda p: (p.label, model.predict(p.features)))
+MSE = valuesAndPreds.map(lambda (v, p): (v - p)**2).reduce(lambda x, y: x + y) / valuesAndPreds.count()
 print("Mean Squared Error = " + str(MSE))
-{% endhighlight %}
+{% endhighlight %}

docs/mllib-clustering.md

@@ -48,14 +48,15 @@ optimal *k* is usually one where there is an "elbow" in the WSSSE graph.
 
 {% highlight scala %}
 import org.apache.spark.mllib.clustering.KMeans
+import org.apache.spark.mllib.linalg.Vectors
 
 // Load and parse the data
-val data = sc.textFile("kmeans_data.txt")
-val parsedData = data.map( _.split(' ').map(_.toDouble))
+val data = sc.textFile("data/kmeans_data.txt")
+val parsedData = data.map(s => Vectors.dense(s.split(' ').map(_.toDouble)))
 
 // Cluster the data into two classes using KMeans
-val numIterations = 20
 val numClusters = 2
+val numIterations = 20
 val clusters = KMeans.train(parsedData, numClusters, numIterations)
 
 // Evaluate clustering by computing Within Set Sum of Squared Errors
@@ -85,12 +86,12 @@ from numpy import array
 from math import sqrt
 
 # Load and parse the data
-data = sc.textFile("kmeans_data.txt")
+data = sc.textFile("data/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")
+        runs=10, initialization_mode="random")
 
 # Evaluate clustering by computing Within Set Sum of Squared Errors
 def error(point):

docs/mllib-guide.md

@@ -7,8 +7,9 @@ title: Machine Learning Library (MLlib)
 MLlib is a Spark implementation of some common machine learning (ML)
 functionality, as well associated tests and data generators.  MLlib
 currently supports four common types of machine learning problem settings,
-namely, binary classification, regression, clustering and collaborative
-filtering, as well as an underlying gradient descent optimization primitive.
+namely classification, regression, clustering and collaborative filtering,
+as well as an underlying gradient descent optimization primitive and several
+linear algebra methods.
 
 # Available Methods
 The following links provide a detailed explanation of the methods and usage examples for each of them:
@@ -32,6 +33,28 @@ The following links provide a detailed explanation of the methods and usage exam
   * Singular Value Decomposition
   * Principal Component Analysis
 
+# Data Types
+
+Most MLlib algorithms operate on RDDs containing vectors. In Java and Scala, the
+[Vector](api/mllib/index.html#org.apache.spark.mllib.linalg.Vector) class is used to
+represent vectors. You can create either dense or sparse vectors using the
+[Vectors](api/mllib/index.html#org.apache.spark.mllib.linalg.Vectors$) factory.
+
+In Python, MLlib can take the following vector types:
+
+* [NumPy](http://www.numpy.org) arrays
+* Standard Python lists (e.g. `[1, 2, 3]`)
+* The MLlib [SparseVector](api/pyspark/pyspark.mllib.linalg.SparseVector-class.html) class
+* [SciPy sparse matrices](http://docs.scipy.org/doc/scipy/reference/sparse.html)
+
+For efficiency, we recommend using NumPy arrays over lists, and using the
+[CSC format](http://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.csc_matrix.html#scipy.sparse.csc_matrix)
+for SciPy matrices, or MLlib's own SparseVector class.
+
+Several other simple data types are used throughout the library, e.g. the LabeledPoint
+class ([Java/Scala](api/mllib/index.html#org.apache.spark.mllib.regression.LabeledPoint),
+[Python](api/pyspark/pyspark.mllib.regression.LabeledPoint-class.html)) for labeled data.
+
 # Dependencies
 MLlib uses the [jblas](https://github.com/mikiobraun/jblas) linear algebra library, which itself
 depends on native Fortran routines. You may need to install the