[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 #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

4 files changed, 107 insertions, 6 deletions

diff --git a/python/examples/kmeans.py b/python/examples/kmeans.py
index ba31af92fc..d8387b0b18 100755
--- a/python/examples/kmeans.py
+++ b/python/examples/kmeans.py
@@ -16,8 +16,13 @@
 #
 
 """
-This example requires numpy (http://www.numpy.org/)
+The K-means algorithm written from scratch against PySpark. In practice,
+one may prefer to use the KMeans algorithm in MLlib, as shown in
+python/examples/mllib/kmeans.py.
+
+This example requires NumPy (http://www.numpy.org/).
 """
+
 import sys
 
 import numpy as np
@@ -49,9 +54,7 @@ if __name__ == "__main__":
     K = int(sys.argv[3])
     convergeDist = float(sys.argv[4])
 
-    # TODO: change this after we port takeSample()
-    #kPoints = data.takeSample(False, K, 34)
-    kPoints = data.take(K)
+    kPoints = data.takeSample(False, K, 1)
     tempDist = 1.0
 
     while tempDist > convergeDist:
diff --git a/python/examples/logistic_regression.py b/python/examples/logistic_regression.py
index 1117dea538..28d52e6a40 100755
--- a/python/examples/logistic_regression.py
+++ b/python/examples/logistic_regression.py
@@ -16,9 +16,13 @@
 #
 
 """
-A logistic regression implementation that uses NumPy (http://www.numpy.org) to act on batches
-of input data using efficient matrix operations.
+A logistic regression implementation that uses NumPy (http://www.numpy.org)
+to act on batches of input data using efficient matrix operations.
+
+In practice, one may prefer to use the LogisticRegression algorithm in
+MLlib, as shown in python/examples/mllib/logistic_regression.py.
 """
+
 from collections import namedtuple
 from math import exp
 from os.path import realpath
diff --git a/python/examples/mllib/kmeans.py b/python/examples/mllib/kmeans.py
new file mode 100755
index 0000000000..dec82ff34f
--- /dev/null
+++ b/python/examples/mllib/kmeans.py
@@ -0,0 +1,44 @@
+#
+# Licensed to the Apache Software Foundation (ASF) under one or more
+# contributor license agreements.  See the NOTICE file distributed with
+# this work for additional information regarding copyright ownership.
+# The ASF licenses this file to You under the Apache License, Version 2.0
+# (the "License"); you may not use this file except in compliance with
+# the License.  You may obtain a copy of the License at
+#
+#    http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+#
+
+"""
+A K-means clustering program using MLlib.
+
+This example requires NumPy (http://www.numpy.org/).
+"""
+
+import sys
+
+import numpy as np
+from pyspark import SparkContext
+from pyspark.mllib.clustering import KMeans
+
+
+def parseVector(line):
+    return np.array([float(x) for x in line.split(' ')])
+
+
+if __name__ == "__main__":
+    if len(sys.argv) < 4:
+        print >> sys.stderr, "Usage: kmeans <master> <file> <k>"
+        exit(-1)
+    sc = SparkContext(sys.argv[1], "KMeans")
+    lines = sc.textFile(sys.argv[2])
+    data = lines.map(parseVector)
+    k = int(sys.argv[3])
+    model = KMeans.train(data, k)
+    print "Final centers: " + str(model.clusterCenters)
diff --git a/python/examples/mllib/logistic_regression.py b/python/examples/mllib/logistic_regression.py
new file mode 100755
index 0000000000..8631051d00
--- /dev/null
+++ b/python/examples/mllib/logistic_regression.py
@@ -0,0 +1,50 @@
+#
+# Licensed to the Apache Software Foundation (ASF) under one or more
+# contributor license agreements.  See the NOTICE file distributed with
+# this work for additional information regarding copyright ownership.
+# The ASF licenses this file to You under the Apache License, Version 2.0
+# (the "License"); you may not use this file except in compliance with
+# the License.  You may obtain a copy of the License at
+#
+#    http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+#
+
+"""
+Logistic regression using MLlib.
+
+This example requires NumPy (http://www.numpy.org/).
+"""
+
+from math import exp
+import sys
+
+import numpy as np
+from pyspark import SparkContext
+from pyspark.mllib.regression import LabeledPoint
+from pyspark.mllib.classification import LogisticRegressionWithSGD
+
+
+# Parse a line of text into an MLlib LabeledPoint object
+def parsePoint(line):
+    values = [float(s) for s in line.split(' ')]
+    if values[0] == -1:   # Convert -1 labels to 0 for MLlib
+        values[0] = 0
+    return LabeledPoint(values[0], values[1:])
+
+
+if __name__ == "__main__":
+    if len(sys.argv) != 4:
+        print >> sys.stderr, "Usage: logistic_regression <master> <file> <iters>"
+        exit(-1)
+    sc = SparkContext(sys.argv[1], "PythonLR")
+    points = sc.textFile(sys.argv[2]).map(parsePoint)
+    iterations = int(sys.argv[3])
+    model = LogisticRegressionWithSGD.train(points, iterations)
+    print "Final weights: " + str(model.weights)
+    print "Final intercept: " + str(model.intercept)