[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

1 files changed, 65 insertions, 10 deletions

diff --git a/python/pyspark/mllib/classification.py b/python/pyspark/mllib/classification.py
index d2f9cdb3f4..3a23e0801f 100644
--- a/python/pyspark/mllib/classification.py
+++ b/python/pyspark/mllib/classification.py
@@ -17,30 +17,55 @@
 
 import numpy
 
-from numpy import array, dot, shape
+from numpy import array, shape
 from pyspark import SparkContext
 from pyspark.mllib._common import \
-    _get_unmangled_rdd, _get_unmangled_double_vector_rdd, \
+    _dot, _get_unmangled_rdd, _get_unmangled_double_vector_rdd, \
     _serialize_double_matrix, _deserialize_double_matrix, \
     _serialize_double_vector, _deserialize_double_vector, \
     _get_initial_weights, _serialize_rating, _regression_train_wrapper, \
-    LinearModel, _linear_predictor_typecheck
+    _linear_predictor_typecheck, _get_unmangled_labeled_point_rdd
+from pyspark.mllib.linalg import SparseVector
+from pyspark.mllib.regression import LabeledPoint, LinearModel
 from math import exp, log
 
 class LogisticRegressionModel(LinearModel):
     """A linear binary classification model derived from logistic regression.
 
-    >>> data = array([0.0, 0.0, 1.0, 1.0, 1.0, 2.0, 1.0, 3.0]).reshape(4,2)
+    >>> data = [
+    ...     LabeledPoint(0.0, [0.0]),
+    ...     LabeledPoint(1.0, [1.0]),
+    ...     LabeledPoint(1.0, [2.0]),
+    ...     LabeledPoint(1.0, [3.0])
+    ... ]
     >>> lrm = LogisticRegressionWithSGD.train(sc.parallelize(data))
     >>> lrm.predict(array([1.0])) > 0
     True
+    >>> lrm.predict(array([0.0])) <= 0
+    True
+    >>> sparse_data = [
+    ...     LabeledPoint(0.0, SparseVector(2, {0: 0.0})),
+    ...     LabeledPoint(1.0, SparseVector(2, {1: 1.0})),
+    ...     LabeledPoint(0.0, SparseVector(2, {0: 0.0})),
+    ...     LabeledPoint(1.0, SparseVector(2, {1: 2.0}))
+    ... ]
+    >>> lrm = LogisticRegressionWithSGD.train(sc.parallelize(sparse_data))
+    >>> lrm.predict(array([0.0, 1.0])) > 0
+    True
+    >>> lrm.predict(array([0.0, 0.0])) <= 0
+    True
+    >>> lrm.predict(SparseVector(2, {1: 1.0})) > 0
+    True
+    >>> lrm.predict(SparseVector(2, {1: 0.0})) <= 0
+    True
     """
     def predict(self, x):
         _linear_predictor_typecheck(x, self._coeff)
-        margin = dot(x, self._coeff) + self._intercept
+        margin = _dot(x, self._coeff) + self._intercept
         prob = 1/(1 + exp(-margin))
         return 1 if prob > 0.5 else 0
 
+
 class LogisticRegressionWithSGD(object):
     @classmethod
     def train(cls, data, iterations=100, step=1.0,
@@ -55,14 +80,30 @@ class LogisticRegressionWithSGD(object):
 class SVMModel(LinearModel):
     """A support vector machine.
 
-    >>> data = array([0.0, 0.0, 1.0, 1.0, 1.0, 2.0, 1.0, 3.0]).reshape(4,2)
+    >>> data = [
+    ...     LabeledPoint(0.0, [0.0]),
+    ...     LabeledPoint(1.0, [1.0]),
+    ...     LabeledPoint(1.0, [2.0]),
+    ...     LabeledPoint(1.0, [3.0])
+    ... ]
     >>> svm = SVMWithSGD.train(sc.parallelize(data))
     >>> svm.predict(array([1.0])) > 0
     True
+    >>> sparse_data = [
+    ...     LabeledPoint(0.0, SparseVector(2, {0: 0.0})),
+    ...     LabeledPoint(1.0, SparseVector(2, {1: 1.0})),
+    ...     LabeledPoint(0.0, SparseVector(2, {0: 0.0})),
+    ...     LabeledPoint(1.0, SparseVector(2, {1: 2.0}))
+    ... ]
+    >>> svm = SVMWithSGD.train(sc.parallelize(sparse_data))
+    >>> svm.predict(SparseVector(2, {1: 1.0})) > 0
+    True
+    >>> svm.predict(SparseVector(2, {1: 0.0})) <= 0
+    True
     """
     def predict(self, x):
         _linear_predictor_typecheck(x, self._coeff)
-        margin = dot(x, self._coeff) + self._intercept
+        margin = _dot(x, self._coeff) + self._intercept
         return 1 if margin >= 0 else 0
 
 class SVMWithSGD(object):
@@ -84,12 +125,26 @@ class NaiveBayesModel(object):
     - pi: vector of logs of class priors (dimension C)
     - theta: matrix of logs of class conditional probabilities (CxD)
 
-    >>> data = array([0.0, 0.0, 1.0, 0.0, 0.0, 2.0, 1.0, 1.0, 0.0]).reshape(3,3)
+    >>> data = [
+    ...     LabeledPoint(0.0, [0.0, 0.0]),
+    ...     LabeledPoint(0.0, [0.0, 1.0]),
+    ...     LabeledPoint(1.0, [1.0, 0.0]),
+    ... ]
     >>> model = NaiveBayes.train(sc.parallelize(data))
     >>> model.predict(array([0.0, 1.0]))
     0.0
     >>> model.predict(array([1.0, 0.0]))
     1.0
+    >>> sparse_data = [
+    ...     LabeledPoint(0.0, SparseVector(2, {1: 0.0})),
+    ...     LabeledPoint(0.0, SparseVector(2, {1: 1.0})),
+    ...     LabeledPoint(1.0, SparseVector(2, {0: 1.0}))
+    ... ]
+    >>> model = NaiveBayes.train(sc.parallelize(sparse_data))
+    >>> model.predict(SparseVector(2, {1: 1.0}))
+    0.0
+    >>> model.predict(SparseVector(2, {0: 1.0}))
+    1.0
     """
 
     def __init__(self, labels, pi, theta):
@@ -99,7 +154,7 @@ class NaiveBayesModel(object):
 
     def predict(self, x):
         """Return the most likely class for a data vector x"""
-        return self.labels[numpy.argmax(self.pi + dot(x, self.theta))]
+        return self.labels[numpy.argmax(self.pi + _dot(x, self.theta))]
 
 class NaiveBayes(object):
     @classmethod
@@ -119,7 +174,7 @@ class NaiveBayes(object):
         @param lambda_: The smoothing parameter
         """
         sc = data.context
-        dataBytes = _get_unmangled_double_vector_rdd(data)
+        dataBytes = _get_unmangled_labeled_point_rdd(data)
         ans = sc._jvm.PythonMLLibAPI().trainNaiveBayes(dataBytes._jrdd, lambda_)
         return NaiveBayesModel(
             _deserialize_double_vector(ans[0]),