[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, 245 insertions, 0 deletions

diff --git a/python/pyspark/mllib/linalg.py b/python/pyspark/mllib/linalg.py
new file mode 100644
index 0000000000..0aa3a51de7
--- /dev/null
+++ b/python/pyspark/mllib/linalg.py
@@ -0,0 +1,245 @@
+#
+# 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.
+#
+
+"""
+MLlib utilities for linear algebra. For dense vectors, MLlib
+uses the NumPy C{array} type, so you can simply pass NumPy arrays
+around. For sparse vectors, users can construct a L{SparseVector}
+object from MLlib or pass SciPy C{scipy.sparse} column vectors if
+SciPy is available in their environment.
+"""
+
+from numpy import array, array_equal, ndarray, float64, int32
+
+
+class SparseVector(object):
+    """
+    A simple sparse vector class for passing data to MLlib. Users may
+    alternatively pass SciPy's {scipy.sparse} data types.
+    """
+
+    def __init__(self, size, *args):
+        """
+        Create a sparse vector, using either a dictionary, a list of
+        (index, value) pairs, or two separate arrays of indices and
+        values (sorted by index).
+
+        @param size: Size of the vector.
+        @param args: Non-zero entries, as a dictionary, list of tupes,
+               or two sorted lists containing indices and values.
+
+        >>> print SparseVector(4, {1: 1.0, 3: 5.5})
+        [1: 1.0, 3: 5.5]
+        >>> print SparseVector(4, [(1, 1.0), (3, 5.5)])
+        [1: 1.0, 3: 5.5]
+        >>> print SparseVector(4, [1, 3], [1.0, 5.5])
+        [1: 1.0, 3: 5.5]
+        """
+        assert type(size) == int, "first argument must be an int"
+        self.size = size
+        assert 1 <= len(args) <= 2, "must pass either 2 or 3 arguments"
+        if len(args) == 1:
+            pairs = args[0]
+            if type(pairs) == dict:
+               pairs = pairs.items()
+            pairs = sorted(pairs)
+            self.indices = array([p[0] for p in pairs], dtype=int32)
+            self.values = array([p[1] for p in pairs], dtype=float64)
+        else:
+            assert len(args[0]) == len(args[1]), "index and value arrays not same length"
+            self.indices = array(args[0], dtype=int32)
+            self.values = array(args[1], dtype=float64)
+            for i in xrange(len(self.indices) - 1):
+                if self.indices[i] >= self.indices[i + 1]:
+                    raise TypeError("indices array must be sorted")
+
+    def dot(self, other):
+        """
+        Dot product with a SparseVector or 1- or 2-dimensional Numpy array.
+
+        >>> a = SparseVector(4, [1, 3], [3.0, 4.0])
+        >>> a.dot(a)
+        25.0
+        >>> a.dot(array([1., 2., 3., 4.]))
+        22.0
+        >>> b = SparseVector(4, [2, 4], [1.0, 2.0])
+        >>> a.dot(b)
+        0.0
+        >>> a.dot(array([[1, 1], [2, 2], [3, 3], [4, 4]]))
+        array([ 22.,  22.])
+        """
+        if type(other) == ndarray:
+            if other.ndim == 1:
+                result = 0.0
+                for i in xrange(len(self.indices)):
+                    result += self.values[i] * other[self.indices[i]]
+                return result
+            elif other.ndim == 2:
+                results = [self.dot(other[:,i]) for i in xrange(other.shape[1])]
+                return array(results)
+            else:
+                raise Exception("Cannot call dot with %d-dimensional array" % other.ndim)
+        else:
+            result = 0.0
+            i, j = 0, 0
+            while i < len(self.indices) and j < len(other.indices):
+                if self.indices[i] == other.indices[j]:
+                    result += self.values[i] * other.values[j]
+                    i += 1
+                    j += 1
+                elif self.indices[i] < other.indices[j]:
+                    i += 1
+                else:
+                    j += 1
+            return result
+
+    def squared_distance(self, other):
+        """
+        Squared distance from a SparseVector or 1-dimensional NumPy array.
+
+        >>> a = SparseVector(4, [1, 3], [3.0, 4.0])
+        >>> a.squared_distance(a)
+        0.0
+        >>> a.squared_distance(array([1., 2., 3., 4.]))
+        11.0
+        >>> b = SparseVector(4, [2, 4], [1.0, 2.0])
+        >>> a.squared_distance(b)
+        30.0
+        >>> b.squared_distance(a)
+        30.0
+        """
+        if type(other) == ndarray:
+            if other.ndim == 1:
+                result = 0.0
+                j = 0   # index into our own array
+                for i in xrange(other.shape[0]):
+                    if j < len(self.indices) and self.indices[j] == i:
+                        diff = self.values[j] - other[i]
+                        result += diff * diff
+                        j += 1
+                    else:
+                        result += other[i] * other[i]
+                return result
+            else:
+                raise Exception("Cannot call squared_distance with %d-dimensional array" %
+                        other.ndim)
+        else:
+            result = 0.0
+            i, j = 0, 0
+            while i < len(self.indices) and j < len(other.indices):
+                if self.indices[i] == other.indices[j]:
+                    diff = self.values[i] - other.values[j]
+                    result += diff * diff
+                    i += 1
+                    j += 1
+                elif self.indices[i] < other.indices[j]:
+                    result += self.values[i] * self.values[i]
+                    i += 1
+                else:
+                    result += other.values[j] * other.values[j]
+                    j += 1
+            while i < len(self.indices):
+                result += self.values[i] * self.values[i]
+                i += 1
+            while j < len(other.indices):
+                result += other.values[j] * other.values[j]
+                j += 1
+            return result
+
+    def __str__(self):
+        inds = self.indices
+        vals = self.values
+        entries = ", ".join(["{0}: {1}".format(inds[i], vals[i]) for i in xrange(len(inds))])
+        return "[" + entries + "]"
+
+    def __repr__(self):
+        inds = self.indices
+        vals = self.values
+        entries = ", ".join(["{0}: {1}".format(inds[i], vals[i]) for i in xrange(len(inds))])
+        return "SparseVector({0}, {{{1}}})".format(self.size, entries)
+
+    def __eq__(self, other):
+        """
+        Test SparseVectors for equality.
+
+        >>> v1 = SparseVector(4, [(1, 1.0), (3, 5.5)])
+        >>> v2 = SparseVector(4, [(1, 1.0), (3, 5.5)])
+        >>> v1 == v2
+        True
+        >>> v1 != v2
+        False
+        """
+
+        return (isinstance(other, self.__class__)
+            and other.size == self.size
+            and array_equal(other.indices, self.indices)
+            and array_equal(other.values, self.values))
+
+    def __ne__(self, other):
+        return not self.__eq__(other)
+
+
+
+class Vectors(object):
+    """
+    Factory methods for working with vectors. Note that dense vectors
+    are simply represented as NumPy array objects, so there is no need
+    to covert them for use in MLlib. For sparse vectors, the factory
+    methods in this class create an MLlib-compatible type, or users
+    can pass in SciPy's C{scipy.sparse} column vectors.
+    """
+
+    @staticmethod
+    def sparse(size, *args):
+        """
+        Create a sparse vector, using either a dictionary, a list of
+        (index, value) pairs, or two separate arrays of indices and
+        values (sorted by index).
+
+        @param size: Size of the vector.
+        @param args: Non-zero entries, as a dictionary, list of tupes,
+                     or two sorted lists containing indices and values.
+
+        >>> print Vectors.sparse(4, {1: 1.0, 3: 5.5})
+        [1: 1.0, 3: 5.5]
+        >>> print Vectors.sparse(4, [(1, 1.0), (3, 5.5)])
+        [1: 1.0, 3: 5.5]
+        >>> print Vectors.sparse(4, [1, 3], [1.0, 5.5])
+        [1: 1.0, 3: 5.5]
+        """
+        return SparseVector(size, *args)
+
+    @staticmethod
+    def dense(elements):
+        """
+        Create a dense vector of 64-bit floats from a Python list. Always
+        returns a NumPy array.
+
+        >>> Vectors.dense([1, 2, 3])
+        array([ 1.,  2.,  3.])
+        """
+        return array(elements, dtype=float64)
+
+
+def _test():
+    import doctest
+    (failure_count, test_count) = doctest.testmod(optionflags=doctest.ELLIPSIS)
+    if failure_count:
+        exit(-1)
+
+if __name__ == "__main__":
+    _test()