python/pyspark/mllib/clustering.py

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import sys
import array as pyarray
import warnings

if sys.version > '3':
    xrange = range
    basestring = str

from math import exp, log

from numpy import array, random, tile

from collections import namedtuple

from pyspark import SparkContext, since
from pyspark.rdd import RDD, ignore_unicode_prefix
from pyspark.mllib.common import JavaModelWrapper, callMLlibFunc, callJavaFunc, _py2java, _java2py
from pyspark.mllib.linalg import SparseVector, _convert_to_vector, DenseVector
from pyspark.mllib.regression import LabeledPoint
from pyspark.mllib.stat.distribution import MultivariateGaussian
from pyspark.mllib.util import Saveable, Loader, inherit_doc, JavaLoader, JavaSaveable
from pyspark.streaming import DStream

__all__ = ['KMeansModel', 'KMeans', 'GaussianMixtureModel', 'GaussianMixture',
           'PowerIterationClusteringModel', 'PowerIterationClustering',
           'StreamingKMeans', 'StreamingKMeansModel',
           'LDA', 'LDAModel']


@inherit_doc
class KMeansModel(Saveable, Loader):

    """A clustering model derived from the k-means method.

    >>> data = array([0.0,0.0, 1.0,1.0, 9.0,8.0, 8.0,9.0]).reshape(4, 2)
    >>> model = KMeans.train(
    ...     sc.parallelize(data), 2, maxIterations=10, runs=30, initializationMode="random",
    ...                    seed=50, initializationSteps=5, epsilon=1e-4)
    >>> model.predict(array([0.0, 0.0])) == model.predict(array([1.0, 1.0]))
    True
    >>> model.predict(array([8.0, 9.0])) == model.predict(array([9.0, 8.0]))
    True
    >>> model.k
    2
    >>> model.computeCost(sc.parallelize(data))
    2.0000000000000004
    >>> model = KMeans.train(sc.parallelize(data), 2)
    >>> sparse_data = [
    ...     SparseVector(3, {1: 1.0}),
    ...     SparseVector(3, {1: 1.1}),
    ...     SparseVector(3, {2: 1.0}),
    ...     SparseVector(3, {2: 1.1})
    ... ]
    >>> model = KMeans.train(sc.parallelize(sparse_data), 2, initializationMode="k-means||",
    ...                                     seed=50, initializationSteps=5, epsilon=1e-4)
    >>> model.predict(array([0., 1., 0.])) == model.predict(array([0, 1.1, 0.]))
    True
    >>> model.predict(array([0., 0., 1.])) == model.predict(array([0, 0, 1.1]))
    True
    >>> model.predict(sparse_data[0]) == model.predict(sparse_data[1])
    True
    >>> model.predict(sparse_data[2]) == model.predict(sparse_data[3])
    True
    >>> isinstance(model.clusterCenters, list)
    True
    >>> import os, tempfile
    >>> path = tempfile.mkdtemp()
    >>> model.save(sc, path)
    >>> sameModel = KMeansModel.load(sc, path)
    >>> sameModel.predict(sparse_data[0]) == model.predict(sparse_data[0])
    True
    >>> from shutil import rmtree
    >>> try:
    ...     rmtree(path)
    ... except OSError:
    ...     pass

    >>> data = array([-383.1,-382.9, 28.7,31.2, 366.2,367.3]).reshape(3, 2)
    >>> model = KMeans.train(sc.parallelize(data), 3, maxIterations=0,
    ...     initialModel = KMeansModel([(-1000.0,-1000.0),(5.0,5.0),(1000.0,1000.0)]))
    >>> model.clusterCenters
    [array([-1000., -1000.]), array([ 5.,  5.]), array([ 1000.,  1000.])]

    .. versionadded:: 0.9.0
    """

    def __init__(self, centers):
        self.centers = centers

    @property
    @since('1.0.0')
    def clusterCenters(self):
        """Get the cluster centers, represented as a list of NumPy arrays."""
        return self.centers

    @property
    @since('1.4.0')
    def k(self):
        """Total number of clusters."""
        return len(self.centers)

    @since('0.9.0')
    def predict(self, x):
        """Find the cluster to which x belongs in this model."""
        best = 0
        best_distance = float("inf")
        if isinstance(x, RDD):
            return x.map(self.predict)

        x = _convert_to_vector(x)
        for i in xrange(len(self.centers)):
            distance = x.squared_distance(self.centers[i])
            if distance < best_distance:
                best = i
                best_distance = distance
        return best

    @since('1.4.0')
    def computeCost(self, rdd):
        """
        Return the K-means cost (sum of squared distances of points to
        their nearest center) for this model on the given data.
        """
        cost = callMLlibFunc("computeCostKmeansModel", rdd.map(_convert_to_vector),
                             [_convert_to_vector(c) for c in self.centers])
        return cost

    @since('1.4.0')
    def save(self, sc, path):
        """
        Save this model to the given path.
        """
        java_centers = _py2java(sc, [_convert_to_vector(c) for c in self.centers])
        java_model = sc._jvm.org.apache.spark.mllib.clustering.KMeansModel(java_centers)
        java_model.save(sc._jsc.sc(), path)

    @classmethod
    @since('1.4.0')
    def load(cls, sc, path):
        """
        Load a model from the given path.
        """
        java_model = sc._jvm.org.apache.spark.mllib.clustering.KMeansModel.load(sc._jsc.sc(), path)
        return KMeansModel(_java2py(sc, java_model.clusterCenters()))


class KMeans(object):
    """
    .. versionadded:: 0.9.0
    """

    @classmethod
    @since('0.9.0')
    def train(cls, rdd, k, maxIterations=100, runs=1, initializationMode="k-means||",
              seed=None, initializationSteps=5, epsilon=1e-4, initialModel=None):
        """Train a k-means clustering model."""
        if runs != 1:
            warnings.warn(
                "Support for runs is deprecated in 1.6.0. This param will have no effect in 1.7.0.")
        clusterInitialModel = []
        if initialModel is not None:
            if not isinstance(initialModel, KMeansModel):
                raise Exception("initialModel is of "+str(type(initialModel))+". It needs "
                                "to be of <type 'KMeansModel'>")
            clusterInitialModel = [_convert_to_vector(c) for c in initialModel.clusterCenters]
        model = callMLlibFunc("trainKMeansModel", rdd.map(_convert_to_vector), k, maxIterations,
                              runs, initializationMode, seed, initializationSteps, epsilon,
                              clusterInitialModel)
        centers = callJavaFunc(rdd.context, model.clusterCenters)
        return KMeansModel([c.toArray() for c in centers])


@inherit_doc
class GaussianMixtureModel(JavaModelWrapper, JavaSaveable, JavaLoader):

    """
    .. note:: Experimental

    A clustering model derived from the Gaussian Mixture Model method.

    >>> from pyspark.mllib.linalg import Vectors, DenseMatrix
    >>> from numpy.testing import assert_equal
    >>> from shutil import rmtree
    >>> import os, tempfile

    >>> clusterdata_1 =  sc.parallelize(array([-0.1,-0.05,-0.01,-0.1,
    ...                                         0.9,0.8,0.75,0.935,
    ...                                        -0.83,-0.68,-0.91,-0.76 ]).reshape(6, 2))
    >>> model = GaussianMixture.train(clusterdata_1, 3, convergenceTol=0.0001,
    ...                                 maxIterations=50, seed=10)
    >>> labels = model.predict(clusterdata_1).collect()
    >>> labels[0]==labels[1]
    False
    >>> labels[1]==labels[2]
    True
    >>> labels[4]==labels[5]
    True

    >>> path = tempfile.mkdtemp()
    >>> model.save(sc, path)
    >>> sameModel = GaussianMixtureModel.load(sc, path)
    >>> assert_equal(model.weights, sameModel.weights)
    >>> mus, sigmas = list(
    ...     zip(*[(g.mu, g.sigma) for g in model.gaussians]))
    >>> sameMus, sameSigmas = list(
    ...     zip(*[(g.mu, g.sigma) for g in sameModel.gaussians]))
    >>> mus == sameMus
    True
    >>> sigmas == sameSigmas
    True
    >>> from shutil import rmtree
    >>> try:
    ...     rmtree(path)
    ... except OSError:
    ...     pass

    >>> data =  array([-5.1971, -2.5359, -3.8220,
    ...                -5.2211, -5.0602,  4.7118,
    ...                 6.8989, 3.4592,  4.6322,
    ...                 5.7048,  4.6567, 5.5026,
    ...                 4.5605,  5.2043,  6.2734])
    >>> clusterdata_2 = sc.parallelize(data.reshape(5,3))
    >>> model = GaussianMixture.train(clusterdata_2, 2, convergenceTol=0.0001,
    ...                               maxIterations=150, seed=10)
    >>> labels = model.predict(clusterdata_2).collect()
    >>> labels[0]==labels[1]
    True
    >>> labels[2]==labels[3]==labels[4]
    True

    .. versionadded:: 1.3.0
    """

    @property
    @since('1.4.0')
    def weights(self):
        """
        Weights for each Gaussian distribution in the mixture, where weights[i] is
        the weight for Gaussian i, and weights.sum == 1.
        """
        return array(self.call("weights"))

    @property
    @since('1.4.0')
    def gaussians(self):
        """
        Array of MultivariateGaussian where gaussians[i] represents
        the Multivariate Gaussian (Normal) Distribution for Gaussian i.
        """
        return [
            MultivariateGaussian(gaussian[0], gaussian[1])
            for gaussian in self.call("gaussians")]

    @property
    @since('1.4.0')
    def k(self):
        """Number of gaussians in mixture."""
        return len(self.weights)

    @since('1.3.0')
    def predict(self, x):
        """
        Find the cluster to which the points in 'x' has maximum membership
        in this model.

        :param x:    RDD of data points.
        :return:     cluster_labels. RDD of cluster labels.
        """
        if isinstance(x, RDD):
            cluster_labels = self.predictSoft(x).map(lambda z: z.index(max(z)))
            return cluster_labels
        else:
            raise TypeError("x should be represented by an RDD, "
                            "but got %s." % type(x))

    @since('1.3.0')
    def predictSoft(self, x):
        """
        Find the membership of each point in 'x' to all mixture components.

        :param x:    RDD of data points.
        :return:     membership_matrix. RDD of array of double values.
        """
        if isinstance(x, RDD):
            means, sigmas = zip(*[(g.mu, g.sigma) for g in self.gaussians])
            membership_matrix = callMLlibFunc("predictSoftGMM", x.map(_convert_to_vector),
                                              _convert_to_vector(self.weights), means, sigmas)
            return membership_matrix.map(lambda x: pyarray.array('d', x))
        else:
            raise TypeError("x should be represented by an RDD, "
                            "but got %s." % type(x))

    @classmethod
    @since('1.5.0')
    def load(cls, sc, path):
        """Load the GaussianMixtureModel from disk.

        :param sc: SparkContext
        :param path: str, path to where the model is stored.
        """
        model = cls._load_java(sc, path)
        wrapper = sc._jvm.GaussianMixtureModelWrapper(model)
        return cls(wrapper)


class GaussianMixture(object):
    """
    .. note:: Experimental

    Learning algorithm for Gaussian Mixtures using the expectation-maximization algorithm.

    :param data:            RDD of data points
    :param k:               Number of components
    :param convergenceTol:  Threshold value to check the convergence criteria. Defaults to 1e-3
    :param maxIterations:   Number of iterations. Default to 100
    :param seed:            Random Seed
    :param initialModel:    GaussianMixtureModel for initializing learning

    .. versionadded:: 1.3.0
    """
    @classmethod
    @since('1.3.0')
    def train(cls, rdd, k, convergenceTol=1e-3, maxIterations=100, seed=None, initialModel=None):
        """Train a Gaussian Mixture clustering model."""
        initialModelWeights = None
        initialModelMu = None
        initialModelSigma = None
        if initialModel is not None:
            if initialModel.k != k:
                raise Exception("Mismatched cluster count, initialModel.k = %s, however k = %s"
                                % (initialModel.k, k))
            initialModelWeights = list(initialModel.weights)
            initialModelMu = [initialModel.gaussians[i].mu for i in range(initialModel.k)]
            initialModelSigma = [initialModel.gaussians[i].sigma for i in range(initialModel.k)]
        java_model = callMLlibFunc("trainGaussianMixtureModel", rdd.map(_convert_to_vector),
                                   k, convergenceTol, maxIterations, seed,
                                   initialModelWeights, initialModelMu, initialModelSigma)
        return GaussianMixtureModel(java_model)


class PowerIterationClusteringModel(JavaModelWrapper, JavaSaveable, JavaLoader):

    """
    .. note:: Experimental

    Model produced by [[PowerIterationClustering]].

    >>> import math
    >>> def genCircle(r, n):
    ...   points = []
    ...   for i in range(0, n):
    ...     theta = 2.0 * math.pi * i / n
    ...     points.append((r * math.cos(theta), r * math.sin(theta)))
    ...   return points
    >>> def sim(x, y):
    ...   dist2 = (x[0] - y[0]) * (x[0] - y[0]) + (x[1] - y[1]) * (x[1] - y[1])
    ...   return math.exp(-dist2 / 2.0)
    >>> r1 = 1.0
    >>> n1 = 10
    >>> r2 = 4.0
    >>> n2 = 40
    >>> n = n1 + n2
    >>> points = genCircle(r1, n1) + genCircle(r2, n2)
    >>> similarities = [(i, j, sim(points[i], points[j])) for i in range(1, n) for j in range(0, i)]
    >>> rdd = sc.parallelize(similarities, 2)
    >>> model = PowerIterationClustering.train(rdd, 2, 40)
    >>> model.k
    2
    >>> result = sorted(model.assignments().collect(), key=lambda x: x.id)
    >>> result[0].cluster == result[1].cluster == result[2].cluster == result[3].cluster
    True
    >>> result[4].cluster == result[5].cluster == result[6].cluster == result[7].cluster
    True
    >>> import os, tempfile
    >>> path = tempfile.mkdtemp()
    >>> model.save(sc, path)
    >>> sameModel = PowerIterationClusteringModel.load(sc, path)
    >>> sameModel.k
    2
    >>> result = sorted(model.assignments().collect(), key=lambda x: x.id)
    >>> result[0].cluster == result[1].cluster == result[2].cluster == result[3].cluster
    True
    >>> result[4].cluster == result[5].cluster == result[6].cluster == result[7].cluster
    True
    >>> from shutil import rmtree
    >>> try:
    ...     rmtree(path)
    ... except OSError:
    ...     pass

    .. versionadded:: 1.5.0
    """

    @property
    @since('1.5.0')
    def k(self):
        """
        Returns the number of clusters.
        """
        return self.call("k")

    @since('1.5.0')
    def assignments(self):
        """
        Returns the cluster assignments of this model.
        """
        return self.call("getAssignments").map(
            lambda x: (PowerIterationClustering.Assignment(*x)))

    @classmethod
    @since('1.5.0')
    def load(cls, sc, path):
        """
        Load a model from the given path.
        """
        model = cls._load_java(sc, path)
        wrapper = sc._jvm.PowerIterationClusteringModelWrapper(model)
        return PowerIterationClusteringModel(wrapper)


class PowerIterationClustering(object):
    """
    .. note:: Experimental

    Power Iteration Clustering (PIC), a scalable graph clustering algorithm
    developed by [[http://www.icml2010.org/papers/387.pdf Lin and Cohen]].
    From the abstract: PIC finds a very low-dimensional embedding of a
    dataset using truncated power iteration on a normalized pair-wise
    similarity matrix of the data.

    .. versionadded:: 1.5.0
    """

    @classmethod
    @since('1.5.0')
    def train(cls, rdd, k, maxIterations=100, initMode="random"):
        """
        :param rdd: an RDD of (i, j, s,,ij,,) tuples representing the
            affinity matrix, which is the matrix A in the PIC paper.
            The similarity s,,ij,, must be nonnegative.
            This is a symmetric matrix and hence s,,ij,, = s,,ji,,.
            For any (i, j) with nonzero similarity, there should be
            either (i, j, s,,ij,,) or (j, i, s,,ji,,) in the input.
            Tuples with i = j are ignored, because we assume
            s,,ij,, = 0.0.
        :param k: Number of clusters.
        :param maxIterations: Maximum number of iterations of the
            PIC algorithm.
        :param initMode: Initialization mode.
        """
        model = callMLlibFunc("trainPowerIterationClusteringModel",
                              rdd.map(_convert_to_vector), int(k), int(maxIterations), initMode)
        return PowerIterationClusteringModel(model)

    class Assignment(namedtuple("Assignment", ["id", "cluster"])):
        """
        Represents an (id, cluster) tuple.

        .. versionadded:: 1.5.0
        """


class StreamingKMeansModel(KMeansModel):
    """
    .. note:: Experimental

    Clustering model which can perform an online update of the centroids.

    The update formula for each centroid is given by

    * c_t+1 = ((c_t * n_t * a) + (x_t * m_t)) / (n_t + m_t)
    * n_t+1 = n_t * a + m_t

    where

    * c_t: Centroid at the n_th iteration.
    * n_t: Number of samples (or) weights associated with the centroid
           at the n_th iteration.
    * x_t: Centroid of the new data closest to c_t.
    * m_t: Number of samples (or) weights of the new data closest to c_t
    * c_t+1: New centroid.
    * n_t+1: New number of weights.
    * a: Decay Factor, which gives the forgetfulness.

    Note that if a is set to 1, it is the weighted mean of the previous
    and new data. If it set to zero, the old centroids are completely
    forgotten.

    :param clusterCenters: Initial cluster centers.
    :param clusterWeights: List of weights assigned to each cluster.

    >>> initCenters = [[0.0, 0.0], [1.0, 1.0]]
    >>> initWeights = [1.0, 1.0]
    >>> stkm = StreamingKMeansModel(initCenters, initWeights)
    >>> data = sc.parallelize([[-0.1, -0.1], [0.1, 0.1],
    ...                        [0.9, 0.9], [1.1, 1.1]])
    >>> stkm = stkm.update(data, 1.0, u"batches")
    >>> stkm.centers
    array([[ 0.,  0.],
           [ 1.,  1.]])
    >>> stkm.predict([-0.1, -0.1])
    0
    >>> stkm.predict([0.9, 0.9])
    1
    >>> stkm.clusterWeights
    [3.0, 3.0]
    >>> decayFactor = 0.0
    >>> data = sc.parallelize([DenseVector([1.5, 1.5]), DenseVector([0.2, 0.2])])
    >>> stkm = stkm.update(data, 0.0, u"batches")
    >>> stkm.centers
    array([[ 0.2,  0.2],
           [ 1.5,  1.5]])
    >>> stkm.clusterWeights
    [1.0, 1.0]
    >>> stkm.predict([0.2, 0.2])
    0
    >>> stkm.predict([1.5, 1.5])
    1

    .. versionadded:: 1.5.0
    """
    def __init__(self, clusterCenters, clusterWeights):
        super(StreamingKMeansModel, self).__init__(centers=clusterCenters)
        self._clusterWeights = list(clusterWeights)

    @property
    @since('1.5.0')
    def clusterWeights(self):
        """Return the cluster weights."""
        return self._clusterWeights

    @ignore_unicode_prefix
    @since('1.5.0')
    def update(self, data, decayFactor, timeUnit):
        """Update the centroids, according to data

        :param data: Should be a RDD that represents the new data.
        :param decayFactor: forgetfulness of the previous centroids.
        :param timeUnit: Can be "batches" or "points". If points, then the
                         decay factor is raised to the power of number of new
                         points and if batches, it is used as it is.
        """
        if not isinstance(data, RDD):
            raise TypeError("Data should be of an RDD, got %s." % type(data))
        data = data.map(_convert_to_vector)
        decayFactor = float(decayFactor)
        if timeUnit not in ["batches", "points"]:
            raise ValueError(
                "timeUnit should be 'batches' or 'points', got %s." % timeUnit)
        vectorCenters = [_convert_to_vector(center) for center in self.centers]
        updatedModel = callMLlibFunc(
            "updateStreamingKMeansModel", vectorCenters, self._clusterWeights,
            data, decayFactor, timeUnit)
        self.centers = array(updatedModel[0])
        self._clusterWeights = list(updatedModel[1])
        return self


class StreamingKMeans(object):
    """
    .. note:: Experimental

    Provides methods to set k, decayFactor, timeUnit to configure the
    KMeans algorithm for fitting and predicting on incoming dstreams.
    More details on how the centroids are updated are provided under the
    docs of StreamingKMeansModel.

    :param k: int, number of clusters
    :param decayFactor: float, forgetfulness of the previous centroids.
    :param timeUnit: can be "batches" or "points". If points, then the
                     decayfactor is raised to the power of no. of new points.

    .. versionadded:: 1.5.0
    """
    def __init__(self, k=2, decayFactor=1.0, timeUnit="batches"):
        self._k = k
        self._decayFactor = decayFactor
        if timeUnit not in ["batches", "points"]:
            raise ValueError(
                "timeUnit should be 'batches' or 'points', got %s." % timeUnit)
        self._timeUnit = timeUnit
        self._model = None

    @since('1.5.0')
    def latestModel(self):
        """Return the latest model"""
        return self._model

    def _validate(self, dstream):
        if self._model is None:
            raise ValueError(
                "Initial centers should be set either by setInitialCenters "
                "or setRandomCenters.")
        if not isinstance(dstream, DStream):
            raise TypeError(
                "Expected dstream to be of type DStream, "
                "got type %s" % type(dstream))

    @since('1.5.0')
    def setK(self, k):
        """Set number of clusters."""
        self._k = k
        return self

    @since('1.5.0')
    def setDecayFactor(self, decayFactor):
        """Set decay factor."""
        self._decayFactor = decayFactor
        return self

    @since('1.5.0')
    def setHalfLife(self, halfLife, timeUnit):
        """
        Set number of batches after which the centroids of that
        particular batch has half the weightage.
        """
        self._timeUnit = timeUnit
        self._decayFactor = exp(log(0.5) / halfLife)
        return self

    @since('1.5.0')
    def setInitialCenters(self, centers, weights):
        """
        Set initial centers. Should be set before calling trainOn.
        """
        self._model = StreamingKMeansModel(centers, weights)
        return self

    @since('1.5.0')
    def setRandomCenters(self, dim, weight, seed):
        """
        Set the initial centres to be random samples from
        a gaussian population with constant weights.
        """
        rng = random.RandomState(seed)
        clusterCenters = rng.randn(self._k, dim)
        clusterWeights = tile(weight, self._k)
        self._model = StreamingKMeansModel(clusterCenters, clusterWeights)
        return self

    @since('1.5.0')
    def trainOn(self, dstream):
        """Train the model on the incoming dstream."""
        self._validate(dstream)

        def update(rdd):
            self._model.update(rdd, self._decayFactor, self._timeUnit)

        dstream.foreachRDD(update)

    @since('1.5.0')
    def predictOn(self, dstream):
        """
        Make predictions on a dstream.
        Returns a transformed dstream object
        """
        self._validate(dstream)
        return dstream.map(lambda x: self._model.predict(x))

    @since('1.5.0')
    def predictOnValues(self, dstream):
        """
        Make predictions on a keyed dstream.
        Returns a transformed dstream object.
        """
        self._validate(dstream)
        return dstream.mapValues(lambda x: self._model.predict(x))


class LDAModel(JavaModelWrapper, JavaSaveable, Loader):

    """ A clustering model derived from the LDA method.

    Latent Dirichlet Allocation (LDA), a topic model designed for text documents.
    Terminology
    - "word" = "term": an element of the vocabulary
    - "token": instance of a term appearing in a document
    - "topic": multinomial distribution over words representing some concept
    References:
    - Original LDA paper (journal version):
    Blei, Ng, and Jordan.  "Latent Dirichlet Allocation."  JMLR, 2003.

    >>> from pyspark.mllib.linalg import Vectors
    >>> from numpy.testing import assert_almost_equal, assert_equal
    >>> data = [
    ...     [1, Vectors.dense([0.0, 1.0])],
    ...     [2, SparseVector(2, {0: 1.0})],
    ... ]
    >>> rdd =  sc.parallelize(data)
    >>> model = LDA.train(rdd, k=2, seed=1)
    >>> model.vocabSize()
    2
    >>> model.describeTopics()
    [([1, 0], [0.5..., 0.49...]), ([0, 1], [0.5..., 0.49...])]
    >>> model.describeTopics(1)
    [([1], [0.5...]), ([0], [0.5...])]

    >>> topics = model.topicsMatrix()
    >>> topics_expect = array([[0.5,  0.5], [0.5, 0.5]])
    >>> assert_almost_equal(topics, topics_expect, 1)

    >>> import os, tempfile
    >>> from shutil import rmtree
    >>> path = tempfile.mkdtemp()
    >>> model.save(sc, path)
    >>> sameModel = LDAModel.load(sc, path)
    >>> assert_equal(sameModel.topicsMatrix(), model.topicsMatrix())
    >>> sameModel.vocabSize() == model.vocabSize()
    True
    >>> try:
    ...     rmtree(path)
    ... except OSError:
    ...     pass

    .. versionadded:: 1.5.0
    """

    @since('1.5.0')
    def topicsMatrix(self):
        """Inferred topics, where each topic is represented by a distribution over terms."""
        return self.call("topicsMatrix").toArray()

    @since('1.5.0')
    def vocabSize(self):
        """Vocabulary size (number of terms or terms in the vocabulary)"""
        return self.call("vocabSize")

    @since('1.6.0')
    def describeTopics(self, maxTermsPerTopic=None):
        """Return the topics described by weighted terms.

        WARNING: If vocabSize and k are large, this can return a large object!

        :param maxTermsPerTopic: Maximum number of terms to collect for each topic.
            (default: vocabulary size)
        :return: Array over topics. Each topic is represented as a pair of matching arrays:
            (term indices, term weights in topic).
            Each topic's terms are sorted in order of decreasing weight.
        """
        if maxTermsPerTopic is None:
            topics = self.call("describeTopics")
        else:
            topics = self.call("describeTopics", maxTermsPerTopic)
        return topics

    @classmethod
    @since('1.5.0')
    def load(cls, sc, path):
        """Load the LDAModel from disk.

        :param sc: SparkContext
        :param path: str, path to where the model is stored.
        """
        if not isinstance(sc, SparkContext):
            raise TypeError("sc should be a SparkContext, got type %s" % type(sc))
        if not isinstance(path, basestring):
            raise TypeError("path should be a basestring, got type %s" % type(path))
        model = callMLlibFunc("loadLDAModel", sc, path)
        return LDAModel(model)


class LDA(object):
    """
    .. versionadded:: 1.5.0
    """

    @classmethod
    @since('1.5.0')
    def train(cls, rdd, k=10, maxIterations=20, docConcentration=-1.0,
              topicConcentration=-1.0, seed=None, checkpointInterval=10, optimizer="em"):
        """Train a LDA model.

        :param rdd:                 RDD of data points
        :param k:                   Number of clusters you want
        :param maxIterations:       Number of iterations. Default to 20
        :param docConcentration:    Concentration parameter (commonly named "alpha")
            for the prior placed on documents' distributions over topics ("theta").
        :param topicConcentration:  Concentration parameter (commonly named "beta" or "eta")
            for the prior placed on topics' distributions over terms.
        :param seed:                Random Seed
        :param checkpointInterval:  Period (in iterations) between checkpoints.
        :param optimizer:           LDAOptimizer used to perform the actual calculation.
            Currently "em", "online" are supported. Default to "em".
        """
        model = callMLlibFunc("trainLDAModel", rdd, k, maxIterations,
                              docConcentration, topicConcentration, seed,
                              checkpointInterval, optimizer)
        return LDAModel(model)


def _test():
    import doctest
    import pyspark.mllib.clustering
    globs = pyspark.mllib.clustering.__dict__.copy()
    globs['sc'] = SparkContext('local[4]', 'PythonTest', batchSize=2)
    (failure_count, test_count) = doctest.testmod(globs=globs, optionflags=doctest.ELLIPSIS)
    globs['sc'].stop()
    if failure_count:
        exit(-1)


if __name__ == "__main__":
    _test()