pyspark.mllib package

pyspark.mllib.classification module

class pyspark.mllib.classification.LogisticRegressionModel(weights, intercept, numFeatures, numClasses)

Classification model trained using Multinomial/Binary Logistic Regression.

Parameters:

• weights – Weights computed for every feature.
• intercept – Intercept computed for this model. (Only used in Binary Logistic Regression. In Multinomial Logistic Regression, the intercepts will not be a single value, so the intercepts will be part of the weights.)
• numFeatures – the dimension of the features.
• numClasses – the number of possible outcomes for k classes classification problem in Multinomial Logistic Regression. By default, it is binary logistic regression so numClasses will be set to 2.

>>> data = [
...     LabeledPoint(0.0, [0.0, 1.0]),
...     LabeledPoint(1.0, [1.0, 0.0]),
... ]
>>> lrm = LogisticRegressionWithSGD.train(sc.parallelize(data), iterations=10)
>>> lrm.predict([1.0, 0.0])
1
>>> lrm.predict([0.0, 1.0])
0
>>> lrm.predict(sc.parallelize([[1.0, 0.0], [0.0, 1.0]])).collect()
[1, 0]
>>> lrm.clearThreshold()
>>> lrm.predict([0.0, 1.0])
0.279...

>>> sparse_data = [
...     LabeledPoint(0.0, SparseVector(2, {0: 0.0})),
...     LabeledPoint(1.0, SparseVector(2, {1: 1.0})),
...     LabeledPoint(0.0, SparseVector(2, {0: 1.0})),
...     LabeledPoint(1.0, SparseVector(2, {1: 2.0}))
... ]
>>> lrm = LogisticRegressionWithSGD.train(sc.parallelize(sparse_data), iterations=10)
>>> lrm.predict(array([0.0, 1.0]))
1
>>> lrm.predict(array([1.0, 0.0]))
0
>>> lrm.predict(SparseVector(2, {1: 1.0}))
1
>>> lrm.predict(SparseVector(2, {0: 1.0}))
0
>>> import os, tempfile
>>> path = tempfile.mkdtemp()
>>> lrm.save(sc, path)
>>> sameModel = LogisticRegressionModel.load(sc, path)
>>> sameModel.predict(array([0.0, 1.0]))
1
>>> sameModel.predict(SparseVector(2, {0: 1.0}))
0
>>> from shutil import rmtree
>>> try:
...    rmtree(path)
... except:
...    pass
>>> multi_class_data = [
...     LabeledPoint(0.0, [0.0, 1.0, 0.0]),
...     LabeledPoint(1.0, [1.0, 0.0, 0.0]),
...     LabeledPoint(2.0, [0.0, 0.0, 1.0])
... ]
>>> data = sc.parallelize(multi_class_data)
>>> mcm = LogisticRegressionWithLBFGS.train(data, iterations=10, numClasses=3)
>>> mcm.predict([0.0, 0.5, 0.0])
0
>>> mcm.predict([0.8, 0.0, 0.0])
1
>>> mcm.predict([0.0, 0.0, 0.3])
2

clearThreshold()

Note

Experimental

Clears the threshold so that predict will output raw prediction scores. It is used for binary classification only.

intercept

classmethod load(sc, path)

numClasses

numFeatures

predict(x)

Predict values for a single data point or an RDD of points using the model trained.

save(sc, path)

setThreshold(value)

Note

Experimental

Sets the threshold that separates positive predictions from negative predictions. An example with prediction score greater than or equal to this threshold is identified as an positive, and negative otherwise. It is used for binary classification only.

threshold

Note

Experimental

Returns the threshold (if any) used for converting raw prediction scores into 0/1 predictions. It is used for binary classification only.

weights

class pyspark.mllib.classification.LogisticRegressionWithSGD

classmethod train(data, iterations=100, step=1.0, miniBatchFraction=1.0, initialWeights=None, regParam=0.01, regType='l2', intercept=False, validateData=True)

Train a logistic regression model on the given data.

Parameters:

• data – The training data, an RDD of LabeledPoint.
• iterations – The number of iterations (default: 100).
• step – The step parameter used in SGD (default: 1.0).
• miniBatchFraction – Fraction of data to be used for each SGD iteration (default: 1.0).
• initialWeights – The initial weights (default: None).
• regParam – The regularizer parameter (default: 0.01).
• regType –

  The type of regularizer used for training our model.

  Allowed values:

  • “l1” for using L1 regularization
  • “l2” for using L2 regularization
  • None for no regularization

  (default: “l2”)

• intercept – Boolean parameter which indicates the use or not of the augmented representation for training data (i.e. whether bias features are activated or not, default: False).
• validateData – Boolean parameter which indicates if the algorithm should validate data before training. (default: True)

class pyspark.mllib.classification.LogisticRegressionWithLBFGS

classmethod train(data, iterations=100, initialWeights=None, regParam=0.01, regType='l2', intercept=False, corrections=10, tolerance=0.0001, validateData=True, numClasses=2)

Train a logistic regression model on the given data.

Parameters:

• data – The training data, an RDD of LabeledPoint.
• iterations – The number of iterations (default: 100).
• initialWeights – The initial weights (default: None).
• regParam – The regularizer parameter (default: 0.01).
• regType –

  The type of regularizer used for training our model.

  Allowed values:

  • “l1” for using L1 regularization
  • “l2” for using L2 regularization
  • None for no regularization

  (default: “l2”)

• intercept – Boolean parameter which indicates the use or not of the augmented representation for training data (i.e. whether bias features are activated or not, default: False).
• corrections – The number of corrections used in the LBFGS update (default: 10).
• tolerance – The convergence tolerance of iterations for L-BFGS (default: 1e-4).
• validateData – Boolean parameter which indicates if the algorithm should validate data before training. (default: True)
• numClasses – The number of classes (i.e., outcomes) a label can take in Multinomial Logistic Regression (default: 2).

>>> data = [
...     LabeledPoint(0.0, [0.0, 1.0]),
...     LabeledPoint(1.0, [1.0, 0.0]),
... ]
>>> lrm = LogisticRegressionWithLBFGS.train(sc.parallelize(data), iterations=10)
>>> lrm.predict([1.0, 0.0])
1
>>> lrm.predict([0.0, 1.0])
0

class pyspark.mllib.classification.SVMModel(weights, intercept)

Model for Support Vector Machines (SVMs).

Parameters:

• weights – Weights computed for every feature.
• intercept – Intercept computed for this model.

>>> 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), iterations=10)
>>> svm.predict([1.0])
1
>>> svm.predict(sc.parallelize([[1.0]])).collect()
[1]
>>> svm.clearThreshold()
>>> svm.predict(array([1.0]))
1.44...

>>> sparse_data = [
...     LabeledPoint(0.0, SparseVector(2, {0: -1.0})),
...     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), iterations=10)
>>> svm.predict(SparseVector(2, {1: 1.0}))
1
>>> svm.predict(SparseVector(2, {0: -1.0}))
0
>>> import os, tempfile
>>> path = tempfile.mkdtemp()
>>> svm.save(sc, path)
>>> sameModel = SVMModel.load(sc, path)
>>> sameModel.predict(SparseVector(2, {1: 1.0}))
1
>>> sameModel.predict(SparseVector(2, {0: -1.0}))
0
>>> from shutil import rmtree
>>> try:
...    rmtree(path)
... except:
...    pass

clearThreshold()

Note

Experimental

Clears the threshold so that predict will output raw prediction scores. It is used for binary classification only.

intercept

classmethod load(sc, path)

predict(x)

Predict values for a single data point or an RDD of points using the model trained.

save(sc, path)

setThreshold(value)

Note

Experimental

Sets the threshold that separates positive predictions from negative predictions. An example with prediction score greater than or equal to this threshold is identified as an positive, and negative otherwise. It is used for binary classification only.

threshold

Note

Experimental

Returns the threshold (if any) used for converting raw prediction scores into 0/1 predictions. It is used for binary classification only.

weights

class pyspark.mllib.classification.SVMWithSGD

classmethod train(data, iterations=100, step=1.0, regParam=0.01, miniBatchFraction=1.0, initialWeights=None, regType='l2', intercept=False, validateData=True)

Train a support vector machine on the given data.

Parameters:

• data – The training data, an RDD of LabeledPoint.
• iterations – The number of iterations (default: 100).
• step – The step parameter used in SGD (default: 1.0).
• regParam – The regularizer parameter (default: 0.01).
• miniBatchFraction – Fraction of data to be used for each SGD iteration (default: 1.0).
• initialWeights – The initial weights (default: None).
• regType –

  The type of regularizer used for training our model.

  Allowed values:

  • “l1” for using L1 regularization
  • “l2” for using L2 regularization
  • None for no regularization

  (default: “l2”)

• intercept – Boolean parameter which indicates the use or not of the augmented representation for training data (i.e. whether bias features are activated or not, default: False).
• validateData – Boolean parameter which indicates if the algorithm should validate data before training. (default: True)

class pyspark.mllib.classification.NaiveBayesModel(labels, pi, theta)

Model for Naive Bayes classifiers.

Parameters:

• labels – list of labels.
• pi – log of class priors, whose dimension is C, number of labels.
• theta – log of class conditional probabilities, whose dimension is C-by-D, where D is number of features.

>>> 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
>>> model.predict(sc.parallelize([[1.0, 0.0]])).collect()
[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
>>> import os, tempfile
>>> path = tempfile.mkdtemp()
>>> model.save(sc, path)
>>> sameModel = NaiveBayesModel.load(sc, path)
>>> sameModel.predict(SparseVector(2, {0: 1.0})) == model.predict(SparseVector(2, {0: 1.0}))
True
>>> from shutil import rmtree
>>> try:
...     rmtree(path)
... except OSError:
...     pass

classmethod load(sc, path)

predict(x)

Return the most likely class for a data vector or an RDD of vectors

save(sc, path)

Save this model to the given path.

This saves:

• human-readable (JSON) model metadata to path/metadata/
• Parquet formatted data to path/data/

The model may be loaded using py:meth:Loader.load.

Parameters:

• sc – Spark context used to save model data.
• path – Path specifying the directory in which to save this model. If the directory already exists, this method throws an exception.

class pyspark.mllib.classification.NaiveBayes

classmethod train(data, lambda_=1.0)

Train a Naive Bayes model given an RDD of (label, features) vectors.

This is the Multinomial NB (U{http://tinyurl.com/lsdw6p}) which can handle all kinds of discrete data. For example, by converting documents into TF-IDF vectors, it can be used for document classification. By making every vector a 0-1 vector, it can also be used as Bernoulli NB (U{http://tinyurl.com/p7c96j6}). The input feature values must be nonnegative.

Parameters:

• data – RDD of LabeledPoint.
• lambda – The smoothing parameter (default: 1.0).

class pyspark.mllib.classification.StreamingLogisticRegressionWithSGD(stepSize=0.1, numIterations=50, miniBatchFraction=1.0, regParam=0.01)

Run LogisticRegression with SGD on a batch of data.

The weights obtained at the end of training a stream are used as initial weights for the next batch.

Parameters:

• stepSize – Step size for each iteration of gradient descent.
• numIterations – Number of iterations run for each batch of data.
• miniBatchFraction – Fraction of data on which SGD is run for each iteration.
• regParam – L2 Regularization parameter.

latestModel()

Returns the latest model.

predictOn(dstream)

Make predictions on a dstream.

Returns:Transformed dstream object.

predictOnValues(dstream)

Make predictions on a keyed dstream.

Returns:Transformed dstream object.

setInitialWeights(initialWeights)

Set the initial value of weights.

This must be set before running trainOn and predictOn.

trainOn(dstream)

Train the model on the incoming dstream.

pyspark.mllib.clustering module

class pyspark.mllib.clustering.KMeansModel(centers)

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

clusterCenters

Get the cluster centers, represented as a list of NumPy arrays.

computeCost(rdd)

Return the K-means cost (sum of squared distances of points to their nearest center) for this model on the given data.

k

Total number of clusters.

classmethod load(sc, path)

predict(x)

Find the cluster to which x belongs in this model.

save(sc, path)

Save this model to the given path.

This saves:

• human-readable (JSON) model metadata to path/metadata/
• Parquet formatted data to path/data/

The model may be loaded using py:meth:Loader.load.

Parameters:

• sc – Spark context used to save model data.
• path – Path specifying the directory in which to save this model. If the directory already exists, this method throws an exception.

class pyspark.mllib.clustering.KMeans

classmethod train(rdd, k, maxIterations=100, runs=1, initializationMode='k-means||', seed=None, initializationSteps=5, epsilon=0.0001)

Train a k-means clustering model.

class pyspark.mllib.clustering.GaussianMixtureModel(java_model)

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

gaussians

Array of MultivariateGaussian where gaussians[i] represents the Multivariate Gaussian (Normal) Distribution for Gaussian i.

k

Number of gaussians in mixture.

classmethod load(sc, path)

Load the GaussianMixtureModel from disk.

Parameters:

• sc – SparkContext
• path – str, path to where the model is stored.

predict(x)

Find the cluster to which the points in ‘x’ has maximum membership in this model.

Parameters:x – RDD of data points. Returns:cluster_labels. RDD of cluster labels.

predictSoft(x)

Find the membership of each point in ‘x’ to all mixture components.

Parameters:x – RDD of data points. Returns:membership_matrix. RDD of array of double values.

weights

Weights for each Gaussian distribution in the mixture, where weights[i] is the weight for Gaussian i, and weights.sum == 1.

class pyspark.mllib.clustering.GaussianMixture

Note

Experimental

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

Parameters:

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

classmethod train(rdd, k, convergenceTol=0.001, maxIterations=100, seed=None, initialModel=None)

Train a Gaussian Mixture clustering model.

class pyspark.mllib.clustering.PowerIterationClusteringModel(java_model)

Note

Experimental

Model produced by [[PowerIterationClustering]].

>>> data = [(0, 1, 1.0), (0, 2, 1.0), (0, 3, 1.0), (1, 2, 1.0), (1, 3, 1.0),
... (2, 3, 1.0), (3, 4, 0.1), (4, 5, 1.0), (4, 15, 1.0), (5, 6, 1.0),
... (6, 7, 1.0), (7, 8, 1.0), (8, 9, 1.0), (9, 10, 1.0), (10, 11, 1.0),
... (11, 12, 1.0), (12, 13, 1.0), (13, 14, 1.0), (14, 15, 1.0)]
>>> rdd = sc.parallelize(data, 2)
>>> model = PowerIterationClustering.train(rdd, 2, 100)
>>> 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

assignments()

Returns the cluster assignments of this model.

k

Returns the number of clusters.

classmethod load(sc, path)

class pyspark.mllib.clustering.PowerIterationClustering

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.

class Assignment

Represents an (id, cluster) tuple.

classmethod PowerIterationClustering.train(rdd, k, maxIterations=100, initMode='random')

Parameters:

• 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.
• k – Number of clusters.
• maxIterations – Maximum number of iterations of the PIC algorithm.
• initMode – Initialization mode.

class pyspark.mllib.clustering.StreamingKMeans(k=2, decayFactor=1.0, timeUnit='batches')

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.

Parameters:

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

latestModel()

Return the latest model

predictOn(dstream)

Make predictions on a dstream. Returns a transformed dstream object

predictOnValues(dstream)

Make predictions on a keyed dstream. Returns a transformed dstream object.

setDecayFactor(decayFactor)

Set decay factor.

setHalfLife(halfLife, timeUnit)

Set number of batches after which the centroids of that particular batch has half the weightage.

setInitialCenters(centers, weights)

Set initial centers. Should be set before calling trainOn.

setK(k)

Set number of clusters.

setRandomCenters(dim, weight, seed)

Set the initial centres to be random samples from a gaussian population with constant weights.

trainOn(dstream)

Train the model on the incoming dstream.

class pyspark.mllib.clustering.StreamingKMeansModel(clusterCenters, clusterWeights)

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.

Parameters:

• clusterCenters – Initial cluster centers.
• 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

clusterWeights

Return the cluster weights.

update(data, decayFactor, timeUnit)

Update the centroids, according to data

Parameters:

• data – Should be a RDD that represents the new data.
• decayFactor – forgetfulness of the previous centroids.
• 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.

class pyspark.mllib.clustering.LDA

classmethod train(rdd, k=10, maxIterations=20, docConcentration=-1.0, topicConcentration=-1.0, seed=None, checkpointInterval=10, optimizer='em')

Train a LDA model.

Parameters:

• rdd – RDD of data points
• k – Number of clusters you want
• maxIterations – Number of iterations. Default to 20
• docConcentration – Concentration parameter (commonly named “alpha”) for the prior placed on documents’ distributions over topics (“theta”).
• topicConcentration – Concentration parameter (commonly named “beta” or “eta”) for the prior placed on topics’ distributions over terms.
• seed – Random Seed
• checkpointInterval – Period (in iterations) between checkpoints.
• optimizer – LDAOptimizer used to perform the actual calculation. Currently “em”, “online” are supported. Default to “em”.

class pyspark.mllib.clustering.LDAModel(java_model)

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)
>>> model.vocabSize()
2
>>> 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

classmethod load(sc, path)

Load the LDAModel from disk.

Parameters:

• sc – SparkContext
• path – str, path to where the model is stored.

save(sc, path)

Save the LDAModel on to disk.

Parameters:

• sc – SparkContext
• path – str, path to where the model needs to be stored.

topicsMatrix()

Inferred topics, where each topic is represented by a distribution over terms.

vocabSize()

Vocabulary size (number of terms or terms in the vocabulary)

pyspark.mllib.evaluation module

class pyspark.mllib.evaluation.BinaryClassificationMetrics(scoreAndLabels)

Evaluator for binary classification.

Parameters:scoreAndLabels – an RDD of (score, label) pairs

>>> scoreAndLabels = sc.parallelize([
...     (0.1, 0.0), (0.1, 1.0), (0.4, 0.0), (0.6, 0.0), (0.6, 1.0), (0.6, 1.0), (0.8, 1.0)], 2)
>>> metrics = BinaryClassificationMetrics(scoreAndLabels)
>>> metrics.areaUnderROC
0.70...
>>> metrics.areaUnderPR
0.83...
>>> metrics.unpersist()

areaUnderPR

Computes the area under the precision-recall curve.

areaUnderROC

Computes the area under the receiver operating characteristic (ROC) curve.

unpersist()

Unpersists intermediate RDDs used in the computation.

class pyspark.mllib.evaluation.RegressionMetrics(predictionAndObservations)

Evaluator for regression.

Parameters:predictionAndObservations – an RDD of (prediction, observation) pairs.

>>> predictionAndObservations = sc.parallelize([
...     (2.5, 3.0), (0.0, -0.5), (2.0, 2.0), (8.0, 7.0)])
>>> metrics = RegressionMetrics(predictionAndObservations)
>>> metrics.explainedVariance
8.859...
>>> metrics.meanAbsoluteError
0.5...
>>> metrics.meanSquaredError
0.37...
>>> metrics.rootMeanSquaredError
0.61...
>>> metrics.r2
0.94...

explainedVariance

Returns the explained variance regression score. explainedVariance = 1 - variance(y - hat{y}) / variance(y)

meanAbsoluteError

Returns the mean absolute error, which is a risk function corresponding to the expected value of the absolute error loss or l1-norm loss.

meanSquaredError

Returns the mean squared error, which is a risk function corresponding to the expected value of the squared error loss or quadratic loss.

r2

Returns R^2^, the coefficient of determination.

rootMeanSquaredError

Returns the root mean squared error, which is defined as the square root of the mean squared error.

class pyspark.mllib.evaluation.MulticlassMetrics(predictionAndLabels)

Evaluator for multiclass classification.

Parameters:predictionAndLabels – an RDD of (prediction, label) pairs.

>>> predictionAndLabels = sc.parallelize([(0.0, 0.0), (0.0, 1.0), (0.0, 0.0),
...     (1.0, 0.0), (1.0, 1.0), (1.0, 1.0), (1.0, 1.0), (2.0, 2.0), (2.0, 0.0)])
>>> metrics = MulticlassMetrics(predictionAndLabels)
>>> metrics.confusionMatrix().toArray()
array([[ 2.,  1.,  1.],
       [ 1.,  3.,  0.],
       [ 0.,  0.,  1.]])
>>> metrics.falsePositiveRate(0.0)
0.2...
>>> metrics.precision(1.0)
0.75...
>>> metrics.recall(2.0)
1.0...
>>> metrics.fMeasure(0.0, 2.0)
0.52...
>>> metrics.precision()
0.66...
>>> metrics.recall()
0.66...
>>> metrics.weightedFalsePositiveRate
0.19...
>>> metrics.weightedPrecision
0.68...
>>> metrics.weightedRecall
0.66...
>>> metrics.weightedFMeasure()
0.66...
>>> metrics.weightedFMeasure(2.0)
0.65...

confusionMatrix()

Returns confusion matrix: predicted classes are in columns, they are ordered by class label ascending, as in “labels”.

fMeasure(label=None, beta=None)

Returns f-measure or f-measure for a given label (category) if specified.

falsePositiveRate(label)

Returns false positive rate for a given label (category).

precision(label=None)

Returns precision or precision for a given label (category) if specified.

recall(label=None)

Returns recall or recall for a given label (category) if specified.

truePositiveRate(label)

Returns true positive rate for a given label (category).

weightedFMeasure(beta=None)

Returns weighted averaged f-measure.

weightedFalsePositiveRate

Returns weighted false positive rate.

weightedPrecision

Returns weighted averaged precision.

weightedRecall

Returns weighted averaged recall. (equals to precision, recall and f-measure)

weightedTruePositiveRate

Returns weighted true positive rate. (equals to precision, recall and f-measure)

class pyspark.mllib.evaluation.RankingMetrics(predictionAndLabels)

Evaluator for ranking algorithms.

Parameters:predictionAndLabels – an RDD of (predicted ranking, ground truth set) pairs.

>>> predictionAndLabels = sc.parallelize([
...     ([1, 6, 2, 7, 8, 3, 9, 10, 4, 5], [1, 2, 3, 4, 5]),
...     ([4, 1, 5, 6, 2, 7, 3, 8, 9, 10], [1, 2, 3]),
...     ([1, 2, 3, 4, 5], [])])
>>> metrics = RankingMetrics(predictionAndLabels)
>>> metrics.precisionAt(1)
0.33...
>>> metrics.precisionAt(5)
0.26...
>>> metrics.precisionAt(15)
0.17...
>>> metrics.meanAveragePrecision
0.35...
>>> metrics.ndcgAt(3)
0.33...
>>> metrics.ndcgAt(10)
0.48...

meanAveragePrecision

Returns the mean average precision (MAP) of all the queries. If a query has an empty ground truth set, the average precision will be zero and a log warining is generated.

ndcgAt(k)

Compute the average NDCG value of all the queries, truncated at ranking position k. The discounted cumulative gain at position k is computed as: sum,,i=1,,^k^ (2^{relevance of ‘’i’‘th item}^ - 1) / log(i + 1), and the NDCG is obtained by dividing the DCG value on the ground truth set. In the current implementation, the relevance value is binary. If a query has an empty ground truth set, zero will be used as NDCG together with a log warning.

precisionAt(k)

Compute the average precision of all the queries, truncated at ranking position k.

If for a query, the ranking algorithm returns n (n < k) results, the precision value will be computed as #(relevant items retrieved) / k. This formula also applies when the size of the ground truth set is less than k.

If a query has an empty ground truth set, zero will be used as precision together with a log warning.

pyspark.mllib.feature module

Python package for feature in MLlib.

class pyspark.mllib.feature.Normalizer(p=2.0)

Bases: pyspark.mllib.feature.VectorTransformer

Note

Experimental

Normalizes samples individually to unit L^p norm

For any 1 <= p < float(‘inf’), normalizes samples using sum(abs(vector) ^p) ^(1/p) as norm.

For p = float(‘inf’), max(abs(vector)) will be used as norm for normalization.

Parameters:p – Normalization in L^p^ space, p = 2 by default.

>>> v = Vectors.dense(range(3))
>>> nor = Normalizer(1)
>>> nor.transform(v)
DenseVector([0.0, 0.3333, 0.6667])

>>> rdd = sc.parallelize([v])
>>> nor.transform(rdd).collect()
[DenseVector([0.0, 0.3333, 0.6667])]

>>> nor2 = Normalizer(float("inf"))
>>> nor2.transform(v)
DenseVector([0.0, 0.5, 1.0])

transform(vector)

Applies unit length normalization on a vector.

Parameters:vector – vector or RDD of vector to be normalized. Returns:normalized vector. If the norm of the input is zero, it will return the input vector.

class pyspark.mllib.feature.StandardScalerModel(java_model)

Bases: pyspark.mllib.feature.JavaVectorTransformer

Note

Experimental

Represents a StandardScaler model that can transform vectors.

setWithMean(withMean)

Setter of the boolean which decides whether it uses mean or not

setWithStd(withStd)

Setter of the boolean which decides whether it uses std or not

transform(vector)

Applies standardization transformation on a vector.

Note: In Python, transform cannot currently be used within

an RDD transformation or action. Call transform directly on the RDD instead.

Parameters:vector – Vector or RDD of Vector to be standardized. Returns:Standardized vector. If the variance of a column is zero, it will return default 0.0 for the column with zero variance.

class pyspark.mllib.feature.StandardScaler(withMean=False, withStd=True)

Bases: object

Note

Experimental

Standardizes features by removing the mean and scaling to unit variance using column summary statistics on the samples in the training set.

Parameters:

• withMean – False by default. Centers the data with mean before scaling. It will build a dense output, so this does not work on sparse input and will raise an exception.
• withStd – True by default. Scales the data to unit standard deviation.

>>> vs = [Vectors.dense([-2.0, 2.3, 0]), Vectors.dense([3.8, 0.0, 1.9])]
>>> dataset = sc.parallelize(vs)
>>> standardizer = StandardScaler(True, True)
>>> model = standardizer.fit(dataset)
>>> result = model.transform(dataset)
>>> for r in result.collect(): r
DenseVector([-0.7071, 0.7071, -0.7071])
DenseVector([0.7071, -0.7071, 0.7071])

fit(dataset)

Computes the mean and variance and stores as a model to be used for later scaling.

Parameters:dataset – The data used to compute the mean and variance to build the transformation model. Returns:a StandardScalarModel

class pyspark.mllib.feature.HashingTF(numFeatures=1048576)

Bases: object

Note

Experimental

Maps a sequence of terms to their term frequencies using the hashing trick.

Note: the terms must be hashable (can not be dict/set/list...).

Parameters:numFeatures – number of features (default: 2^20)

>>> htf = HashingTF(100)
>>> doc = "a a b b c d".split(" ")
>>> htf.transform(doc)
SparseVector(100, {...})

indexOf(term)

Returns the index of the input term.

transform(document)

Transforms the input document (list of terms) to term frequency vectors, or transform the RDD of document to RDD of term frequency vectors.

class pyspark.mllib.feature.IDFModel(java_model)

Bases: pyspark.mllib.feature.JavaVectorTransformer

Represents an IDF model that can transform term frequency vectors.

idf()

Returns the current IDF vector.

transform(x)

Transforms term frequency (TF) vectors to TF-IDF vectors.

If minDocFreq was set for the IDF calculation, the terms which occur in fewer than minDocFreq documents will have an entry of 0.

Note: In Python, transform cannot currently be used within

an RDD transformation or action. Call transform directly on the RDD instead.

Parameters:x – an RDD of term frequency vectors or a term frequency vector Returns:an RDD of TF-IDF vectors or a TF-IDF vector

class pyspark.mllib.feature.IDF(minDocFreq=0)

Bases: object

Note

Experimental

Inverse document frequency (IDF).

The standard formulation is used: idf = log((m + 1) / (d(t) + 1)), where m is the total number of documents and d(t) is the number of documents that contain term t.

This implementation supports filtering out terms which do not appear in a minimum number of documents (controlled by the variable minDocFreq). For terms that are not in at least minDocFreq documents, the IDF is found as 0, resulting in TF-IDFs of 0.

Parameters:minDocFreq – minimum of documents in which a term should appear for filtering

>>> n = 4
>>> freqs = [Vectors.sparse(n, (1, 3), (1.0, 2.0)),
...          Vectors.dense([0.0, 1.0, 2.0, 3.0]),
...          Vectors.sparse(n, [1], [1.0])]
>>> data = sc.parallelize(freqs)
>>> idf = IDF()
>>> model = idf.fit(data)
>>> tfidf = model.transform(data)
>>> for r in tfidf.collect(): r
SparseVector(4, {1: 0.0, 3: 0.5754})
DenseVector([0.0, 0.0, 1.3863, 0.863])
SparseVector(4, {1: 0.0})
>>> model.transform(Vectors.dense([0.0, 1.0, 2.0, 3.0]))
DenseVector([0.0, 0.0, 1.3863, 0.863])
>>> model.transform([0.0, 1.0, 2.0, 3.0])
DenseVector([0.0, 0.0, 1.3863, 0.863])
>>> model.transform(Vectors.sparse(n, (1, 3), (1.0, 2.0)))
SparseVector(4, {1: 0.0, 3: 0.5754})

fit(dataset)

Computes the inverse document frequency.

Parameters:dataset – an RDD of term frequency vectors

class pyspark.mllib.feature.Word2Vec

Bases: object

Word2Vec creates vector representation of words in a text corpus. The algorithm first constructs a vocabulary from the corpus and then learns vector representation of words in the vocabulary. The vector representation can be used as features in natural language processing and machine learning algorithms.

We used skip-gram model in our implementation and hierarchical softmax method to train the model. The variable names in the implementation matches the original C implementation.

For original C implementation, see https://code.google.com/p/word2vec/ For research papers, see Efficient Estimation of Word Representations in Vector Space and Distributed Representations of Words and Phrases and their Compositionality.

>>> sentence = "a b " * 100 + "a c " * 10
>>> localDoc = [sentence, sentence]
>>> doc = sc.parallelize(localDoc).map(lambda line: line.split(" "))
>>> model = Word2Vec().setVectorSize(10).setSeed(42).fit(doc)

>>> syms = model.findSynonyms("a", 2)
>>> [s[0] for s in syms]
[u'b', u'c']
>>> vec = model.transform("a")
>>> syms = model.findSynonyms(vec, 2)
>>> [s[0] for s in syms]
[u'b', u'c']

>>> import os, tempfile
>>> path = tempfile.mkdtemp()
>>> model.save(sc, path)
>>> sameModel = Word2VecModel.load(sc, path)
>>> model.transform("a") == sameModel.transform("a")
True
>>> from shutil import rmtree
>>> try:
...     rmtree(path)
... except OSError:
...     pass

fit(data)

Computes the vector representation of each word in vocabulary.

Parameters:data – training data. RDD of list of string Returns:Word2VecModel instance

setLearningRate(learningRate)

Sets initial learning rate (default: 0.025).

setMinCount(minCount)

Sets minCount, the minimum number of times a token must appear to be included in the word2vec model’s vocabulary (default: 5).

setNumIterations(numIterations)

Sets number of iterations (default: 1), which should be smaller than or equal to number of partitions.

setNumPartitions(numPartitions)

Sets number of partitions (default: 1). Use a small number for accuracy.

setSeed(seed)

Sets random seed.

setVectorSize(vectorSize)

Sets vector size (default: 100).

class pyspark.mllib.feature.Word2VecModel(java_model)

Bases: pyspark.mllib.feature.JavaVectorTransformer, pyspark.mllib.util.JavaSaveable, pyspark.mllib.util.JavaLoader

class for Word2Vec model

findSynonyms(word, num)

Find synonyms of a word

Parameters:

• word – a word or a vector representation of word
• num – number of synonyms to find

Returns:

array of (word, cosineSimilarity)

Note: local use only

getVectors()

Returns a map of words to their vector representations.

classmethod load(sc, path)

transform(word)

Transforms a word to its vector representation

Note: local use only

Parameters:word – a word Returns:vector representation of word(s)

class pyspark.mllib.feature.ChiSqSelector(numTopFeatures)

Bases: object

Note

Experimental

Creates a ChiSquared feature selector.

Parameters:numTopFeatures – number of features that selector will select.

>>> data = [
...     LabeledPoint(0.0, SparseVector(3, {0: 8.0, 1: 7.0})),
...     LabeledPoint(1.0, SparseVector(3, {1: 9.0, 2: 6.0})),
...     LabeledPoint(1.0, [0.0, 9.0, 8.0]),
...     LabeledPoint(2.0, [8.0, 9.0, 5.0])
... ]
>>> model = ChiSqSelector(1).fit(sc.parallelize(data))
>>> model.transform(SparseVector(3, {1: 9.0, 2: 6.0}))
SparseVector(1, {0: 6.0})
>>> model.transform(DenseVector([8.0, 9.0, 5.0]))
DenseVector([5.0])

fit(data)

Returns a ChiSquared feature selector.

Parameters:data – an RDD[LabeledPoint] containing the labeled dataset with categorical features. Real-valued features will be treated as categorical for each distinct value. Apply feature discretizer before using this function.

class pyspark.mllib.feature.ChiSqSelectorModel(java_model)

Bases: pyspark.mllib.feature.JavaVectorTransformer

Note

Experimental

Represents a Chi Squared selector model.

transform(vector)

Applies transformation on a vector.

Parameters:vector – Vector or RDD of Vector to be transformed. Returns:transformed vector.

class pyspark.mllib.feature.ElementwiseProduct(scalingVector)

Bases: pyspark.mllib.feature.VectorTransformer

Note

Experimental

Scales each column of the vector, with the supplied weight vector. i.e the elementwise product.

>>> weight = Vectors.dense([1.0, 2.0, 3.0])
>>> eprod = ElementwiseProduct(weight)
>>> a = Vectors.dense([2.0, 1.0, 3.0])
>>> eprod.transform(a)
DenseVector([2.0, 2.0, 9.0])
>>> b = Vectors.dense([9.0, 3.0, 4.0])
>>> rdd = sc.parallelize([a, b])
>>> eprod.transform(rdd).collect()
[DenseVector([2.0, 2.0, 9.0]), DenseVector([9.0, 6.0, 12.0])]

transform(vector)

Computes the Hadamard product of the vector.

pyspark.mllib.fpm module

class pyspark.mllib.fpm.FPGrowth

Note

Experimental

A Parallel FP-growth algorithm to mine frequent itemsets.

class FreqItemset

Represents an (items, freq) tuple.

classmethod FPGrowth.train(data, minSupport=0.3, numPartitions=-1)

Computes an FP-Growth model that contains frequent itemsets.

Parameters:

• data – The input data set, each element contains a transaction.
• minSupport – The minimal support level (default: 0.3).
• numPartitions – The number of partitions used by parallel FP-growth (default: same as input data).

class pyspark.mllib.fpm.FPGrowthModel(java_model)

Note

Experimental

A FP-Growth model for mining frequent itemsets using the Parallel FP-Growth algorithm.

>>> data = [["a", "b", "c"], ["a", "b", "d", "e"], ["a", "c", "e"], ["a", "c", "f"]]
>>> rdd = sc.parallelize(data, 2)
>>> model = FPGrowth.train(rdd, 0.6, 2)
>>> sorted(model.freqItemsets().collect())
[FreqItemset(items=[u'a'], freq=4), FreqItemset(items=[u'c'], freq=3), ...

freqItemsets()

Returns the frequent itemsets of this model.

pyspark.mllib.linalg module

MLlib utilities for linear algebra. For dense vectors, MLlib uses the NumPy array type, so you can simply pass NumPy arrays around. For sparse vectors, users can construct a SparseVector object from MLlib or pass SciPy scipy.sparse column vectors if SciPy is available in their environment.

class pyspark.mllib.linalg.Vector

Bases: object

toArray()

Convert the vector into an numpy.ndarray

Returns:numpy.ndarray

class pyspark.mllib.linalg.DenseVector(ar)

Bases: pyspark.mllib.linalg.Vector

A dense vector represented by a value array. We use numpy array for storage and arithmetics will be delegated to the underlying numpy array.

>>> v = Vectors.dense([1.0, 2.0])
>>> u = Vectors.dense([3.0, 4.0])
>>> v + u
DenseVector([4.0, 6.0])
>>> 2 - v
DenseVector([1.0, 0.0])
>>> v / 2
DenseVector([0.5, 1.0])
>>> v * u
DenseVector([3.0, 8.0])
>>> u / v
DenseVector([3.0, 2.0])
>>> u % 2
DenseVector([1.0, 0.0])

dot(other)

Compute the dot product of two Vectors. We support (Numpy array, list, SparseVector, or SciPy sparse) and a target NumPy array that is either 1- or 2-dimensional. Equivalent to calling numpy.dot of the two vectors.

>>> dense = DenseVector(array.array('d', [1., 2.]))
>>> dense.dot(dense)
5.0
>>> dense.dot(SparseVector(2, [0, 1], [2., 1.]))
4.0
>>> dense.dot(range(1, 3))
5.0
>>> dense.dot(np.array(range(1, 3)))
5.0
>>> dense.dot([1.,])
Traceback (most recent call last):
    ...
AssertionError: dimension mismatch
>>> dense.dot(np.reshape([1., 2., 3., 4.], (2, 2), order='F'))
array([  5.,  11.])
>>> dense.dot(np.reshape([1., 2., 3.], (3, 1), order='F'))
Traceback (most recent call last):
    ...
AssertionError: dimension mismatch

norm(p)

Calculte the norm of a DenseVector.

>>> a = DenseVector([0, -1, 2, -3])
>>> a.norm(2)
3.7...
>>> a.norm(1)
6.0

numNonzeros()

static parse(s)

Parse string representation back into the DenseVector.

>>> DenseVector.parse(' [ 0.0,1.0,2.0,  3.0]')
DenseVector([0.0, 1.0, 2.0, 3.0])

squared_distance(other)

Squared distance of two Vectors.

>>> dense1 = DenseVector(array.array('d', [1., 2.]))
>>> dense1.squared_distance(dense1)
0.0
>>> dense2 = np.array([2., 1.])
>>> dense1.squared_distance(dense2)
2.0
>>> dense3 = [2., 1.]
>>> dense1.squared_distance(dense3)
2.0
>>> sparse1 = SparseVector(2, [0, 1], [2., 1.])
>>> dense1.squared_distance(sparse1)
2.0
>>> dense1.squared_distance([1.,])
Traceback (most recent call last):
    ...
AssertionError: dimension mismatch
>>> dense1.squared_distance(SparseVector(1, [0,], [1.,]))
Traceback (most recent call last):
    ...
AssertionError: dimension mismatch

toArray()

class pyspark.mllib.linalg.SparseVector(size, *args)

Bases: pyspark.mllib.linalg.Vector

A simple sparse vector class for passing data to MLlib. Users may alternatively pass SciPy’s {scipy.sparse} data types.

dot(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.array('d', [1., 2., 3., 4.]))
22.0
>>> b = SparseVector(4, [2], [1.0])
>>> a.dot(b)
0.0
>>> a.dot(np.array([[1, 1], [2, 2], [3, 3], [4, 4]]))
array([ 22.,  22.])
>>> a.dot([1., 2., 3.])
Traceback (most recent call last):
    ...
AssertionError: dimension mismatch
>>> a.dot(np.array([1., 2.]))
Traceback (most recent call last):
    ...
AssertionError: dimension mismatch
>>> a.dot(DenseVector([1., 2.]))
Traceback (most recent call last):
    ...
AssertionError: dimension mismatch
>>> a.dot(np.zeros((3, 2)))
Traceback (most recent call last):
    ...
AssertionError: dimension mismatch

indices = None

A list of indices corresponding to active entries.

norm(p)

Calculte the norm of a SparseVector.

>>> a = SparseVector(4, [0, 1], [3., -4.])
>>> a.norm(1)
7.0
>>> a.norm(2)
5.0

numNonzeros()

static parse(s)

Parse string representation back into the DenseVector.

>>> SparseVector.parse(' (4, [0,1 ],[ 4.0,5.0] )')
SparseVector(4, {0: 4.0, 1: 5.0})

size = None

Size of the vector.

squared_distance(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.array('d', [1., 2., 3., 4.]))
11.0
>>> a.squared_distance(np.array([1., 2., 3., 4.]))
11.0
>>> b = SparseVector(4, [2], [1.0])
>>> a.squared_distance(b)
26.0
>>> b.squared_distance(a)
26.0
>>> b.squared_distance([1., 2.])
Traceback (most recent call last):
    ...
AssertionError: dimension mismatch
>>> b.squared_distance(SparseVector(3, [1,], [1.0,]))
Traceback (most recent call last):
    ...
AssertionError: dimension mismatch

toArray()

Returns a copy of this SparseVector as a 1-dimensional NumPy array.

values = None

A list of values corresponding to active entries.

class pyspark.mllib.linalg.Vectors

Bases: 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 scipy.sparse column vectors.

static dense(*elements)

Create a dense vector of 64-bit floats from a Python list or numbers.

>>> Vectors.dense([1, 2, 3])
DenseVector([1.0, 2.0, 3.0])
>>> Vectors.dense(1.0, 2.0)
DenseVector([1.0, 2.0])

static norm(vector, p)

Find norm of the given vector.

static parse(s)

Parse a string representation back into the Vector.

>>> Vectors.parse('[2,1,2 ]')
DenseVector([2.0, 1.0, 2.0])
>>> Vectors.parse(' ( 100,  [0],  [2])')
SparseVector(100, {0: 2.0})

static 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).

Parameters:

• size – Size of the vector.
• args – Non-zero entries, as a dictionary, list of tupes, or two sorted lists containing indices and values.

>>> Vectors.sparse(4, {1: 1.0, 3: 5.5})
SparseVector(4, {1: 1.0, 3: 5.5})
>>> Vectors.sparse(4, [(1, 1.0), (3, 5.5)])
SparseVector(4, {1: 1.0, 3: 5.5})
>>> Vectors.sparse(4, [1, 3], [1.0, 5.5])
SparseVector(4, {1: 1.0, 3: 5.5})

static squared_distance(v1, v2)

Squared distance between two vectors. a and b can be of type SparseVector, DenseVector, np.ndarray or array.array.

>>> a = Vectors.sparse(4, [(0, 1), (3, 4)])
>>> b = Vectors.dense([2, 5, 4, 1])
>>> a.squared_distance(b)
51.0

static stringify(vector)

Converts a vector into a string, which can be recognized by Vectors.parse().

>>> Vectors.stringify(Vectors.sparse(2, [1], [1.0]))
'(2,[1],[1.0])'
>>> Vectors.stringify(Vectors.dense([0.0, 1.0]))
'[0.0,1.0]'

static zeros(size)

class pyspark.mllib.linalg.Matrix(numRows, numCols, isTransposed=False)

Bases: object

toArray()

Returns its elements in a NumPy ndarray.

class pyspark.mllib.linalg.DenseMatrix(numRows, numCols, values, isTransposed=False)

Bases: pyspark.mllib.linalg.Matrix

Column-major dense matrix.

toArray()

Return an numpy.ndarray

>>> m = DenseMatrix(2, 2, range(4))
>>> m.toArray()
array([[ 0.,  2.],
       [ 1.,  3.]])

toSparse()

Convert to SparseMatrix

class pyspark.mllib.linalg.SparseMatrix(numRows, numCols, colPtrs, rowIndices, values, isTransposed=False)

Bases: pyspark.mllib.linalg.Matrix

Sparse Matrix stored in CSC format.

toArray()

Return an numpy.ndarray

toDense()

class pyspark.mllib.linalg.Matrices

Bases: object

static dense(numRows, numCols, values)

Create a DenseMatrix

static sparse(numRows, numCols, colPtrs, rowIndices, values)

Create a SparseMatrix

pyspark.mllib.linalg.distributed module

Package for distributed linear algebra.

class pyspark.mllib.linalg.distributed.DistributedMatrix

Bases: object

Note

Experimental

Represents a distributively stored matrix backed by one or more RDDs.

numCols()

Get or compute the number of cols.

numRows()

Get or compute the number of rows.

class pyspark.mllib.linalg.distributed.RowMatrix(rows, numRows=0, numCols=0)

Bases: pyspark.mllib.linalg.distributed.DistributedMatrix

Note

Experimental

Represents a row-oriented distributed Matrix with no meaningful row indices.

Parameters:

• rows – An RDD of vectors.
• numRows – Number of rows in the matrix. A non-positive value means unknown, at which point the number of rows will be determined by the number of records in the rows RDD.
• numCols – Number of columns in the matrix. A non-positive value means unknown, at which point the number of columns will be determined by the size of the first row.

numCols()

Get or compute the number of cols.

>>> rows = sc.parallelize([[1, 2, 3], [4, 5, 6],
...                        [7, 8, 9], [10, 11, 12]])

>>> mat = RowMatrix(rows)
>>> print(mat.numCols())
3

>>> mat = RowMatrix(rows, 7, 6)
>>> print(mat.numCols())
6

numRows()

Get or compute the number of rows.

>>> rows = sc.parallelize([[1, 2, 3], [4, 5, 6],
...                        [7, 8, 9], [10, 11, 12]])

>>> mat = RowMatrix(rows)
>>> print(mat.numRows())
4

>>> mat = RowMatrix(rows, 7, 6)
>>> print(mat.numRows())
7

rows

Rows of the RowMatrix stored as an RDD of vectors.

>>> mat = RowMatrix(sc.parallelize([[1, 2, 3], [4, 5, 6]]))
>>> rows = mat.rows
>>> rows.first()
DenseVector([1.0, 2.0, 3.0])

class pyspark.mllib.linalg.distributed.IndexedRow(index, vector)

Bases: object

Note

Experimental

Represents a row of an IndexedRowMatrix.

Just a wrapper over a (long, vector) tuple.

Parameters:

• index – The index for the given row.
• vector – The row in the matrix at the given index.

class pyspark.mllib.linalg.distributed.IndexedRowMatrix(rows, numRows=0, numCols=0)

Bases: pyspark.mllib.linalg.distributed.DistributedMatrix

Note

Experimental

Represents a row-oriented distributed Matrix with indexed rows.

Parameters:

• rows – An RDD of IndexedRows or (long, vector) tuples.
• numRows – Number of rows in the matrix. A non-positive value means unknown, at which point the number of rows will be determined by the max row index plus one.
• numCols – Number of columns in the matrix. A non-positive value means unknown, at which point the number of columns will be determined by the size of the first row.

numCols()

Get or compute the number of cols.

>>> rows = sc.parallelize([IndexedRow(0, [1, 2, 3]),
...                        IndexedRow(1, [4, 5, 6]),
...                        IndexedRow(2, [7, 8, 9]),
...                        IndexedRow(3, [10, 11, 12])])

>>> mat = IndexedRowMatrix(rows)
>>> print(mat.numCols())
3

>>> mat = IndexedRowMatrix(rows, 7, 6)
>>> print(mat.numCols())
6

numRows()

Get or compute the number of rows.

>>> rows = sc.parallelize([IndexedRow(0, [1, 2, 3]),
...                        IndexedRow(1, [4, 5, 6]),
...                        IndexedRow(2, [7, 8, 9]),
...                        IndexedRow(3, [10, 11, 12])])

>>> mat = IndexedRowMatrix(rows)
>>> print(mat.numRows())
4

>>> mat = IndexedRowMatrix(rows, 7, 6)
>>> print(mat.numRows())
7

rows

Rows of the IndexedRowMatrix stored as an RDD of IndexedRows.

>>> mat = IndexedRowMatrix(sc.parallelize([IndexedRow(0, [1, 2, 3]),
...                                        IndexedRow(1, [4, 5, 6])]))
>>> rows = mat.rows
>>> rows.first()
IndexedRow(0, [1.0,2.0,3.0])

toBlockMatrix(rowsPerBlock=1024, colsPerBlock=1024)

Convert this matrix to a BlockMatrix.

Parameters:

• rowsPerBlock – Number of rows that make up each block. The blocks forming the final rows are not required to have the given number of rows.
• colsPerBlock – Number of columns that make up each block. The blocks forming the final columns are not required to have the given number of columns.

>>> rows = sc.parallelize([IndexedRow(0, [1, 2, 3]),
...                        IndexedRow(6, [4, 5, 6])])
>>> mat = IndexedRowMatrix(rows).toBlockMatrix()

>>> # This IndexedRowMatrix will have 7 effective rows, due to
>>> # the highest row index being 6, and the ensuing
>>> # BlockMatrix will have 7 rows as well.
>>> print(mat.numRows())
7

>>> print(mat.numCols())
3

toCoordinateMatrix()

Convert this matrix to a CoordinateMatrix.

>>> rows = sc.parallelize([IndexedRow(0, [1, 0]),
...                        IndexedRow(6, [0, 5])])
>>> mat = IndexedRowMatrix(rows).toCoordinateMatrix()
>>> mat.entries.take(3)
[MatrixEntry(0, 0, 1.0), MatrixEntry(0, 1, 0.0), MatrixEntry(6, 0, 0.0)]

toRowMatrix()

Convert this matrix to a RowMatrix.

>>> rows = sc.parallelize([IndexedRow(0, [1, 2, 3]),
...                        IndexedRow(6, [4, 5, 6])])
>>> mat = IndexedRowMatrix(rows).toRowMatrix()
>>> mat.rows.collect()
[DenseVector([1.0, 2.0, 3.0]), DenseVector([4.0, 5.0, 6.0])]

class pyspark.mllib.linalg.distributed.MatrixEntry(i, j, value)

Bases: object

Note

Experimental

Represents an entry of a CoordinateMatrix.

Just a wrapper over a (long, long, float) tuple.

Parameters:

• i – The row index of the matrix.
• j – The column index of the matrix.
• value – The (i, j)th entry of the matrix, as a float.

class pyspark.mllib.linalg.distributed.CoordinateMatrix(entries, numRows=0, numCols=0)

Bases: pyspark.mllib.linalg.distributed.DistributedMatrix

Note

Experimental

Represents a matrix in coordinate format.

Parameters:

• entries – An RDD of MatrixEntry inputs or (long, long, float) tuples.
• numRows – Number of rows in the matrix. A non-positive value means unknown, at which point the number of rows will be determined by the max row index plus one.
• numCols – Number of columns in the matrix. A non-positive value means unknown, at which point the number of columns will be determined by the max row index plus one.

entries

Entries of the CoordinateMatrix stored as an RDD of MatrixEntries.

>>> mat = CoordinateMatrix(sc.parallelize([MatrixEntry(0, 0, 1.2),
...                                        MatrixEntry(6, 4, 2.1)]))
>>> entries = mat.entries
>>> entries.first()
MatrixEntry(0, 0, 1.2)

numCols()

Get or compute the number of cols.

>>> entries = sc.parallelize([MatrixEntry(0, 0, 1.2),
...                           MatrixEntry(1, 0, 2),
...                           MatrixEntry(2, 1, 3.7)])

>>> mat = CoordinateMatrix(entries)
>>> print(mat.numCols())
2

>>> mat = CoordinateMatrix(entries, 7, 6)
>>> print(mat.numCols())
6

numRows()

Get or compute the number of rows.

>>> entries = sc.parallelize([MatrixEntry(0, 0, 1.2),
...                           MatrixEntry(1, 0, 2),
...                           MatrixEntry(2, 1, 3.7)])

>>> mat = CoordinateMatrix(entries)
>>> print(mat.numRows())
3

>>> mat = CoordinateMatrix(entries, 7, 6)
>>> print(mat.numRows())
7

toBlockMatrix(rowsPerBlock=1024, colsPerBlock=1024)

Convert this matrix to a BlockMatrix.

Parameters:

• rowsPerBlock – Number of rows that make up each block. The blocks forming the final rows are not required to have the given number of rows.
• colsPerBlock – Number of columns that make up each block. The blocks forming the final columns are not required to have the given number of columns.

>>> entries = sc.parallelize([MatrixEntry(0, 0, 1.2),
...                           MatrixEntry(6, 4, 2.1)])
>>> mat = CoordinateMatrix(entries).toBlockMatrix()

>>> # This CoordinateMatrix will have 7 effective rows, due to
>>> # the highest row index being 6, and the ensuing
>>> # BlockMatrix will have 7 rows as well.
>>> print(mat.numRows())
7

>>> # This CoordinateMatrix will have 5 columns, due to the
>>> # highest column index being 4, and the ensuing
>>> # BlockMatrix will have 5 columns as well.
>>> print(mat.numCols())
5

toIndexedRowMatrix()

Convert this matrix to an IndexedRowMatrix.

>>> entries = sc.parallelize([MatrixEntry(0, 0, 1.2),
...                           MatrixEntry(6, 4, 2.1)])
>>> mat = CoordinateMatrix(entries).toIndexedRowMatrix()

>>> # This CoordinateMatrix will have 7 effective rows, due to
>>> # the highest row index being 6, and the ensuing
>>> # IndexedRowMatrix will have 7 rows as well.
>>> print(mat.numRows())
7

>>> # This CoordinateMatrix will have 5 columns, due to the
>>> # highest column index being 4, and the ensuing
>>> # IndexedRowMatrix will have 5 columns as well.
>>> print(mat.numCols())
5

toRowMatrix()

Convert this matrix to a RowMatrix.

>>> entries = sc.parallelize([MatrixEntry(0, 0, 1.2),
...                           MatrixEntry(6, 4, 2.1)])
>>> mat = CoordinateMatrix(entries).toRowMatrix()

>>> # This CoordinateMatrix will have 7 effective rows, due to
>>> # the highest row index being 6, but the ensuing RowMatrix
>>> # will only have 2 rows since there are only entries on 2
>>> # unique rows.
>>> print(mat.numRows())
2

>>> # This CoordinateMatrix will have 5 columns, due to the
>>> # highest column index being 4, and the ensuing RowMatrix
>>> # will have 5 columns as well.
>>> print(mat.numCols())
5

class pyspark.mllib.linalg.distributed.BlockMatrix(blocks, rowsPerBlock, colsPerBlock, numRows=0, numCols=0)

Bases: pyspark.mllib.linalg.distributed.DistributedMatrix

Note

Experimental

Represents a distributed matrix in blocks of local matrices.

Parameters:

• blocks – An RDD of sub-matrix blocks ((blockRowIndex, blockColIndex), sub-matrix) that form this distributed matrix. If multiple blocks with the same index exist, the results for operations like add and multiply will be unpredictable.
• rowsPerBlock – Number of rows that make up each block. The blocks forming the final rows are not required to have the given number of rows.
• colsPerBlock – Number of columns that make up each block. The blocks forming the final columns are not required to have the given number of columns.
• numRows – Number of rows of this matrix. If the supplied value is less than or equal to zero, the number of rows will be calculated when numRows is invoked.
• numCols – Number of columns of this matrix. If the supplied value is less than or equal to zero, the number of columns will be calculated when numCols is invoked.

blocks

The RDD of sub-matrix blocks ((blockRowIndex, blockColIndex), sub-matrix) that form this distributed matrix.

>>> mat = BlockMatrix(
...     sc.parallelize([((0, 0), Matrices.dense(3, 2, [1, 2, 3, 4, 5, 6])),
...                     ((1, 0), Matrices.dense(3, 2, [7, 8, 9, 10, 11, 12]))]), 3, 2)
>>> blocks = mat.blocks
>>> blocks.first()
((0, 0), DenseMatrix(3, 2, [1.0, 2.0, 3.0, 4.0, 5.0, 6.0], 0))

colsPerBlock

Number of columns that make up each block.

>>> blocks = sc.parallelize([((0, 0), Matrices.dense(3, 2, [1, 2, 3, 4, 5, 6])),
...                          ((1, 0), Matrices.dense(3, 2, [7, 8, 9, 10, 11, 12]))])
>>> mat = BlockMatrix(blocks, 3, 2)
>>> mat.colsPerBlock
2

numColBlocks

Number of columns of blocks in the BlockMatrix.

>>> blocks = sc.parallelize([((0, 0), Matrices.dense(3, 2, [1, 2, 3, 4, 5, 6])),
...                          ((1, 0), Matrices.dense(3, 2, [7, 8, 9, 10, 11, 12]))])
>>> mat = BlockMatrix(blocks, 3, 2)
>>> mat.numColBlocks
1

numCols()

Get or compute the number of cols.

>>> blocks = sc.parallelize([((0, 0), Matrices.dense(3, 2, [1, 2, 3, 4, 5, 6])),
...                          ((1, 0), Matrices.dense(3, 2, [7, 8, 9, 10, 11, 12]))])

>>> mat = BlockMatrix(blocks, 3, 2)
>>> print(mat.numCols())
2

>>> mat = BlockMatrix(blocks, 3, 2, 7, 6)
>>> print(mat.numCols())
6

numRowBlocks

Number of rows of blocks in the BlockMatrix.

>>> blocks = sc.parallelize([((0, 0), Matrices.dense(3, 2, [1, 2, 3, 4, 5, 6])),
...                          ((1, 0), Matrices.dense(3, 2, [7, 8, 9, 10, 11, 12]))])
>>> mat = BlockMatrix(blocks, 3, 2)
>>> mat.numRowBlocks
2

numRows()

Get or compute the number of rows.

>>> blocks = sc.parallelize([((0, 0), Matrices.dense(3, 2, [1, 2, 3, 4, 5, 6])),
...                          ((1, 0), Matrices.dense(3, 2, [7, 8, 9, 10, 11, 12]))])

>>> mat = BlockMatrix(blocks, 3, 2)
>>> print(mat.numRows())
6

>>> mat = BlockMatrix(blocks, 3, 2, 7, 6)
>>> print(mat.numRows())
7

rowsPerBlock

Number of rows that make up each block.

>>> blocks = sc.parallelize([((0, 0), Matrices.dense(3, 2, [1, 2, 3, 4, 5, 6])),
...                          ((1, 0), Matrices.dense(3, 2, [7, 8, 9, 10, 11, 12]))])
>>> mat = BlockMatrix(blocks, 3, 2)
>>> mat.rowsPerBlock
3

toCoordinateMatrix()

Convert this matrix to a CoordinateMatrix.

>>> blocks = sc.parallelize([((0, 0), Matrices.dense(1, 2, [1, 2])),
...                          ((1, 0), Matrices.dense(1, 2, [7, 8]))])
>>> mat = BlockMatrix(blocks, 1, 2).toCoordinateMatrix()
>>> mat.entries.take(3)
[MatrixEntry(0, 0, 1.0), MatrixEntry(0, 1, 2.0), MatrixEntry(1, 0, 7.0)]

toIndexedRowMatrix()

Convert this matrix to an IndexedRowMatrix.

>>> blocks = sc.parallelize([((0, 0), Matrices.dense(3, 2, [1, 2, 3, 4, 5, 6])),
...                          ((1, 0), Matrices.dense(3, 2, [7, 8, 9, 10, 11, 12]))])
>>> mat = BlockMatrix(blocks, 3, 2).toIndexedRowMatrix()

>>> # This BlockMatrix will have 6 effective rows, due to
>>> # having two sub-matrix blocks stacked, each with 3 rows.
>>> # The ensuing IndexedRowMatrix will also have 6 rows.
>>> print(mat.numRows())
6

>>> # This BlockMatrix will have 2 effective columns, due to
>>> # having two sub-matrix blocks stacked, each with 2 columns.
>>> # The ensuing IndexedRowMatrix will also have 2 columns.
>>> print(mat.numCols())
2

toLocalMatrix()

Collect the distributed matrix on the driver as a DenseMatrix.

>>> blocks = sc.parallelize([((0, 0), Matrices.dense(3, 2, [1, 2, 3, 4, 5, 6])),
...                          ((1, 0), Matrices.dense(3, 2, [7, 8, 9, 10, 11, 12]))])
>>> mat = BlockMatrix(blocks, 3, 2).toLocalMatrix()

>>> # This BlockMatrix will have 6 effective rows, due to
>>> # having two sub-matrix blocks stacked, each with 3 rows.
>>> # The ensuing DenseMatrix will also have 6 rows.
>>> print(mat.numRows)
6

>>> # This BlockMatrix will have 2 effective columns, due to
>>> # having two sub-matrix blocks stacked, each with 2
>>> # columns. The ensuing DenseMatrix will also have 2 columns.
>>> print(mat.numCols)
2

pyspark.mllib.random module

Python package for random data generation.

class pyspark.mllib.random.RandomRDDs

Generator methods for creating RDDs comprised of i.i.d samples from some distribution.

static exponentialRDD(sc, mean, size, numPartitions=None, seed=None)

Generates an RDD comprised of i.i.d. samples from the Exponential distribution with the input mean.

Parameters:

• sc – SparkContext used to create the RDD.
• mean – Mean, or 1 / lambda, for the Exponential distribution.
• size – Size of the RDD.
• numPartitions – Number of partitions in the RDD (default: sc.defaultParallelism).
• seed – Random seed (default: a random long integer).

Returns:

RDD of float comprised of i.i.d. samples ~ Exp(mean).

>>> mean = 2.0
>>> x = RandomRDDs.exponentialRDD(sc, mean, 1000, seed=2)
>>> stats = x.stats()
>>> stats.count()
1000
>>> abs(stats.mean() - mean) < 0.5
True
>>> from math import sqrt
>>> abs(stats.stdev() - sqrt(mean)) < 0.5
True

static exponentialVectorRDD(sc, *a, **kw)

Generates an RDD comprised of vectors containing i.i.d. samples drawn from the Exponential distribution with the input mean.

Parameters:

• sc – SparkContext used to create the RDD.
• mean – Mean, or 1 / lambda, for the Exponential distribution.
• numRows – Number of Vectors in the RDD.
• numCols – Number of elements in each Vector.
• numPartitions – Number of partitions in the RDD (default: sc.defaultParallelism)
• seed – Random seed (default: a random long integer).

Returns:

RDD of Vector with vectors containing i.i.d. samples ~ Exp(mean).

>>> import numpy as np
>>> mean = 0.5
>>> rdd = RandomRDDs.exponentialVectorRDD(sc, mean, 100, 100, seed=1)
>>> mat = np.mat(rdd.collect())
>>> mat.shape
(100, 100)
>>> abs(mat.mean() - mean) < 0.5
True
>>> from math import sqrt
>>> abs(mat.std() - sqrt(mean)) < 0.5
True

static gammaRDD(sc, shape, scale, size, numPartitions=None, seed=None)

Generates an RDD comprised of i.i.d. samples from the Gamma distribution with the input shape and scale.

Parameters:

• sc – SparkContext used to create the RDD.
• shape – shape (> 0) parameter for the Gamma distribution
• scale – scale (> 0) parameter for the Gamma distribution
• size – Size of the RDD.
• numPartitions – Number of partitions in the RDD (default: sc.defaultParallelism).
• seed – Random seed (default: a random long integer).

Returns:

RDD of float comprised of i.i.d. samples ~ Gamma(shape, scale).

>>> from math import sqrt
>>> shape = 1.0
>>> scale = 2.0
>>> expMean = shape * scale
>>> expStd = sqrt(shape * scale * scale)
>>> x = RandomRDDs.gammaRDD(sc, shape, scale, 1000, seed=2)
>>> stats = x.stats()
>>> stats.count()
1000
>>> abs(stats.mean() - expMean) < 0.5
True
>>> abs(stats.stdev() - expStd) < 0.5
True

static gammaVectorRDD(sc, *a, **kw)

Generates an RDD comprised of vectors containing i.i.d. samples drawn from the Gamma distribution.

Parameters:

• sc – SparkContext used to create the RDD.
• shape – Shape (> 0) of the Gamma distribution
• scale – Scale (> 0) of the Gamma distribution
• numRows – Number of Vectors in the RDD.
• numCols – Number of elements in each Vector.
• numPartitions – Number of partitions in the RDD (default: sc.defaultParallelism).
• seed – Random seed (default: a random long integer).

Returns:

RDD of Vector with vectors containing i.i.d. samples ~ Gamma(shape, scale).

>>> import numpy as np
>>> from math import sqrt
>>> shape = 1.0
>>> scale = 2.0
>>> expMean = shape * scale
>>> expStd = sqrt(shape * scale * scale)
>>> mat = np.matrix(RandomRDDs.gammaVectorRDD(sc, shape, scale, 100, 100, seed=1).collect())
>>> mat.shape
(100, 100)
>>> abs(mat.mean() - expMean) < 0.1
True
>>> abs(mat.std() - expStd) < 0.1
True

static logNormalRDD(sc, mean, std, size, numPartitions=None, seed=None)

Generates an RDD comprised of i.i.d. samples from the log normal distribution with the input mean and standard distribution.

Parameters:

• sc – SparkContext used to create the RDD.
• mean – mean for the log Normal distribution
• std – std for the log Normal distribution
• size – Size of the RDD.
• numPartitions – Number of partitions in the RDD (default: sc.defaultParallelism).
• seed – Random seed (default: a random long integer).

Returns:

RDD of float comprised of i.i.d. samples ~ log N(mean, std).

>>> from math import sqrt, exp
>>> mean = 0.0
>>> std = 1.0
>>> expMean = exp(mean + 0.5 * std * std)
>>> expStd = sqrt((exp(std * std) - 1.0) * exp(2.0 * mean + std * std))
>>> x = RandomRDDs.logNormalRDD(sc, mean, std, 1000, seed=2)
>>> stats = x.stats()
>>> stats.count()
1000
>>> abs(stats.mean() - expMean) < 0.5
True
>>> from math import sqrt
>>> abs(stats.stdev() - expStd) < 0.5
True

static logNormalVectorRDD(sc, *a, **kw)

Generates an RDD comprised of vectors containing i.i.d. samples drawn from the log normal distribution.

Parameters:

• sc – SparkContext used to create the RDD.
• mean – Mean of the log normal distribution
• std – Standard Deviation of the log normal distribution
• numRows – Number of Vectors in the RDD.
• numCols – Number of elements in each Vector.
• numPartitions – Number of partitions in the RDD (default: sc.defaultParallelism).
• seed – Random seed (default: a random long integer).

Returns:

RDD of Vector with vectors containing i.i.d. samples ~ log N(mean, std).

>>> import numpy as np
>>> from math import sqrt, exp
>>> mean = 0.0
>>> std = 1.0
>>> expMean = exp(mean + 0.5 * std * std)
>>> expStd = sqrt((exp(std * std) - 1.0) * exp(2.0 * mean + std * std))
>>> m = RandomRDDs.logNormalVectorRDD(sc, mean, std, 100, 100, seed=1).collect()
>>> mat = np.matrix(m)
>>> mat.shape
(100, 100)
>>> abs(mat.mean() - expMean) < 0.1
True
>>> abs(mat.std() - expStd) < 0.1
True

static normalRDD(sc, size, numPartitions=None, seed=None)

Generates an RDD comprised of i.i.d. samples from the standard normal distribution.

To transform the distribution in the generated RDD from standard normal to some other normal N(mean, sigma^2), use RandomRDDs.normal(sc, n, p, seed) .map(lambda v: mean + sigma * v)

Parameters:

• sc – SparkContext used to create the RDD.
• size – Size of the RDD.
• numPartitions – Number of partitions in the RDD (default: sc.defaultParallelism).
• seed – Random seed (default: a random long integer).

Returns:

RDD of float comprised of i.i.d. samples ~ N(0.0, 1.0).

>>> x = RandomRDDs.normalRDD(sc, 1000, seed=1)
>>> stats = x.stats()
>>> stats.count()
1000
>>> abs(stats.mean() - 0.0) < 0.1
True
>>> abs(stats.stdev() - 1.0) < 0.1
True

static normalVectorRDD(sc, *a, **kw)

Generates an RDD comprised of vectors containing i.i.d. samples drawn from the standard normal distribution.

Parameters:

• sc – SparkContext used to create the RDD.
• numRows – Number of Vectors in the RDD.
• numCols – Number of elements in each Vector.
• numPartitions – Number of partitions in the RDD (default: sc.defaultParallelism).
• seed – Random seed (default: a random long integer).

Returns:

RDD of Vector with vectors containing i.i.d. samples ~ N(0.0, 1.0).

>>> import numpy as np
>>> mat = np.matrix(RandomRDDs.normalVectorRDD(sc, 100, 100, seed=1).collect())
>>> mat.shape
(100, 100)
>>> abs(mat.mean() - 0.0) < 0.1
True
>>> abs(mat.std() - 1.0) < 0.1
True

static poissonRDD(sc, mean, size, numPartitions=None, seed=None)

Generates an RDD comprised of i.i.d. samples from the Poisson distribution with the input mean.

Parameters:

• sc – SparkContext used to create the RDD.
• mean – Mean, or lambda, for the Poisson distribution.
• size – Size of the RDD.
• numPartitions – Number of partitions in the RDD (default: sc.defaultParallelism).
• seed – Random seed (default: a random long integer).

Returns:

RDD of float comprised of i.i.d. samples ~ Pois(mean).

>>> mean = 100.0
>>> x = RandomRDDs.poissonRDD(sc, mean, 1000, seed=2)
>>> stats = x.stats()
>>> stats.count()
1000
>>> abs(stats.mean() - mean) < 0.5
True
>>> from math import sqrt
>>> abs(stats.stdev() - sqrt(mean)) < 0.5
True

static poissonVectorRDD(sc, *a, **kw)

Generates an RDD comprised of vectors containing i.i.d. samples drawn from the Poisson distribution with the input mean.

Parameters:

• sc – SparkContext used to create the RDD.
• mean – Mean, or lambda, for the Poisson distribution.
• numRows – Number of Vectors in the RDD.
• numCols – Number of elements in each Vector.
• numPartitions – Number of partitions in the RDD (default: sc.defaultParallelism)
• seed – Random seed (default: a random long integer).

Returns:

RDD of Vector with vectors containing i.i.d. samples ~ Pois(mean).

>>> import numpy as np
>>> mean = 100.0
>>> rdd = RandomRDDs.poissonVectorRDD(sc, mean, 100, 100, seed=1)
>>> mat = np.mat(rdd.collect())
>>> mat.shape
(100, 100)
>>> abs(mat.mean() - mean) < 0.5
True
>>> from math import sqrt
>>> abs(mat.std() - sqrt(mean)) < 0.5
True

static uniformRDD(sc, size, numPartitions=None, seed=None)

Generates an RDD comprised of i.i.d. samples from the uniform distribution U(0.0, 1.0).

To transform the distribution in the generated RDD from U(0.0, 1.0) to U(a, b), use RandomRDDs.uniformRDD(sc, n, p, seed) .map(lambda v: a + (b - a) * v)

Parameters:

• sc – SparkContext used to create the RDD.
• size – Size of the RDD.
• numPartitions – Number of partitions in the RDD (default: sc.defaultParallelism).
• seed – Random seed (default: a random long integer).

Returns:

RDD of float comprised of i.i.d. samples ~ U(0.0, 1.0).

>>> x = RandomRDDs.uniformRDD(sc, 100).collect()
>>> len(x)
100
>>> max(x) <= 1.0 and min(x) >= 0.0
True
>>> RandomRDDs.uniformRDD(sc, 100, 4).getNumPartitions()
4
>>> parts = RandomRDDs.uniformRDD(sc, 100, seed=4).getNumPartitions()
>>> parts == sc.defaultParallelism
True

static uniformVectorRDD(sc, *a, **kw)

Generates an RDD comprised of vectors containing i.i.d. samples drawn from the uniform distribution U(0.0, 1.0).

Parameters:

• sc – SparkContext used to create the RDD.
• numRows – Number of Vectors in the RDD.
• numCols – Number of elements in each Vector.
• numPartitions – Number of partitions in the RDD.
• seed – Seed for the RNG that generates the seed for the generator in each partition.

Returns:

RDD of Vector with vectors containing i.i.d samples ~ U(0.0, 1.0).

>>> import numpy as np
>>> mat = np.matrix(RandomRDDs.uniformVectorRDD(sc, 10, 10).collect())
>>> mat.shape
(10, 10)
>>> mat.max() <= 1.0 and mat.min() >= 0.0
True
>>> RandomRDDs.uniformVectorRDD(sc, 10, 10, 4).getNumPartitions()
4

pyspark.mllib.recommendation module

class pyspark.mllib.recommendation.MatrixFactorizationModel(java_model)

A matrix factorisation model trained by regularized alternating least-squares.

>>> r1 = (1, 1, 1.0)
>>> r2 = (1, 2, 2.0)
>>> r3 = (2, 1, 2.0)
>>> ratings = sc.parallelize([r1, r2, r3])
>>> model = ALS.trainImplicit(ratings, 1, seed=10)
>>> model.predict(2, 2)
0.4...

>>> testset = sc.parallelize([(1, 2), (1, 1)])
>>> model = ALS.train(ratings, 2, seed=0)
>>> model.predictAll(testset).collect()
[Rating(user=1, product=1, rating=1.0...), Rating(user=1, product=2, rating=1.9...)]

>>> model = ALS.train(ratings, 4, seed=10)
>>> model.userFeatures().collect()
[(1, array('d', [...])), (2, array('d', [...]))]

>>> model.recommendUsers(1, 2)
[Rating(user=2, product=1, rating=1.9...), Rating(user=1, product=1, rating=1.0...)]
>>> model.recommendProducts(1, 2)
[Rating(user=1, product=2, rating=1.9...), Rating(user=1, product=1, rating=1.0...)]
>>> model.rank
4

>>> first_user = model.userFeatures().take(1)[0]
>>> latents = first_user[1]
>>> len(latents) == 4
True

>>> model.productFeatures().collect()
[(1, array('d', [...])), (2, array('d', [...]))]

>>> first_product = model.productFeatures().take(1)[0]
>>> latents = first_product[1]
>>> len(latents) == 4
True

>>> model = ALS.train(ratings, 1, nonnegative=True, seed=10)
>>> model.predict(2, 2)
3.8...

>>> df = sqlContext.createDataFrame([Rating(1, 1, 1.0), Rating(1, 2, 2.0), Rating(2, 1, 2.0)])
>>> model = ALS.train(df, 1, nonnegative=True, seed=10)
>>> model.predict(2, 2)
3.8...

>>> model = ALS.trainImplicit(ratings, 1, nonnegative=True, seed=10)
>>> model.predict(2, 2)
0.4...

>>> import os, tempfile
>>> path = tempfile.mkdtemp()
>>> model.save(sc, path)
>>> sameModel = MatrixFactorizationModel.load(sc, path)
>>> sameModel.predict(2, 2)
0.4...
>>> sameModel.predictAll(testset).collect()
[Rating(...
>>> from shutil import rmtree
>>> try:
...     rmtree(path)
... except OSError:
...     pass

classmethod load(sc, path)

predict(user, product)

Predicts rating for the given user and product.

predictAll(user_product)

Returns a list of predicted ratings for input user and product pairs.

productFeatures()

Returns a paired RDD, where the first element is the product and the second is an array of features corresponding to that product.

rank

recommendProducts(user, num)

Recommends the top “num” number of products for a given user and returns a list of Rating objects sorted by the predicted rating in descending order.

recommendUsers(product, num)

Recommends the top “num” number of users for a given product and returns a list of Rating objects sorted by the predicted rating in descending order.

userFeatures()

Returns a paired RDD, where the first element is the user and the second is an array of features corresponding to that user.

class pyspark.mllib.recommendation.ALS

classmethod train(ratings, rank, iterations=5, lambda_=0.01, blocks=-1, nonnegative=False, seed=None)

classmethod trainImplicit(ratings, rank, iterations=5, lambda_=0.01, blocks=-1, alpha=0.01, nonnegative=False, seed=None)

class pyspark.mllib.recommendation.Rating

Represents a (user, product, rating) tuple.

>>> r = Rating(1, 2, 5.0)
>>> (r.user, r.product, r.rating)
(1, 2, 5.0)
>>> (r[0], r[1], r[2])
(1, 2, 5.0)

pyspark.mllib.regression module

class pyspark.mllib.regression.LabeledPoint(label, features)

Class that represents the features and labels of a data point.

Parameters:

• label – Label for this data point.
• features – Vector of features for this point (NumPy array, list, pyspark.mllib.linalg.SparseVector, or scipy.sparse column matrix)

Note: ‘label’ and ‘features’ are accessible as class attributes.

class pyspark.mllib.regression.LinearModel(weights, intercept)

A linear model that has a vector of coefficients and an intercept.

Parameters:

• weights – Weights computed for every feature.
• intercept – Intercept computed for this model.

intercept

weights

class pyspark.mllib.regression.LinearRegressionModel(weights, intercept)

A linear regression model derived from a least-squares fit.

>>> from pyspark.mllib.regression import LabeledPoint
>>> data = [
...     LabeledPoint(0.0, [0.0]),
...     LabeledPoint(1.0, [1.0]),
...     LabeledPoint(3.0, [2.0]),
...     LabeledPoint(2.0, [3.0])
... ]
>>> lrm = LinearRegressionWithSGD.train(sc.parallelize(data), iterations=10,
...     initialWeights=np.array([1.0]))
>>> abs(lrm.predict(np.array([0.0])) - 0) < 0.5
True
>>> abs(lrm.predict(np.array([1.0])) - 1) < 0.5
True
>>> abs(lrm.predict(SparseVector(1, {0: 1.0})) - 1) < 0.5
True
>>> abs(lrm.predict(sc.parallelize([[1.0]])).collect()[0] - 1) < 0.5
True
>>> import os, tempfile
>>> path = tempfile.mkdtemp()
>>> lrm.save(sc, path)
>>> sameModel = LinearRegressionModel.load(sc, path)
>>> abs(sameModel.predict(np.array([0.0])) - 0) < 0.5
True
>>> abs(sameModel.predict(np.array([1.0])) - 1) < 0.5
True
>>> abs(sameModel.predict(SparseVector(1, {0: 1.0})) - 1) < 0.5
True
>>> from shutil import rmtree
>>> try:
...     rmtree(path)
... except:
...     pass
>>> data = [
...     LabeledPoint(0.0, SparseVector(1, {0: 0.0})),
...     LabeledPoint(1.0, SparseVector(1, {0: 1.0})),
...     LabeledPoint(3.0, SparseVector(1, {0: 2.0})),
...     LabeledPoint(2.0, SparseVector(1, {0: 3.0}))
... ]
>>> lrm = LinearRegressionWithSGD.train(sc.parallelize(data), iterations=10,
...     initialWeights=array([1.0]))
>>> abs(lrm.predict(array([0.0])) - 0) < 0.5
True
>>> abs(lrm.predict(SparseVector(1, {0: 1.0})) - 1) < 0.5
True
>>> lrm = LinearRegressionWithSGD.train(sc.parallelize(data), iterations=10, step=1.0,
...    miniBatchFraction=1.0, initialWeights=array([1.0]), regParam=0.1, regType="l2",
...    intercept=True, validateData=True)
>>> abs(lrm.predict(array([0.0])) - 0) < 0.5
True
>>> abs(lrm.predict(SparseVector(1, {0: 1.0})) - 1) < 0.5
True

intercept

classmethod load(sc, path)

predict(x)

Predict the value of the dependent variable given a vector or an RDD of vectors containing values for the independent variables.

save(sc, path)

weights

class pyspark.mllib.regression.LinearRegressionWithSGD

classmethod train(data, iterations=100, step=1.0, miniBatchFraction=1.0, initialWeights=None, regParam=0.0, regType=None, intercept=False, validateData=True)

Train a linear regression model using Stochastic Gradient Descent (SGD). This solves the least squares regression formulation

f(weights) = 1/(2n) ||A weights - y||^2,

which is the mean squared error. Here the data matrix has n rows, and the input RDD holds the set of rows of A, each with its corresponding right hand side label y. See also the documentation for the precise formulation.

Parameters:

• data – The training data, an RDD of LabeledPoint.
• iterations – The number of iterations (default: 100).
• step – The step parameter used in SGD (default: 1.0).
• miniBatchFraction – Fraction of data to be used for each SGD iteration (default: 1.0).
• initialWeights – The initial weights (default: None).
• regParam – The regularizer parameter (default: 0.0).
• regType –

  The type of regularizer used for training our model.

  Allowed values:

  • “l1” for using L1 regularization (lasso),
  • “l2” for using L2 regularization (ridge),
  • None for no regularization

  (default: None)

• intercept – Boolean parameter which indicates the use or not of the augmented representation for training data (i.e. whether bias features are activated or not, default: False).
• validateData – Boolean parameter which indicates if the algorithm should validate data before training. (default: True)

class pyspark.mllib.regression.RidgeRegressionModel(weights, intercept)

A linear regression model derived from a least-squares fit with an l_2 penalty term.

>>> from pyspark.mllib.regression import LabeledPoint
>>> data = [
...     LabeledPoint(0.0, [0.0]),
...     LabeledPoint(1.0, [1.0]),
...     LabeledPoint(3.0, [2.0]),
...     LabeledPoint(2.0, [3.0])
... ]
>>> lrm = RidgeRegressionWithSGD.train(sc.parallelize(data), iterations=10,
...     initialWeights=array([1.0]))
>>> abs(lrm.predict(np.array([0.0])) - 0) < 0.5
True
>>> abs(lrm.predict(np.array([1.0])) - 1) < 0.5
True
>>> abs(lrm.predict(SparseVector(1, {0: 1.0})) - 1) < 0.5
True
>>> abs(lrm.predict(sc.parallelize([[1.0]])).collect()[0] - 1) < 0.5
True
>>> import os, tempfile
>>> path = tempfile.mkdtemp()
>>> lrm.save(sc, path)
>>> sameModel = RidgeRegressionModel.load(sc, path)
>>> abs(sameModel.predict(np.array([0.0])) - 0) < 0.5
True
>>> abs(sameModel.predict(np.array([1.0])) - 1) < 0.5
True
>>> abs(sameModel.predict(SparseVector(1, {0: 1.0})) - 1) < 0.5
True
>>> from shutil import rmtree
>>> try:
...    rmtree(path)
... except:
...    pass
>>> data = [
...     LabeledPoint(0.0, SparseVector(1, {0: 0.0})),
...     LabeledPoint(1.0, SparseVector(1, {0: 1.0})),
...     LabeledPoint(3.0, SparseVector(1, {0: 2.0})),
...     LabeledPoint(2.0, SparseVector(1, {0: 3.0}))
... ]
>>> lrm = LinearRegressionWithSGD.train(sc.parallelize(data), iterations=10,
...     initialWeights=array([1.0]))
>>> abs(lrm.predict(np.array([0.0])) - 0) < 0.5
True
>>> abs(lrm.predict(SparseVector(1, {0: 1.0})) - 1) < 0.5
True
>>> lrm = RidgeRegressionWithSGD.train(sc.parallelize(data), iterations=10, step=1.0,
...     regParam=0.01, miniBatchFraction=1.0, initialWeights=array([1.0]), intercept=True,
...     validateData=True)
>>> abs(lrm.predict(np.array([0.0])) - 0) < 0.5
True
>>> abs(lrm.predict(SparseVector(1, {0: 1.0})) - 1) < 0.5
True

intercept

classmethod load(sc, path)

predict(x)

Predict the value of the dependent variable given a vector or an RDD of vectors containing values for the independent variables.

save(sc, path)

weights

class pyspark.mllib.regression.RidgeRegressionWithSGD

classmethod train(data, iterations=100, step=1.0, regParam=0.01, miniBatchFraction=1.0, initialWeights=None, intercept=False, validateData=True)

Train a regression model with L2-regularization using Stochastic Gradient Descent. This solves the l2-regularized least squares regression formulation

f(weights) = 1/(2n) ||A weights - y||^2 + regParam/2 ||weights||^2.

Here the data matrix has n rows, and the input RDD holds the set of rows of A, each with its corresponding right hand side label y. See also the documentation for the precise formulation.

Parameters:

• data – The training data, an RDD of LabeledPoint.
• iterations – The number of iterations (default: 100).
• step – The step parameter used in SGD (default: 1.0).
• regParam – The regularizer parameter (default: 0.01).
• miniBatchFraction – Fraction of data to be used for each SGD iteration (default: 1.0).
• initialWeights – The initial weights (default: None).
• intercept – Boolean parameter which indicates the use or not of the augmented representation for training data (i.e. whether bias features are activated or not, default: False).
• validateData – Boolean parameter which indicates if the algorithm should validate data before training. (default: True)

class pyspark.mllib.regression.LassoModel(weights, intercept)

A linear regression model derived from a least-squares fit with an l_1 penalty term.

>>> from pyspark.mllib.regression import LabeledPoint
>>> data = [
...     LabeledPoint(0.0, [0.0]),
...     LabeledPoint(1.0, [1.0]),
...     LabeledPoint(3.0, [2.0]),
...     LabeledPoint(2.0, [3.0])
... ]
>>> lrm = LassoWithSGD.train(sc.parallelize(data), iterations=10, initialWeights=array([1.0]))
>>> abs(lrm.predict(np.array([0.0])) - 0) < 0.5
True
>>> abs(lrm.predict(np.array([1.0])) - 1) < 0.5
True
>>> abs(lrm.predict(SparseVector(1, {0: 1.0})) - 1) < 0.5
True
>>> abs(lrm.predict(sc.parallelize([[1.0]])).collect()[0] - 1) < 0.5
True
>>> import os, tempfile
>>> path = tempfile.mkdtemp()
>>> lrm.save(sc, path)
>>> sameModel = LassoModel.load(sc, path)
>>> abs(sameModel.predict(np.array([0.0])) - 0) < 0.5
True
>>> abs(sameModel.predict(np.array([1.0])) - 1) < 0.5
True
>>> abs(sameModel.predict(SparseVector(1, {0: 1.0})) - 1) < 0.5
True
>>> from shutil import rmtree
>>> try:
...    rmtree(path)
... except:
...    pass
>>> data = [
...     LabeledPoint(0.0, SparseVector(1, {0: 0.0})),
...     LabeledPoint(1.0, SparseVector(1, {0: 1.0})),
...     LabeledPoint(3.0, SparseVector(1, {0: 2.0})),
...     LabeledPoint(2.0, SparseVector(1, {0: 3.0}))
... ]
>>> lrm = LinearRegressionWithSGD.train(sc.parallelize(data), iterations=10,
...     initialWeights=array([1.0]))
>>> abs(lrm.predict(np.array([0.0])) - 0) < 0.5
True
>>> abs(lrm.predict(SparseVector(1, {0: 1.0})) - 1) < 0.5
True
>>> lrm = LassoWithSGD.train(sc.parallelize(data), iterations=10, step=1.0,
...     regParam=0.01, miniBatchFraction=1.0, initialWeights=array([1.0]), intercept=True,
...     validateData=True)
>>> abs(lrm.predict(np.array([0.0])) - 0) < 0.5
True
>>> abs(lrm.predict(SparseVector(1, {0: 1.0})) - 1) < 0.5
True

intercept

classmethod load(sc, path)

predict(x)

Predict the value of the dependent variable given a vector or an RDD of vectors containing values for the independent variables.

save(sc, path)

weights

class pyspark.mllib.regression.LassoWithSGD

classmethod train(data, iterations=100, step=1.0, regParam=0.01, miniBatchFraction=1.0, initialWeights=None, intercept=False, validateData=True)

Train a regression model with L1-regularization using Stochastic Gradient Descent. This solves the l1-regularized least squares regression formulation

f(weights) = 1/(2n) ||A weights - y||^2 + regParam ||weights||_1.

Here the data matrix has n rows, and the input RDD holds the set of rows of A, each with its corresponding right hand side label y. See also the documentation for the precise formulation.

Parameters:

• data – The training data, an RDD of LabeledPoint.
• iterations – The number of iterations (default: 100).
• step – The step parameter used in SGD (default: 1.0).
• regParam – The regularizer parameter (default: 0.01).
• miniBatchFraction – Fraction of data to be used for each SGD iteration (default: 1.0).
• initialWeights – The initial weights (default: None).
• intercept – Boolean parameter which indicates the use or not of the augmented representation for training data (i.e. whether bias features are activated or not, default: False).
• validateData – Boolean parameter which indicates if the algorithm should validate data before training. (default: True)

class pyspark.mllib.regression.IsotonicRegressionModel(boundaries, predictions, isotonic)

Regression model for isotonic regression.

Parameters:

• boundaries – Array of boundaries for which predictions are known. Boundaries must be sorted in increasing order.
• predictions – Array of predictions associated to the boundaries at the same index. Results of isotonic regression and therefore monotone.
• isotonic – indicates whether this is isotonic or antitonic.

>>> data = [(1, 0, 1), (2, 1, 1), (3, 2, 1), (1, 3, 1), (6, 4, 1), (17, 5, 1), (16, 6, 1)]
>>> irm = IsotonicRegression.train(sc.parallelize(data))
>>> irm.predict(3)
2.0
>>> irm.predict(5)
16.5
>>> irm.predict(sc.parallelize([3, 5])).collect()
[2.0, 16.5]
>>> import os, tempfile
>>> path = tempfile.mkdtemp()
>>> irm.save(sc, path)
>>> sameModel = IsotonicRegressionModel.load(sc, path)
>>> sameModel.predict(3)
2.0
>>> sameModel.predict(5)
16.5
>>> from shutil import rmtree
>>> try:
...     rmtree(path)
... except OSError:
...     pass

classmethod load(sc, path)

predict(x)

Predict labels for provided features. Using a piecewise linear function. 1) If x exactly matches a boundary then associated prediction is returned. In case there are multiple predictions with the same boundary then one of them is returned. Which one is undefined (same as java.util.Arrays.binarySearch). 2) If x is lower or higher than all boundaries then first or last prediction is returned respectively. In case there are multiple predictions with the same boundary then the lowest or highest is returned respectively. 3) If x falls between two values in boundary array then prediction is treated as piecewise linear function and interpolated value is returned. In case there are multiple values with the same boundary then the same rules as in 2) are used.

Parameters:x – Feature or RDD of Features to be labeled.

save(sc, path)

class pyspark.mllib.regression.IsotonicRegression

classmethod train(data, isotonic=True)

Train a isotonic regression model on the given data.

Parameters:

• data – RDD of (label, feature, weight) tuples.
• isotonic – Whether this is isotonic or antitonic.

pyspark.mllib.stat module

Python package for statistical functions in MLlib.

class pyspark.mllib.stat.Statistics

static chiSqTest(observed, expected=None)

Note

Experimental

If observed is Vector, conduct Pearson’s chi-squared goodness of fit test of the observed data against the expected distribution, or againt the uniform distribution (by default), with each category having an expected frequency of 1 / len(observed). (Note: observed cannot contain negative values)

If observed is matrix, conduct Pearson’s independence test on the input contingency matrix, which cannot contain negative entries or columns or rows that sum up to 0.

If observed is an RDD of LabeledPoint, conduct Pearson’s independence test for every feature against the label across the input RDD. For each feature, the (feature, label) pairs are converted into a contingency matrix for which the chi-squared statistic is computed. All label and feature values must be categorical.

Parameters:

• observed – it could be a vector containing the observed categorical counts/relative frequencies, or the contingency matrix (containing either counts or relative frequencies), or an RDD of LabeledPoint containing the labeled dataset with categorical features. Real-valued features will be treated as categorical for each distinct value.
• expected – Vector containing the expected categorical counts/relative frequencies. expected is rescaled if the expected sum differs from the observed sum.

Returns:

ChiSquaredTest object containing the test statistic, degrees of freedom, p-value, the method used, and the null hypothesis.

>>> from pyspark.mllib.linalg import Vectors, Matrices
>>> observed = Vectors.dense([4, 6, 5])
>>> pearson = Statistics.chiSqTest(observed)
>>> print(pearson.statistic)
0.4
>>> pearson.degreesOfFreedom
2
>>> print(round(pearson.pValue, 4))
0.8187
>>> pearson.method
u'pearson'
>>> pearson.nullHypothesis
u'observed follows the same distribution as expected.'

>>> observed = Vectors.dense([21, 38, 43, 80])
>>> expected = Vectors.dense([3, 5, 7, 20])
>>> pearson = Statistics.chiSqTest(observed, expected)
>>> print(round(pearson.pValue, 4))
0.0027

>>> data = [40.0, 24.0, 29.0, 56.0, 32.0, 42.0, 31.0, 10.0, 0.0, 30.0, 15.0, 12.0]
>>> chi = Statistics.chiSqTest(Matrices.dense(3, 4, data))
>>> print(round(chi.statistic, 4))
21.9958

>>> data = [LabeledPoint(0.0, Vectors.dense([0.5, 10.0])),
...         LabeledPoint(0.0, Vectors.dense([1.5, 20.0])),
...         LabeledPoint(1.0, Vectors.dense([1.5, 30.0])),
...         LabeledPoint(0.0, Vectors.dense([3.5, 30.0])),
...         LabeledPoint(0.0, Vectors.dense([3.5, 40.0])),
...         LabeledPoint(1.0, Vectors.dense([3.5, 40.0])),]
>>> rdd = sc.parallelize(data, 4)
>>> chi = Statistics.chiSqTest(rdd)
>>> print(chi[0].statistic)
0.75
>>> print(chi[1].statistic)
1.5

static colStats(rdd)

Computes column-wise summary statistics for the input RDD[Vector].

Parameters:rdd – an RDD[Vector] for which column-wise summary statistics are to be computed. Returns:MultivariateStatisticalSummary object containing column-wise summary statistics.

>>> from pyspark.mllib.linalg import Vectors
>>> rdd = sc.parallelize([Vectors.dense([2, 0, 0, -2]),
...                       Vectors.dense([4, 5, 0,  3]),
...                       Vectors.dense([6, 7, 0,  8])])
>>> cStats = Statistics.colStats(rdd)
>>> cStats.mean()
array([ 4.,  4.,  0.,  3.])
>>> cStats.variance()
array([  4.,  13.,   0.,  25.])
>>> cStats.count()
3
>>> cStats.numNonzeros()
array([ 3.,  2.,  0.,  3.])
>>> cStats.max()
array([ 6.,  7.,  0.,  8.])
>>> cStats.min()
array([ 2.,  0.,  0., -2.])

static corr(x, y=None, method=None)

Compute the correlation (matrix) for the input RDD(s) using the specified method. Methods currently supported: pearson (default), spearman.

If a single RDD of Vectors is passed in, a correlation matrix comparing the columns in the input RDD is returned. Use method= to specify the method to be used for single RDD inout. If two RDDs of floats are passed in, a single float is returned.

Parameters:

• x – an RDD of vector for which the correlation matrix is to be computed, or an RDD of float of the same cardinality as y when y is specified.
• y – an RDD of float of the same cardinality as x.
• method – String specifying the method to use for computing correlation. Supported: pearson (default), spearman

Returns:

Correlation matrix comparing columns in x.

>>> x = sc.parallelize([1.0, 0.0, -2.0], 2)
>>> y = sc.parallelize([4.0, 5.0, 3.0], 2)
>>> zeros = sc.parallelize([0.0, 0.0, 0.0], 2)
>>> abs(Statistics.corr(x, y) - 0.6546537) < 1e-7
True
>>> Statistics.corr(x, y) == Statistics.corr(x, y, "pearson")
True
>>> Statistics.corr(x, y, "spearman")
0.5
>>> from math import isnan
>>> isnan(Statistics.corr(x, zeros))
True
>>> from pyspark.mllib.linalg import Vectors
>>> rdd = sc.parallelize([Vectors.dense([1, 0, 0, -2]), Vectors.dense([4, 5, 0, 3]),
...                       Vectors.dense([6, 7, 0,  8]), Vectors.dense([9, 0, 0, 1])])
>>> pearsonCorr = Statistics.corr(rdd)
>>> print(str(pearsonCorr).replace('nan', 'NaN'))
[[ 1.          0.05564149         NaN  0.40047142]
 [ 0.05564149  1.                 NaN  0.91359586]
 [        NaN         NaN  1.                 NaN]
 [ 0.40047142  0.91359586         NaN  1.        ]]
>>> spearmanCorr = Statistics.corr(rdd, method="spearman")
>>> print(str(spearmanCorr).replace('nan', 'NaN'))
[[ 1.          0.10540926         NaN  0.4       ]
 [ 0.10540926  1.                 NaN  0.9486833 ]
 [        NaN         NaN  1.                 NaN]
 [ 0.4         0.9486833          NaN  1.        ]]
>>> try:
...     Statistics.corr(rdd, "spearman")
...     print("Method name as second argument without 'method=' shouldn't be allowed.")
... except TypeError:
...     pass

static kolmogorovSmirnovTest(data, distName='norm', *params)

Note

Experimental

Performs the Kolmogorov-Smirnov (KS) test for data sampled from a continuous distribution. It tests the null hypothesis that the data is generated from a particular distribution.

The given data is sorted and the Empirical Cumulative Distribution Function (ECDF) is calculated which for a given point is the number of points having a CDF value lesser than it divided by the total number of points.

Since the data is sorted, this is a step function that rises by (1 / length of data) for every ordered point.

The KS statistic gives us the maximum distance between the ECDF and the CDF. Intuitively if this statistic is large, the probabilty that the null hypothesis is true becomes small. For specific details of the implementation, please have a look at the Scala documentation.

Parameters:

• data – RDD, samples from the data
• distName – string, currently only “norm” is supported. (Normal distribution) to calculate the theoretical distribution of the data.
• params – additional values which need to be provided for a certain distribution. If not provided, the default values are used.

Returns:

KolmogorovSmirnovTestResult object containing the test statistic, degrees of freedom, p-value, the method used, and the null hypothesis.

>>> kstest = Statistics.kolmogorovSmirnovTest
>>> data = sc.parallelize([-1.0, 0.0, 1.0])
>>> ksmodel = kstest(data, "norm")
>>> print(round(ksmodel.pValue, 3))
1.0
>>> print(round(ksmodel.statistic, 3))
0.175
>>> ksmodel.nullHypothesis
u'Sample follows theoretical distribution'

>>> data = sc.parallelize([2.0, 3.0, 4.0])
>>> ksmodel = kstest(data, "norm", 3.0, 1.0)
>>> print(round(ksmodel.pValue, 3))
1.0
>>> print(round(ksmodel.statistic, 3))
0.175

class pyspark.mllib.stat.MultivariateStatisticalSummary(java_model)

Trait for multivariate statistical summary of a data matrix.

count()

max()

mean()

min()

normL1()

normL2()

numNonzeros()

variance()

class pyspark.mllib.stat.ChiSqTestResult(java_model)

Contains test results for the chi-squared hypothesis test.

method

Name of the test method

class pyspark.mllib.stat.MultivariateGaussian

Represents a (mu, sigma) tuple

>>> m = MultivariateGaussian(Vectors.dense([11,12]),DenseMatrix(2, 2, (1.0, 3.0, 5.0, 2.0)))
>>> (m.mu, m.sigma.toArray())
(DenseVector([11.0, 12.0]), array([[ 1., 5.],[ 3., 2.]]))
>>> (m[0], m[1])
(DenseVector([11.0, 12.0]), array([[ 1., 5.],[ 3., 2.]]))

class pyspark.mllib.stat.KernelDensity

Note

Experimental

Estimate probability density at required points given a RDD of samples from the population.

>>> kd = KernelDensity()
>>> sample = sc.parallelize([0.0, 1.0])
>>> kd.setSample(sample)
>>> kd.estimate([0.0, 1.0])
array([ 0.12938758,  0.12938758])

estimate(points)

Estimate the probability density at points

setBandwidth(bandwidth)

Set bandwidth of each sample. Defaults to 1.0

setSample(sample)

Set sample points from the population. Should be a RDD

pyspark.mllib.tree module

class pyspark.mllib.tree.DecisionTreeModel(java_model)

Note

Experimental

A decision tree model for classification or regression.

call(name, *a)

Call method of java_model

depth()

classmethod load(sc, path)

numNodes()

predict(x)

Predict the label of one or more examples.

Note: In Python, predict cannot currently be used within an RDD

transformation or action. Call predict directly on the RDD instead.

Parameters:x – Data point (feature vector), or an RDD of data points (feature vectors).

save(sc, path)

Save this model to the given path.

This saves:

• human-readable (JSON) model metadata to path/metadata/
• Parquet formatted data to path/data/

The model may be loaded using py:meth:Loader.load.

Parameters:

• sc – Spark context used to save model data.
• path – Path specifying the directory in which to save this model. If the directory already exists, this method throws an exception.

toDebugString()

full model.

class pyspark.mllib.tree.DecisionTree

Note

Experimental

Learning algorithm for a decision tree model for classification or regression.

classmethod trainClassifier(data, numClasses, categoricalFeaturesInfo, impurity='gini', maxDepth=5, maxBins=32, minInstancesPerNode=1, minInfoGain=0.0)

Train a DecisionTreeModel for classification.

Parameters:

• data – Training data: RDD of LabeledPoint. Labels are integers {0,1,...,numClasses}.
• numClasses – Number of classes for classification.
• categoricalFeaturesInfo – Map from categorical feature index to number of categories. Any feature not in this map is treated as continuous.
• impurity – Supported values: “entropy” or “gini”
• maxDepth – Max depth of tree. E.g., depth 0 means 1 leaf node. Depth 1 means 1 internal node + 2 leaf nodes.
• maxBins – Number of bins used for finding splits at each node.
• minInstancesPerNode – Min number of instances required at child nodes to create the parent split
• minInfoGain – Min info gain required to create a split

Returns:

DecisionTreeModel

Example usage:

>>> from numpy import array
>>> from pyspark.mllib.regression import LabeledPoint
>>> from pyspark.mllib.tree import DecisionTree
>>>
>>> data = [
...     LabeledPoint(0.0, [0.0]),
...     LabeledPoint(1.0, [1.0]),
...     LabeledPoint(1.0, [2.0]),
...     LabeledPoint(1.0, [3.0])
... ]
>>> model = DecisionTree.trainClassifier(sc.parallelize(data), 2, {})
>>> print(model)
DecisionTreeModel classifier of depth 1 with 3 nodes

>>> print(model.toDebugString())
DecisionTreeModel classifier of depth 1 with 3 nodes
  If (feature 0 <= 0.0)
   Predict: 0.0
  Else (feature 0 > 0.0)
   Predict: 1.0

>>> model.predict(array([1.0]))
1.0
>>> model.predict(array([0.0]))
0.0
>>> rdd = sc.parallelize([[1.0], [0.0]])
>>> model.predict(rdd).collect()
[1.0, 0.0]

classmethod trainRegressor(data, categoricalFeaturesInfo, impurity='variance', maxDepth=5, maxBins=32, minInstancesPerNode=1, minInfoGain=0.0)

Train a DecisionTreeModel for regression.

Parameters:

• data – Training data: RDD of LabeledPoint. Labels are real numbers.
• categoricalFeaturesInfo – Map from categorical feature index to number of categories. Any feature not in this map is treated as continuous.
• impurity – Supported values: “variance”
• maxDepth – Max depth of tree. E.g., depth 0 means 1 leaf node. Depth 1 means 1 internal node + 2 leaf nodes.
• maxBins – Number of bins used for finding splits at each node.
• minInstancesPerNode – Min number of instances required at child nodes to create the parent split
• minInfoGain – Min info gain required to create a split

Returns:

DecisionTreeModel

Example usage:

>>> from pyspark.mllib.regression import LabeledPoint
>>> from pyspark.mllib.tree import DecisionTree
>>> from pyspark.mllib.linalg import SparseVector
>>>
>>> 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}))
... ]
>>>
>>> model = DecisionTree.trainRegressor(sc.parallelize(sparse_data), {})
>>> model.predict(SparseVector(2, {1: 1.0}))
1.0
>>> model.predict(SparseVector(2, {1: 0.0}))
0.0
>>> rdd = sc.parallelize([[0.0, 1.0], [0.0, 0.0]])
>>> model.predict(rdd).collect()
[1.0, 0.0]

class pyspark.mllib.tree.RandomForestModel(java_model)

Note

Experimental

Represents a random forest model.

call(name, *a)

Call method of java_model

classmethod load(sc, path)

numTrees()

Get number of trees in ensemble.

predict(x)

Predict values for a single data point or an RDD of points using the model trained.

Note: In Python, predict cannot currently be used within an RDD

transformation or action. Call predict directly on the RDD instead.

save(sc, path)

Save this model to the given path.

This saves:

• human-readable (JSON) model metadata to path/metadata/
• Parquet formatted data to path/data/

The model may be loaded using py:meth:Loader.load.

Parameters:

• sc – Spark context used to save model data.
• path – Path specifying the directory in which to save this model. If the directory already exists, this method throws an exception.

toDebugString()

Full model

totalNumNodes()

Get total number of nodes, summed over all trees in the ensemble.

class pyspark.mllib.tree.RandomForest

Note

Experimental

Learning algorithm for a random forest model for classification or regression.

supportedFeatureSubsetStrategies = ('auto', 'all', 'sqrt', 'log2', 'onethird')

classmethod trainClassifier(data, numClasses, categoricalFeaturesInfo, numTrees, featureSubsetStrategy='auto', impurity='gini', maxDepth=4, maxBins=32, seed=None)

Method to train a decision tree model for binary or multiclass classification.

Parameters:

• data – Training dataset: RDD of LabeledPoint. Labels should take values {0, 1, ..., numClasses-1}.
• numClasses – number of classes for classification.
• categoricalFeaturesInfo – Map storing arity of categorical features. E.g., an entry (n -> k) indicates that feature n is categorical with k categories indexed from 0: {0, 1, ..., k-1}.
• numTrees – Number of trees in the random forest.
• featureSubsetStrategy – Number of features to consider for splits at each node. Supported: “auto” (default), “all”, “sqrt”, “log2”, “onethird”. If “auto” is set, this parameter is set based on numTrees: if numTrees == 1, set to “all”; if numTrees > 1 (forest) set to “sqrt”.
• impurity – Criterion used for information gain calculation. Supported values: “gini” (recommended) or “entropy”.
• maxDepth – Maximum depth of the tree. E.g., depth 0 means 1 leaf node; depth 1 means 1 internal node + 2 leaf nodes. (default: 4)
• maxBins – maximum number of bins used for splitting features (default: 32)
• seed – Random seed for bootstrapping and choosing feature subsets.

Returns:

RandomForestModel that can be used for prediction

Example usage:

>>> from pyspark.mllib.regression import LabeledPoint
>>> from pyspark.mllib.tree import RandomForest
>>>
>>> data = [
...     LabeledPoint(0.0, [0.0]),
...     LabeledPoint(0.0, [1.0]),
...     LabeledPoint(1.0, [2.0]),
...     LabeledPoint(1.0, [3.0])
... ]
>>> model = RandomForest.trainClassifier(sc.parallelize(data), 2, {}, 3, seed=42)
>>> model.numTrees()
3
>>> model.totalNumNodes()
7
>>> print(model)
TreeEnsembleModel classifier with 3 trees

>>> print(model.toDebugString())
TreeEnsembleModel classifier with 3 trees

  Tree 0:
    Predict: 1.0
  Tree 1:
    If (feature 0 <= 1.0)
     Predict: 0.0
    Else (feature 0 > 1.0)
     Predict: 1.0
  Tree 2:
    If (feature 0 <= 1.0)
     Predict: 0.0
    Else (feature 0 > 1.0)
     Predict: 1.0

>>> model.predict([2.0])
1.0
>>> model.predict([0.0])
0.0
>>> rdd = sc.parallelize([[3.0], [1.0]])
>>> model.predict(rdd).collect()
[1.0, 0.0]

classmethod trainRegressor(data, categoricalFeaturesInfo, numTrees, featureSubsetStrategy='auto', impurity='variance', maxDepth=4, maxBins=32, seed=None)

Method to train a decision tree model for regression.

Parameters:

• data – Training dataset: RDD of LabeledPoint. Labels are real numbers.
• categoricalFeaturesInfo – Map storing arity of categorical features. E.g., an entry (n -> k) indicates that feature n is categorical with k categories indexed from 0: {0, 1, ..., k-1}.
• numTrees – Number of trees in the random forest.
• featureSubsetStrategy – Number of features to consider for splits at each node. Supported: “auto” (default), “all”, “sqrt”, “log2”, “onethird”. If “auto” is set, this parameter is set based on numTrees: if numTrees == 1, set to “all”; if numTrees > 1 (forest) set to “onethird” for regression.
• impurity – Criterion used for information gain calculation. Supported values: “variance”.
• maxDepth – Maximum depth of the tree. E.g., depth 0 means 1 leaf node; depth 1 means 1 internal node + 2 leaf nodes. (default: 4)
• maxBins – maximum number of bins used for splitting features (default: 32)
• seed – Random seed for bootstrapping and choosing feature subsets.

Returns:

RandomForestModel that can be used for prediction

Example usage:

>>> from pyspark.mllib.regression import LabeledPoint
>>> from pyspark.mllib.tree import RandomForest
>>> from pyspark.mllib.linalg import SparseVector
>>>
>>> sparse_data = [
...     LabeledPoint(0.0, SparseVector(2, {0: 1.0})),
...     LabeledPoint(1.0, SparseVector(2, {1: 1.0})),
...     LabeledPoint(0.0, SparseVector(2, {0: 1.0})),
...     LabeledPoint(1.0, SparseVector(2, {1: 2.0}))
... ]
>>>
>>> model = RandomForest.trainRegressor(sc.parallelize(sparse_data), {}, 2, seed=42)
>>> model.numTrees()
2
>>> model.totalNumNodes()
4
>>> model.predict(SparseVector(2, {1: 1.0}))
1.0
>>> model.predict(SparseVector(2, {0: 1.0}))
0.5
>>> rdd = sc.parallelize([[0.0, 1.0], [1.0, 0.0]])
>>> model.predict(rdd).collect()
[1.0, 0.5]

class pyspark.mllib.tree.GradientBoostedTreesModel(java_model)

Note

Experimental

Represents a gradient-boosted tree model.

call(name, *a)

Call method of java_model

classmethod load(sc, path)

numTrees()

Get number of trees in ensemble.

predict(x)

Predict values for a single data point or an RDD of points using the model trained.

Note: In Python, predict cannot currently be used within an RDD

transformation or action. Call predict directly on the RDD instead.

save(sc, path)

Save this model to the given path.

This saves:

• human-readable (JSON) model metadata to path/metadata/
• Parquet formatted data to path/data/

The model may be loaded using py:meth:Loader.load.

Parameters:

• sc – Spark context used to save model data.
• path – Path specifying the directory in which to save this model. If the directory already exists, this method throws an exception.

toDebugString()

Full model

totalNumNodes()

Get total number of nodes, summed over all trees in the ensemble.

class pyspark.mllib.tree.GradientBoostedTrees

Note

Experimental

Learning algorithm for a gradient boosted trees model for classification or regression.

classmethod trainClassifier(data, categoricalFeaturesInfo, loss='logLoss', numIterations=100, learningRate=0.1, maxDepth=3, maxBins=32)

Method to train a gradient-boosted trees model for classification.

Parameters:

• data – Training dataset: RDD of LabeledPoint. Labels should take values {0, 1}.
• categoricalFeaturesInfo – Map storing arity of categorical features. E.g., an entry (n -> k) indicates that feature n is categorical with k categories indexed from 0: {0, 1, ..., k-1}.
• loss – Loss function used for minimization during gradient boosting. Supported: {“logLoss” (default), “leastSquaresError”, “leastAbsoluteError”}.
• numIterations – Number of iterations of boosting. (default: 100)
• learningRate – Learning rate for shrinking the contribution of each estimator. The learning rate should be between in the interval (0, 1]. (default: 0.1)
• maxDepth – Maximum depth of the tree. E.g., depth 0 means 1 leaf node; depth 1 means 1 internal node + 2 leaf nodes. (default: 3)
• maxBins – maximum number of bins used for splitting features (default: 32) DecisionTree requires maxBins >= max categories

Returns:

GradientBoostedTreesModel that can be used for prediction

Example usage:

>>> from pyspark.mllib.regression import LabeledPoint
>>> from pyspark.mllib.tree import GradientBoostedTrees
>>>
>>> data = [
...     LabeledPoint(0.0, [0.0]),
...     LabeledPoint(0.0, [1.0]),
...     LabeledPoint(1.0, [2.0]),
...     LabeledPoint(1.0, [3.0])
... ]
>>>
>>> model = GradientBoostedTrees.trainClassifier(sc.parallelize(data), {}, numIterations=10)
>>> model.numTrees()
10
>>> model.totalNumNodes()
30
>>> print(model)  # it already has newline
TreeEnsembleModel classifier with 10 trees

>>> model.predict([2.0])
1.0
>>> model.predict([0.0])
0.0
>>> rdd = sc.parallelize([[2.0], [0.0]])
>>> model.predict(rdd).collect()
[1.0, 0.0]

classmethod trainRegressor(data, categoricalFeaturesInfo, loss='leastSquaresError', numIterations=100, learningRate=0.1, maxDepth=3, maxBins=32)

Method to train a gradient-boosted trees model for regression.

Parameters:

• data – Training dataset: RDD of LabeledPoint. Labels are real numbers.
• categoricalFeaturesInfo – Map storing arity of categorical features. E.g., an entry (n -> k) indicates that feature n is categorical with k categories indexed from 0: {0, 1, ..., k-1}.
• loss – Loss function used for minimization during gradient boosting. Supported: {“logLoss” (default), “leastSquaresError”, “leastAbsoluteError”}.
• numIterations – Number of iterations of boosting. (default: 100)
• learningRate – Learning rate for shrinking the contribution of each estimator. The learning rate should be between in the interval (0, 1]. (default: 0.1)
• maxBins – maximum number of bins used for splitting features (default: 32) DecisionTree requires maxBins >= max categories
• maxDepth – Maximum depth of the tree. E.g., depth 0 means 1 leaf node; depth 1 means 1 internal node + 2 leaf nodes. (default: 3)

Returns:

GradientBoostedTreesModel that can be used for prediction

Example usage:

>>> from pyspark.mllib.regression import LabeledPoint
>>> from pyspark.mllib.tree import GradientBoostedTrees
>>> from pyspark.mllib.linalg import SparseVector
>>>
>>> sparse_data = [
...     LabeledPoint(0.0, SparseVector(2, {0: 1.0})),
...     LabeledPoint(1.0, SparseVector(2, {1: 1.0})),
...     LabeledPoint(0.0, SparseVector(2, {0: 1.0})),
...     LabeledPoint(1.0, SparseVector(2, {1: 2.0}))
... ]
>>>
>>> data = sc.parallelize(sparse_data)
>>> model = GradientBoostedTrees.trainRegressor(data, {}, numIterations=10)
>>> model.numTrees()
10
>>> model.totalNumNodes()
12
>>> model.predict(SparseVector(2, {1: 1.0}))
1.0
>>> model.predict(SparseVector(2, {0: 1.0}))
0.0
>>> rdd = sc.parallelize([[0.0, 1.0], [1.0, 0.0]])
>>> model.predict(rdd).collect()
[1.0, 0.0]

pyspark.mllib.util module

class pyspark.mllib.util.JavaLoader

Mixin for classes which can load saved models using its Scala implementation.

classmethod load(sc, path)

class pyspark.mllib.util.JavaSaveable

Mixin for models that provide save() through their Scala implementation.

save(sc, path)

Save this model to the given path.

This saves:

• human-readable (JSON) model metadata to path/metadata/
• Parquet formatted data to path/data/

The model may be loaded using py:meth:Loader.load.

Parameters:

• sc – Spark context used to save model data.
• path – Path specifying the directory in which to save this model. If the directory already exists, this method throws an exception.

class pyspark.mllib.util.LinearDataGenerator

Utils for generating linear data

static generateLinearInput(intercept, weights, xMean, xVariance, nPoints, seed, eps)

Param:intercept bias factor, the term c in X’w + c Param:weights feature vector, the term w in X’w + c Param:xMean Point around which the data X is centered. Param:xVariance Variance of the given data Param:nPoints Number of points to be generated Param:seed Random Seed Param:eps Used to scale the noise. If eps is set high, the amount of gaussian noise added is more.

Returns a list of LabeledPoints of length nPoints

static generateLinearRDD(sc, nexamples, nfeatures, eps, nParts=2, intercept=0.0)

Generate a RDD of LabeledPoints.

class pyspark.mllib.util.Loader

Mixin for classes which can load saved models from files.

classmethod load(sc, path)

Load a model from the given path. The model should have been saved using py:meth:Saveable.save.

Parameters:

• sc – Spark context used for loading model files.
• path – Path specifying the directory to which the model was saved.

Returns:

model instance

class pyspark.mllib.util.MLUtils

Helper methods to load, save and pre-process data used in MLlib.

static appendBias(data)

Returns a new vector with 1.0 (bias) appended to the end of the input vector.

static loadLabeledPoints(sc, path, minPartitions=None)

Load labeled points saved using RDD.saveAsTextFile.

Parameters:

• sc – Spark context
• path – file or directory path in any Hadoop-supported file system URI
• minPartitions – min number of partitions

Returns:

labeled data stored as an RDD of LabeledPoint

>>> from tempfile import NamedTemporaryFile
>>> from pyspark.mllib.util import MLUtils
>>> from pyspark.mllib.regression import LabeledPoint
>>> examples = [LabeledPoint(1.1, Vectors.sparse(3, [(0, -1.23), (2, 4.56e-7)])),                         LabeledPoint(0.0, Vectors.dense([1.01, 2.02, 3.03]))]
>>> tempFile = NamedTemporaryFile(delete=True)
>>> tempFile.close()
>>> sc.parallelize(examples, 1).saveAsTextFile(tempFile.name)
>>> MLUtils.loadLabeledPoints(sc, tempFile.name).collect()
[LabeledPoint(1.1, (3,[0,2],[-1.23,4.56e-07])), LabeledPoint(0.0, [1.01,2.02,3.03])]

static loadLibSVMFile(sc, path, numFeatures=-1, minPartitions=None, multiclass=None)

Loads labeled data in the LIBSVM format into an RDD of LabeledPoint. The LIBSVM format is a text-based format used by LIBSVM and LIBLINEAR. Each line represents a labeled sparse feature vector using the following format:

label index1:value1 index2:value2 ...

where the indices are one-based and in ascending order. This method parses each line into a LabeledPoint, where the feature indices are converted to zero-based.

Parameters:

• sc – Spark context
• path – file or directory path in any Hadoop-supported file system URI
• numFeatures – number of features, which will be determined from the input data if a nonpositive value is given. This is useful when the dataset is already split into multiple files and you want to load them separately, because some features may not present in certain files, which leads to inconsistent feature dimensions.
• minPartitions – min number of partitions

Returns:

labeled data stored as an RDD of LabeledPoint

>>> from tempfile import NamedTemporaryFile
>>> from pyspark.mllib.util import MLUtils
>>> from pyspark.mllib.regression import LabeledPoint
>>> tempFile = NamedTemporaryFile(delete=True)
>>> _ = tempFile.write(b"+1 1:1.0 3:2.0 5:3.0\n-1\n-1 2:4.0 4:5.0 6:6.0")
>>> tempFile.flush()
>>> examples = MLUtils.loadLibSVMFile(sc, tempFile.name).collect()
>>> tempFile.close()
>>> examples[0]
LabeledPoint(1.0, (6,[0,2,4],[1.0,2.0,3.0]))
>>> examples[1]
LabeledPoint(-1.0, (6,[],[]))
>>> examples[2]
LabeledPoint(-1.0, (6,[1,3,5],[4.0,5.0,6.0]))

static loadVectors(sc, path)

Loads vectors saved using RDD[Vector].saveAsTextFile with the default number of partitions.

static saveAsLibSVMFile(data, dir)

Save labeled data in LIBSVM format.

Parameters:

• data – an RDD of LabeledPoint to be saved
• dir – directory to save the data

>>> from tempfile import NamedTemporaryFile
>>> from fileinput import input
>>> from pyspark.mllib.regression import LabeledPoint
>>> from glob import glob
>>> from pyspark.mllib.util import MLUtils
>>> examples = [LabeledPoint(1.1, Vectors.sparse(3, [(0, 1.23), (2, 4.56)])),                         LabeledPoint(0.0, Vectors.dense([1.01, 2.02, 3.03]))]
>>> tempFile = NamedTemporaryFile(delete=True)
>>> tempFile.close()
>>> MLUtils.saveAsLibSVMFile(sc.parallelize(examples), tempFile.name)
>>> ''.join(sorted(input(glob(tempFile.name + "/part-0000*"))))
'0.0 1:1.01 2:2.02 3:3.03\n1.1 1:1.23 3:4.56\n'

class pyspark.mllib.util.Saveable

Mixin for models and transformers which may be saved as files.

save(sc, path)

Save this model to the given path.

This saves:

• human-readable (JSON) model metadata to path/metadata/
• Parquet formatted data to path/data/

The model may be loaded using py:meth:Loader.load.

Parameters:

• sc – Spark context used to save model data.
• path – Path specifying the directory in which to save this model. If the directory already exists, this method throws an exception.