RowMatrix¶

class pyspark.mllib.linalg.distributed.RowMatrix(rows, numRows=0, numCols=0)[source]¶

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

Parameters

rowspyspark.RDD or pyspark.sql.DataFrame: An RDD or DataFrame of vectors. If a DataFrame is provided, it must have a single vector typed column.
numRowsint, optional: 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.
numColsint, optional: 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.

Methods

`columnSimilarities`([threshold])	Compute similarities between columns of this matrix.
`computeColumnSummaryStatistics`()	Computes column-wise summary statistics.
`computeCovariance`()	Computes the covariance matrix, treating each row as an observation.
`computeGramianMatrix`()	Computes the Gramian matrix A^T A.
`computePrincipalComponents`(k)	Computes the k principal components of the given row matrix
`computeSVD`(k[, computeU, rCond])	Computes the singular value decomposition of the RowMatrix.
`multiply`(matrix)	Multiply this matrix by a local dense matrix on the right.
`numCols`()	Get or compute the number of cols.
`numRows`()	Get or compute the number of rows.
`tallSkinnyQR`([computeQ])	Compute the QR decomposition of this RowMatrix.

Attributes

rows

Rows of the RowMatrix stored as an RDD of vectors.

Methods Documentation

columnSimilarities(threshold=0.0)[source]¶

Compute similarities between columns of this matrix.

The threshold parameter is a trade-off knob between estimate quality and computational cost.

The default threshold setting of 0 guarantees deterministically correct results, but uses the brute-force approach of computing normalized dot products.

Setting the threshold to positive values uses a sampling approach and incurs strictly less computational cost than the brute-force approach. However the similarities computed will be estimates.

The sampling guarantees relative-error correctness for those pairs of columns that have similarity greater than the given similarity threshold.

To describe the guarantee, we set some notation:

Let A be the smallest in magnitude non-zero element of this matrix.
Let B be the largest in magnitude non-zero element of this matrix.
Let L be the maximum number of non-zeros per row.

For example, for {0,1} matrices: A=B=1. Another example, for the Netflix matrix: A=1, B=5

For those column pairs that are above the threshold, the computed similarity is correct to within 20% relative error with probability at least 1 - (0.981)^10/B^

The shuffle size is bounded by the smaller of the following two expressions:

O(n log(n) L / (threshold * A))
O(m L^2^)

The latter is the cost of the brute-force approach, so for non-zero thresholds, the cost is always cheaper than the brute-force approach.

New in version 2.0.0.

Parameters

thresholdfloat, optional: Set to 0 for deterministic guaranteed correctness. Similarities above this threshold are estimated with the cost vs estimate quality trade-off described above.

Returns

CoordinateMatrix: An n x n sparse upper-triangular CoordinateMatrix of cosine similarities between columns of this matrix.

Examples

>>> rows = sc.parallelize([[1, 2], [1, 5]])
>>> mat = RowMatrix(rows)

>>> sims = mat.columnSimilarities()
>>> sims.entries.first().value
0.91914503...

New in version 2.0.0.

computeColumnSummaryStatistics()[source]¶

Computes column-wise summary statistics.

New in version 2.0.0.

Returns

MultivariateStatisticalSummary: object containing column-wise summary statistics.

Examples

>>> rows = sc.parallelize([[1, 2, 3], [4, 5, 6]])
>>> mat = RowMatrix(rows)

>>> colStats = mat.computeColumnSummaryStatistics()
>>> colStats.mean()
array([ 2.5,  3.5,  4.5])

computeCovariance()[source]¶

Computes the covariance matrix, treating each row as an observation.

New in version 2.0.0.

Notes

This cannot be computed on matrices with more than 65535 columns.

Examples

>>> rows = sc.parallelize([[1, 2], [2, 1]])
>>> mat = RowMatrix(rows)

>>> mat.computeCovariance()
DenseMatrix(2, 2, [0.5, -0.5, -0.5, 0.5], 0)

computeGramianMatrix()[source]¶

Computes the Gramian matrix A^T A.

New in version 2.0.0.

Notes

This cannot be computed on matrices with more than 65535 columns.

Examples

>>> rows = sc.parallelize([[1, 2, 3], [4, 5, 6]])
>>> mat = RowMatrix(rows)

>>> mat.computeGramianMatrix()
DenseMatrix(3, 3, [17.0, 22.0, 27.0, 22.0, 29.0, 36.0, 27.0, 36.0, 45.0], 0)

computePrincipalComponents(k)[source]¶

Computes the k principal components of the given row matrix

New in version 2.2.0.

Parameters

kint: Number of principal components to keep.

Returns

pyspark.mllib.linalg.DenseMatrix

Notes

This cannot be computed on matrices with more than 65535 columns.

Examples

>>> rows = sc.parallelize([[1, 2, 3], [2, 4, 5], [3, 6, 1]])
>>> rm = RowMatrix(rows)

>>> # Returns the two principal components of rm
>>> pca = rm.computePrincipalComponents(2)
>>> pca
DenseMatrix(3, 2, [-0.349, -0.6981, 0.6252, -0.2796, -0.5592, -0.7805], 0)

>>> # Transform into new dimensions with the greatest variance.
>>> rm.multiply(pca).rows.collect() 
[DenseVector([0.1305, -3.7394]), DenseVector([-0.3642, -6.6983]),         DenseVector([-4.6102, -4.9745])]

computeSVD(k, computeU=False, rCond=1e-09)[source]¶

Computes the singular value decomposition of the RowMatrix.

The given row matrix A of dimension (m X n) is decomposed into U * s * V’T where

U: (m X k) (left singular vectors) is a RowMatrix whose columns are the eigenvectors of (A X A’)
s: DenseVector consisting of square root of the eigenvalues (singular values) in descending order.
v: (n X k) (right singular vectors) is a Matrix whose columns are the eigenvectors of (A’ X A)

For more specific details on implementation, please refer the Scala documentation.

New in version 2.2.0.

Parameters

kint: Number of leading singular values to keep (0 < k <= n). It might return less than k if there are numerically zero singular values or there are not enough Ritz values converged before the maximum number of Arnoldi update iterations is reached (in case that matrix A is ill-conditioned).
computeUbool, optional: Whether or not to compute U. If set to be True, then U is computed by A * V * s^-1
rCondfloat, optional: Reciprocal condition number. All singular values smaller than rCond * s[0] are treated as zero where s[0] is the largest singular value.

Returns

SingularValueDecomposition

Examples

>>> rows = sc.parallelize([[3, 1, 1], [-1, 3, 1]])
>>> rm = RowMatrix(rows)

>>> svd_model = rm.computeSVD(2, True)
>>> svd_model.U.rows.collect()
[DenseVector([-0.7071, 0.7071]), DenseVector([-0.7071, -0.7071])]
>>> svd_model.s
DenseVector([3.4641, 3.1623])
>>> svd_model.V
DenseMatrix(3, 2, [-0.4082, -0.8165, -0.4082, 0.8944, -0.4472, 0.0], 0)

multiply(matrix)[source]¶

Multiply this matrix by a local dense matrix on the right.

New in version 2.2.0.

Parameters

matrixpyspark.mllib.linalg.Matrix: a local dense matrix whose number of rows must match the number of columns of this matrix

Returns

RowMatrix

Examples

>>> rm = RowMatrix(sc.parallelize([[0, 1], [2, 3]]))
>>> rm.multiply(DenseMatrix(2, 2, [0, 2, 1, 3])).rows.collect()
[DenseVector([2.0, 3.0]), DenseVector([6.0, 11.0])]

numCols()[source]¶

Get or compute the number of cols.

Examples

>>> 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()[source]¶

Get or compute the number of rows.

Examples

>>> 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

tallSkinnyQR(computeQ=False)[source]¶

Compute the QR decomposition of this RowMatrix.

The implementation is designed to optimize the QR decomposition (factorization) for the RowMatrix of a tall and skinny shape [1].

1: Paul G. Constantine, David F. Gleich. “Tall and skinny QR factorizations in MapReduce architectures” https://doi.org/10.1145/1996092.1996103

New in version 2.0.0.

Parameters

computeQbool, optional: whether to computeQ

Returns

pyspark.mllib.linalg.QRDecomposition: QRDecomposition(Q: RowMatrix, R: Matrix), where Q = None if computeQ = false.

Examples

>>> rows = sc.parallelize([[3, -6], [4, -8], [0, 1]])
>>> mat = RowMatrix(rows)
>>> decomp = mat.tallSkinnyQR(True)
>>> Q = decomp.Q
>>> R = decomp.R

>>> # Test with absolute values
>>> absQRows = Q.rows.map(lambda row: abs(row.toArray()).tolist())
>>> absQRows.collect()
[[0.6..., 0.0], [0.8..., 0.0], [0.0, 1.0]]

>>> # Test with absolute values
>>> abs(R.toArray()).tolist()
[[5.0, 10.0], [0.0, 1.0]]

Attributes Documentation

rows¶

Rows of the RowMatrix stored as an RDD of vectors.

Examples

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

MatrixEntry

SingularValueDecomposition