# Data Types - RDD-based API

MLlib supports local vectors and matrices stored on a single machine, as well as distributed matrices backed by one or more RDDs. Local vectors and local matrices are simple data models that serve as public interfaces. The underlying linear algebra operations are provided by Breeze. A training example used in supervised learning is called a “labeled point” in MLlib.

## Local vector

A local vector has integer-typed and 0-based indices and double-typed values, stored on a single machine. MLlib supports two types of local vectors: dense and sparse. A dense vector is backed by a double array representing its entry values, while a sparse vector is backed by two parallel arrays: indices and values. For example, a vector (1.0, 0.0, 3.0) can be represented in dense format as [1.0, 0.0, 3.0] or in sparse format as (3, [0, 2], [1.0, 3.0]), where 3 is the size of the vector.

The base class of local vectors is Vector, and we provide two implementations: DenseVector and SparseVector. We recommend using the factory methods implemented in Vectors to create local vectors.

Refer to the Vector Scala docs and Vectors Scala docs for details on the API.

import org.apache.spark.mllib.linalg.{Vector, Vectors}

// Create a dense vector (1.0, 0.0, 3.0).
val dv: Vector = Vectors.dense(1.0, 0.0, 3.0)
// Create a sparse vector (1.0, 0.0, 3.0) by specifying its indices and values corresponding to nonzero entries.
val sv1: Vector = Vectors.sparse(3, Array(0, 2), Array(1.0, 3.0))
// Create a sparse vector (1.0, 0.0, 3.0) by specifying its nonzero entries.
val sv2: Vector = Vectors.sparse(3, Seq((0, 1.0), (2, 3.0)))

Note: Scala imports scala.collection.immutable.Vector by default, so you have to import org.apache.spark.mllib.linalg.Vector explicitly to use MLlib’s Vector.

The base class of local vectors is Vector, and we provide two implementations: DenseVector and SparseVector. We recommend using the factory methods implemented in Vectors to create local vectors.

Refer to the Vector Java docs and Vectors Java docs for details on the API.

import org.apache.spark.mllib.linalg.Vector;
import org.apache.spark.mllib.linalg.Vectors;

// Create a dense vector (1.0, 0.0, 3.0).
Vector dv = Vectors.dense(1.0, 0.0, 3.0);
// Create a sparse vector (1.0, 0.0, 3.0) by specifying its indices and values corresponding to nonzero entries.
Vector sv = Vectors.sparse(3, new int[] {0, 2}, new double[] {1.0, 3.0});

MLlib recognizes the following types as dense vectors:

and the following as sparse vectors:

We recommend using NumPy arrays over lists for efficiency, and using the factory methods implemented in Vectors to create sparse vectors.

Refer to the Vectors Python docs for more details on the API.

import numpy as np
import scipy.sparse as sps
from pyspark.mllib.linalg import Vectors

# Use a NumPy array as a dense vector.
dv1 = np.array([1.0, 0.0, 3.0])
# Use a Python list as a dense vector.
dv2 = [1.0, 0.0, 3.0]
# Create a SparseVector.
sv1 = Vectors.sparse(3, [0, 2], [1.0, 3.0])
# Use a single-column SciPy csc_matrix as a sparse vector.
sv2 = sps.csc_matrix((np.array([1.0, 3.0]), np.array([0, 2]), np.array([0, 2])), shape=(3, 1))

## Labeled point

A labeled point is a local vector, either dense or sparse, associated with a label/response. In MLlib, labeled points are used in supervised learning algorithms. We use a double to store a label, so we can use labeled points in both regression and classification. For binary classification, a label should be either 0 (negative) or 1 (positive). For multiclass classification, labels should be class indices starting from zero: 0, 1, 2, ....

A labeled point is represented by the case class LabeledPoint.

Refer to the LabeledPoint Scala docs for details on the API.

import org.apache.spark.mllib.linalg.Vectors
import org.apache.spark.mllib.regression.LabeledPoint

// Create a labeled point with a positive label and a dense feature vector.
val pos = LabeledPoint(1.0, Vectors.dense(1.0, 0.0, 3.0))

// Create a labeled point with a negative label and a sparse feature vector.
val neg = LabeledPoint(0.0, Vectors.sparse(3, Array(0, 2), Array(1.0, 3.0)))

A labeled point is represented by LabeledPoint.

Refer to the LabeledPoint Java docs for details on the API.

import org.apache.spark.mllib.linalg.Vectors;
import org.apache.spark.mllib.regression.LabeledPoint;

// Create a labeled point with a positive label and a dense feature vector.
LabeledPoint pos = new LabeledPoint(1.0, Vectors.dense(1.0, 0.0, 3.0));

// Create a labeled point with a negative label and a sparse feature vector.
LabeledPoint neg = new LabeledPoint(0.0, Vectors.sparse(3, new int[] {0, 2}, new double[] {1.0, 3.0}));

A labeled point is represented by LabeledPoint.

Refer to the LabeledPoint Python docs for more details on the API.

from pyspark.mllib.linalg import SparseVector
from pyspark.mllib.regression import LabeledPoint

# Create a labeled point with a positive label and a dense feature vector.
pos = LabeledPoint(1.0, [1.0, 0.0, 3.0])

# Create a labeled point with a negative label and a sparse feature vector.
neg = LabeledPoint(0.0, SparseVector(3, [0, 2], [1.0, 3.0]))

Sparse data

It is very common in practice to have sparse training data. MLlib supports reading training examples stored in LIBSVM format, which is the default format used by LIBSVM and LIBLINEAR. It is a text format in which 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. After loading, the feature indices are converted to zero-based.

MLUtils.loadLibSVMFile reads training examples stored in LIBSVM format.

Refer to the MLUtils Scala docs for details on the API.

import org.apache.spark.mllib.regression.LabeledPoint
import org.apache.spark.mllib.util.MLUtils
import org.apache.spark.rdd.RDD

val examples: RDD[LabeledPoint] = MLUtils.loadLibSVMFile(sc, "data/mllib/sample_libsvm_data.txt")

MLUtils.loadLibSVMFile reads training examples stored in LIBSVM format.

Refer to the MLUtils Java docs for details on the API.

import org.apache.spark.mllib.regression.LabeledPoint;
import org.apache.spark.mllib.util.MLUtils;
import org.apache.spark.api.java.JavaRDD;

JavaRDD<LabeledPoint> examples =
MLUtils.loadLibSVMFile(jsc.sc(), "data/mllib/sample_libsvm_data.txt").toJavaRDD();

MLUtils.loadLibSVMFile reads training examples stored in LIBSVM format.

Refer to the MLUtils Python docs for more details on the API.

from pyspark.mllib.util import MLUtils

examples = MLUtils.loadLibSVMFile(sc, "data/mllib/sample_libsvm_data.txt")

## Local matrix

A local matrix has integer-typed row and column indices and double-typed values, stored on a single machine. MLlib supports dense matrices, whose entry values are stored in a single double array in column-major order, and sparse matrices, whose non-zero entry values are stored in the Compressed Sparse Column (CSC) format in column-major order. For example, the following dense matrix $\begin{pmatrix} 1.0 & 2.0 \\ 3.0 & 4.0 \\ 5.0 & 6.0 \end{pmatrix}$ is stored in a one-dimensional array [1.0, 3.0, 5.0, 2.0, 4.0, 6.0] with the matrix size (3, 2).

The base class of local matrices is Matrix, and we provide two implementations: DenseMatrix, and SparseMatrix. We recommend using the factory methods implemented in Matrices to create local matrices. Remember, local matrices in MLlib are stored in column-major order.

Refer to the Matrix Scala docs and Matrices Scala docs for details on the API.

import org.apache.spark.mllib.linalg.{Matrix, Matrices}

// Create a dense matrix ((1.0, 2.0), (3.0, 4.0), (5.0, 6.0))
val dm: Matrix = Matrices.dense(3, 2, Array(1.0, 3.0, 5.0, 2.0, 4.0, 6.0))

// Create a sparse matrix ((9.0, 0.0), (0.0, 8.0), (0.0, 6.0))
val sm: Matrix = Matrices.sparse(3, 2, Array(0, 1, 3), Array(0, 2, 1), Array(9, 6, 8))

The base class of local matrices is Matrix, and we provide two implementations: DenseMatrix, and SparseMatrix. We recommend using the factory methods implemented in Matrices to create local matrices. Remember, local matrices in MLlib are stored in column-major order.

Refer to the Matrix Java docs and Matrices Java docs for details on the API.

import org.apache.spark.mllib.linalg.Matrix;
import org.apache.spark.mllib.linalg.Matrices;

// Create a dense matrix ((1.0, 2.0), (3.0, 4.0), (5.0, 6.0))
Matrix dm = Matrices.dense(3, 2, new double[] {1.0, 3.0, 5.0, 2.0, 4.0, 6.0});

// Create a sparse matrix ((9.0, 0.0), (0.0, 8.0), (0.0, 6.0))
Matrix sm = Matrices.sparse(3, 2, new int[] {0, 1, 3}, new int[] {0, 2, 1}, new double[] {9, 6, 8});

The base class of local matrices is Matrix, and we provide two implementations: DenseMatrix, and SparseMatrix. We recommend using the factory methods implemented in Matrices to create local matrices. Remember, local matrices in MLlib are stored in column-major order.

Refer to the Matrix Python docs and Matrices Python docs for more details on the API.

from pyspark.mllib.linalg import Matrix, Matrices

# Create a dense matrix ((1.0, 2.0), (3.0, 4.0), (5.0, 6.0))
dm2 = Matrices.dense(3, 2, [1, 2, 3, 4, 5, 6])

# Create a sparse matrix ((9.0, 0.0), (0.0, 8.0), (0.0, 6.0))
sm = Matrices.sparse(3, 2, [0, 1, 3], [0, 2, 1], [9, 6, 8])

## Distributed matrix

A distributed matrix has long-typed row and column indices and double-typed values, stored distributively in one or more RDDs. It is very important to choose the right format to store large and distributed matrices. Converting a distributed matrix to a different format may require a global shuffle, which is quite expensive. Four types of distributed matrices have been implemented so far.

The basic type is called RowMatrix. A RowMatrix is a row-oriented distributed matrix without meaningful row indices, e.g., a collection of feature vectors. It is backed by an RDD of its rows, where each row is a local vector. We assume that the number of columns is not huge for a RowMatrix so that a single local vector can be reasonably communicated to the driver and can also be stored / operated on using a single node. An IndexedRowMatrix is similar to a RowMatrix but with row indices, which can be used for identifying rows and executing joins. A CoordinateMatrix is a distributed matrix stored in coordinate list (COO) format, backed by an RDD of its entries. A BlockMatrix is a distributed matrix backed by an RDD of MatrixBlock which is a tuple of (Int, Int, Matrix).

Note

The underlying RDDs of a distributed matrix must be deterministic, because we cache the matrix size. In general the use of non-deterministic RDDs can lead to errors.

### RowMatrix

A RowMatrix is a row-oriented distributed matrix without meaningful row indices, backed by an RDD of its rows, where each row is a local vector. Since each row is represented by a local vector, the number of columns is limited by the integer range but it should be much smaller in practice.

A RowMatrix can be created from an RDD[Vector] instance. Then we can compute its column summary statistics and decompositions. QR decomposition is of the form A = QR where Q is an orthogonal matrix and R is an upper triangular matrix. For singular value decomposition (SVD) and principal component analysis (PCA), please refer to Dimensionality reduction.

Refer to the RowMatrix Scala docs for details on the API.

import org.apache.spark.mllib.linalg.Vector
import org.apache.spark.mllib.linalg.distributed.RowMatrix

val rows: RDD[Vector] = ... // an RDD of local vectors
// Create a RowMatrix from an RDD[Vector].
val mat: RowMatrix = new RowMatrix(rows)

// Get its size.
val m = mat.numRows()
val n = mat.numCols()

// QR decomposition
val qrResult = mat.tallSkinnyQR(true)

A RowMatrix can be created from a JavaRDD<Vector> instance. Then we can compute its column summary statistics.

Refer to the RowMatrix Java docs for details on the API.

import org.apache.spark.api.java.JavaRDD;
import org.apache.spark.mllib.linalg.Vector;
import org.apache.spark.mllib.linalg.distributed.RowMatrix;

JavaRDD<Vector> rows = ... // a JavaRDD of local vectors
// Create a RowMatrix from an JavaRDD<Vector>.
RowMatrix mat = new RowMatrix(rows.rdd());

// Get its size.
long m = mat.numRows();
long n = mat.numCols();

// QR decomposition
QRDecomposition<RowMatrix, Matrix> result = mat.tallSkinnyQR(true);

A RowMatrix can be created from an RDD of vectors.

Refer to the RowMatrix Python docs for more details on the API.

from pyspark.mllib.linalg.distributed import RowMatrix

# Create an RDD of vectors.
rows = sc.parallelize([[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12]])

# Create a RowMatrix from an RDD of vectors.
mat = RowMatrix(rows)

# Get its size.
m = mat.numRows()  # 4
n = mat.numCols()  # 3

# Get the rows as an RDD of vectors again.
rowsRDD = mat.rows

### IndexedRowMatrix

An IndexedRowMatrix is similar to a RowMatrix but with meaningful row indices. It is backed by an RDD of indexed rows, so that each row is represented by its index (long-typed) and a local vector.

An IndexedRowMatrix can be created from an RDD[IndexedRow] instance, where IndexedRow is a wrapper over (Long, Vector). An IndexedRowMatrix can be converted to a RowMatrix by dropping its row indices.

Refer to the IndexedRowMatrix Scala docs for details on the API.

import org.apache.spark.mllib.linalg.distributed.{IndexedRow, IndexedRowMatrix, RowMatrix}

val rows: RDD[IndexedRow] = ... // an RDD of indexed rows
// Create an IndexedRowMatrix from an RDD[IndexedRow].
val mat: IndexedRowMatrix = new IndexedRowMatrix(rows)

// Get its size.
val m = mat.numRows()
val n = mat.numCols()

// Drop its row indices.
val rowMat: RowMatrix = mat.toRowMatrix()

An IndexedRowMatrix can be created from an JavaRDD<IndexedRow> instance, where IndexedRow is a wrapper over (long, Vector). An IndexedRowMatrix can be converted to a RowMatrix by dropping its row indices.

Refer to the IndexedRowMatrix Java docs for details on the API.

import org.apache.spark.api.java.JavaRDD;
import org.apache.spark.mllib.linalg.distributed.IndexedRow;
import org.apache.spark.mllib.linalg.distributed.IndexedRowMatrix;
import org.apache.spark.mllib.linalg.distributed.RowMatrix;

JavaRDD<IndexedRow> rows = ... // a JavaRDD of indexed rows
// Create an IndexedRowMatrix from a JavaRDD<IndexedRow>.
IndexedRowMatrix mat = new IndexedRowMatrix(rows.rdd());

// Get its size.
long m = mat.numRows();
long n = mat.numCols();

// Drop its row indices.
RowMatrix rowMat = mat.toRowMatrix();

An IndexedRowMatrix can be created from an RDD of IndexedRows, where IndexedRow is a wrapper over (long, vector). An IndexedRowMatrix can be converted to a RowMatrix by dropping its row indices.

Refer to the IndexedRowMatrix Python docs for more details on the API.

from pyspark.mllib.linalg.distributed import IndexedRow, IndexedRowMatrix

# Create an RDD of indexed rows.
#   - This can be done explicitly with the IndexedRow class:
indexedRows = sc.parallelize([IndexedRow(0, [1, 2, 3]),
IndexedRow(1, [4, 5, 6]),
IndexedRow(2, [7, 8, 9]),
IndexedRow(3, [10, 11, 12])])
#   - or by using (long, vector) tuples:
indexedRows = sc.parallelize([(0, [1, 2, 3]), (1, [4, 5, 6]),
(2, [7, 8, 9]), (3, [10, 11, 12])])

# Create an IndexedRowMatrix from an RDD of IndexedRows.
mat = IndexedRowMatrix(indexedRows)

# Get its size.
m = mat.numRows()  # 4
n = mat.numCols()  # 3

# Get the rows as an RDD of IndexedRows.
rowsRDD = mat.rows

# Convert to a RowMatrix by dropping the row indices.
rowMat = mat.toRowMatrix()

### CoordinateMatrix

A CoordinateMatrix is a distributed matrix backed by an RDD of its entries. Each entry is a tuple of (i: Long, j: Long, value: Double), where i is the row index, j is the column index, and value is the entry value. A CoordinateMatrix should be used only when both dimensions of the matrix are huge and the matrix is very sparse.

A CoordinateMatrix can be created from an RDD[MatrixEntry] instance, where MatrixEntry is a wrapper over (Long, Long, Double). A CoordinateMatrix can be converted to an IndexedRowMatrix with sparse rows by calling toIndexedRowMatrix. Other computations for CoordinateMatrix are not currently supported.

Refer to the CoordinateMatrix Scala docs for details on the API.

import org.apache.spark.mllib.linalg.distributed.{CoordinateMatrix, MatrixEntry}

val entries: RDD[MatrixEntry] = ... // an RDD of matrix entries
// Create a CoordinateMatrix from an RDD[MatrixEntry].
val mat: CoordinateMatrix = new CoordinateMatrix(entries)

// Get its size.
val m = mat.numRows()
val n = mat.numCols()

// Convert it to an IndexRowMatrix whose rows are sparse vectors.
val indexedRowMatrix = mat.toIndexedRowMatrix()

A CoordinateMatrix can be created from a JavaRDD<MatrixEntry> instance, where MatrixEntry is a wrapper over (long, long, double). A CoordinateMatrix can be converted to an IndexedRowMatrix with sparse rows by calling toIndexedRowMatrix. Other computations for CoordinateMatrix are not currently supported.

Refer to the CoordinateMatrix Java docs for details on the API.

import org.apache.spark.api.java.JavaRDD;
import org.apache.spark.mllib.linalg.distributed.CoordinateMatrix;
import org.apache.spark.mllib.linalg.distributed.IndexedRowMatrix;
import org.apache.spark.mllib.linalg.distributed.MatrixEntry;

JavaRDD<MatrixEntry> entries = ... // a JavaRDD of matrix entries
// Create a CoordinateMatrix from a JavaRDD<MatrixEntry>.
CoordinateMatrix mat = new CoordinateMatrix(entries.rdd());

// Get its size.
long m = mat.numRows();
long n = mat.numCols();

// Convert it to an IndexRowMatrix whose rows are sparse vectors.
IndexedRowMatrix indexedRowMatrix = mat.toIndexedRowMatrix();

A CoordinateMatrix can be created from an RDD of MatrixEntry entries, where MatrixEntry is a wrapper over (long, long, float). A CoordinateMatrix can be converted to a RowMatrix by calling toRowMatrix, or to an IndexedRowMatrix with sparse rows by calling toIndexedRowMatrix.

Refer to the CoordinateMatrix Python docs for more details on the API.

from pyspark.mllib.linalg.distributed import CoordinateMatrix, MatrixEntry

# Create an RDD of coordinate entries.
#   - This can be done explicitly with the MatrixEntry class:
entries = sc.parallelize([MatrixEntry(0, 0, 1.2), MatrixEntry(1, 0, 2.1), MatrixEntry(6, 1, 3.7)])
#   - or using (long, long, float) tuples:
entries = sc.parallelize([(0, 0, 1.2), (1, 0, 2.1), (2, 1, 3.7)])

# Create an CoordinateMatrix from an RDD of MatrixEntries.
mat = CoordinateMatrix(entries)

# Get its size.
m = mat.numRows()  # 3
n = mat.numCols()  # 2

# Get the entries as an RDD of MatrixEntries.
entriesRDD = mat.entries

# Convert to a RowMatrix.
rowMat = mat.toRowMatrix()

# Convert to an IndexedRowMatrix.
indexedRowMat = mat.toIndexedRowMatrix()

# Convert to a BlockMatrix.
blockMat = mat.toBlockMatrix()

### BlockMatrix

A BlockMatrix is a distributed matrix backed by an RDD of MatrixBlocks, where a MatrixBlock is a tuple of ((Int, Int), Matrix), where the (Int, Int) is the index of the block, and Matrix is the sub-matrix at the given index with size rowsPerBlock x colsPerBlock. BlockMatrix supports methods such as add and multiply with another BlockMatrix. BlockMatrix also has a helper function validate which can be used to check whether the BlockMatrix is set up properly.

A BlockMatrix can be most easily created from an IndexedRowMatrix or CoordinateMatrix by calling toBlockMatrix. toBlockMatrix creates blocks of size 1024 x 1024 by default. Users may change the block size by supplying the values through toBlockMatrix(rowsPerBlock, colsPerBlock).

Refer to the BlockMatrix Scala docs for details on the API.

import org.apache.spark.mllib.linalg.distributed.{BlockMatrix, CoordinateMatrix, MatrixEntry}

val entries: RDD[MatrixEntry] = ... // an RDD of (i, j, v) matrix entries
// Create a CoordinateMatrix from an RDD[MatrixEntry].
val coordMat: CoordinateMatrix = new CoordinateMatrix(entries)
// Transform the CoordinateMatrix to a BlockMatrix
val matA: BlockMatrix = coordMat.toBlockMatrix().cache()

// Validate whether the BlockMatrix is set up properly. Throws an Exception when it is not valid.
// Nothing happens if it is valid.
matA.validate()

// Calculate A^T A.
val ata = matA.transpose.multiply(matA)

A BlockMatrix can be most easily created from an IndexedRowMatrix or CoordinateMatrix by calling toBlockMatrix. toBlockMatrix creates blocks of size 1024 x 1024 by default. Users may change the block size by supplying the values through toBlockMatrix(rowsPerBlock, colsPerBlock).

Refer to the BlockMatrix Java docs for details on the API.

import org.apache.spark.api.java.JavaRDD;
import org.apache.spark.mllib.linalg.distributed.BlockMatrix;
import org.apache.spark.mllib.linalg.distributed.CoordinateMatrix;
import org.apache.spark.mllib.linalg.distributed.IndexedRowMatrix;

JavaRDD<MatrixEntry> entries = ... // a JavaRDD of (i, j, v) Matrix Entries
// Create a CoordinateMatrix from a JavaRDD<MatrixEntry>.
CoordinateMatrix coordMat = new CoordinateMatrix(entries.rdd());
// Transform the CoordinateMatrix to a BlockMatrix
BlockMatrix matA = coordMat.toBlockMatrix().cache();

// Validate whether the BlockMatrix is set up properly. Throws an Exception when it is not valid.
// Nothing happens if it is valid.
matA.validate();

// Calculate A^T A.
BlockMatrix ata = matA.transpose().multiply(matA);

A BlockMatrix can be created from an RDD of sub-matrix blocks, where a sub-matrix block is a ((blockRowIndex, blockColIndex), sub-matrix) tuple.

Refer to the BlockMatrix Python docs for more details on the API.

from pyspark.mllib.linalg import Matrices
from pyspark.mllib.linalg.distributed import BlockMatrix

# Create an RDD of sub-matrix blocks.
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]))])

# Create a BlockMatrix from an RDD of sub-matrix blocks.
mat = BlockMatrix(blocks, 3, 2)

# Get its size.
m = mat.numRows()  # 6
n = mat.numCols()  # 2

# Get the blocks as an RDD of sub-matrix blocks.
blocksRDD = mat.blocks

# Convert to a LocalMatrix.
localMat = mat.toLocalMatrix()

# Convert to an IndexedRowMatrix.
indexedRowMat = mat.toIndexedRowMatrix()

# Convert to a CoordinateMatrix.
coordinateMat = mat.toCoordinateMatrix()