Spark 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 Scala library Breeze.
import breeze.linalg._
val x = DenseVector.zeros[Double](5)
x = DenseVector(0.0, 0.0, 0.0, 0.0, 0.0)
DenseVector(0.0, 0.0, 0.0, 0.0, 0.0)
import org.apache.spark.ml.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)))
dv = [1.0,0.0,3.0] sv1 = (3,[0,2],[1.0,3.0]) sv2 = (3,[0,2],[1.0,3.0])
(3,[0,2],[1.0,3.0])
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)))
pos = (1.0,[1.0,0.0,3.0]) neg = (0.0,(3,[0,2],[1.0,3.0]))
(0.0,(3,[0,2],[1.0,3.0]))
import org.apache.spark.ml.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))
dm = sm =
1.0 2.0 3.0 4.0 5.0 6.0 3 x 2 CSCMatrix (0,0) 9.0 (2,1) 6.0 (1,1) 8.0
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.
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)
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()
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()
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)