SVD
===========

Type
--------- 

transform

Class
--------- 

fire.nodes.ml.NodeSVD

Fields
--------- 

.. list-table::
      :widths: 10 5 10
      :header-rows: 1

      * - Name
        - Title
        - Description
      * - columnName
        - Column Name
        - 
      * - k
        - k
        - 


Details
-------
Singular value decomposition (SVD) factorizes a matrix into three matrices: U, Σ, and V such that


A=UΣVT,


where


U is an orthonormal matrix, whose columns are called left singular vectors,

Σ is a diagonal matrix with non-negative diagonals in descending order, whose diagonals are called singular values,

V is an orthonormal matrix, whose columns are called right singular vectors


More details are available at: https://spark.apache.org/docs/2.0.0/mllib-dimensionality-reduction.html#singular-value-decomposition-svd


Examples
-------
The below example is available at : https://spark.apache.org/docs/2.0.0/mllib-dimensionality-reduction.html#singular-value-decomposition-svd
+++++++++++++++


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

import org.apache.spark.mllib.linalg.SingularValueDecomposition

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

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

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


val data = Array(

  Vectors.sparse(5, Seq((1, 1.0), (3, 7.0))),

  Vectors.dense(2.0, 0.0, 3.0, 4.0, 5.0),

  Vectors.dense(4.0, 0.0, 0.0, 6.0, 7.0))


val dataRDD = sc.parallelize(data, 2)


val mat: RowMatrix = new RowMatrix(dataRDD)


// Compute the top 5 singular values and corresponding singular vectors.

val svd: SingularValueDecomposition[RowMatrix, Matrix] = mat.computeSVD(5, computeU = true)

val U: RowMatrix = svd.U  // The U factor is a RowMatrix.

val s: Vector = svd.s  // The singular values are stored in a local dense vector.

val V: Matrix = svd.V  // The V factor is a local dense matrix.