How to reconstruct original matrix from svd components with Spark

Question

I want to reconstruct (the approximation of) the original matrix decomposed in SVD. Is there a way to do this without having to convert the V factor local Matrix into a DenseMatrix?

Here is the decomposition based on the documentation (note that the comments are from the doc example)

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.distributed.RowMatrix

val data = Array(
  Vectors.dense(1.0, 0.0, 7.0, 0.0, 0.0),
  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.

To reconstruct the original matrix, I have to compute U * diagonal(s) * transpose(V).

First thing is to convert the singular value vector s into a diagonal matrix S.

import org.apache.spark.mllib.linalg.Matrices
val S = Matrices.diag(s)

But when I try to compute U * diagonal(s) * transpose(V): I get the following error.

val dataApprox = U.multiply(S.multiply(V.transpose))

I get the following error:

error: type mismatch; found: org.apache.spark.mllib.linalg.Matrix required: org.apache.spark.mllib.linalg.DenseMatrix

It works if I convert Matrix V to a DenseMatrix Vdense

import org.apache.spark.mllib.linalg.DenseMatrix
val Vdense = new DenseMatrix(V.numRows, V.numCols,  V.toArray)
val dataApprox = U.multiply(S.multiply(Vdense.transpose))

Is there a way to get the approx of the original matrix dataApprox out of the output of svd without this conversion?

Answer 1

Following Code Worked for Me

//numTopSingularValues=Features used for SVD
val latentFeatureArray=s.toArray

//Making a ListBuffer to Make a DenseMatrix for s
var denseMatListBuffer=ListBuffer.empty[Double]
val zeroListBuffer=ListBuffer.empty[Double]
var addZeroIndex=0
while (addZeroIndex < numTopSingularValues )
  {
    zeroListBuffer+=0.0D
    addZeroIndex+=1
  }
var addDiagElemIndex=0
while(addDiagElemIndex<(numTopSingularValues-1))
  {
    denseMatListBuffer+=latentFeatureArray(addDiagElemIndex)
    denseMatListBuffer.appendAll(zeroListBuffer)
    addDiagElemIndex+=1
  }
denseMatListBuffer+=latentFeatureArray(numTopSingularValues-1)

val sDenseMatrix=new DenseMatrix(numTopSingularValues,numTopSingularValues,denseMatListBuffer.toArray)

val vMultiplyS=V.multiply(sDenseMatrix)

val postMulWithUDenseMat=vMultiplyS.transpose

val dataApprox=U.multiply(postMulWithUDenseMat)