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From rezazadeh <...@git.apache.org>
Subject [GitHub] spark pull request: Principal Component Analysis
Date Wed, 19 Mar 2014 04:04:40 GMT
Github user rezazadeh commented on a diff in the pull request:

    https://github.com/apache/spark/pull/88#discussion_r10736539
  
    --- Diff: mllib/src/main/scala/org/apache/spark/mllib/linalg/SVD.scala ---
    @@ -142,17 +155,175 @@ object SVD {
         val vsirdd = sc.makeRDD(Array.tabulate(V.rows, sigma.length)
                     { (i,j) => ((i, j), V.get(i,j) / sigma(j))  }.flatten)
     
    -    // Multiply A by VS^-1
    -    val aCols = data.map(entry => (entry.j, (entry.i, entry.mval)))
    -    val bRows = vsirdd.map(entry => (entry._1._1, (entry._1._2, entry._2)))
    -    val retUdata = aCols.join(bRows).map( {case (key, ( (rowInd, rowVal), (colInd, colVal)))
    -        => ((rowInd, colInd), rowVal*colVal)}).reduceByKey(_ + _)
    -          .map{ case ((row, col), mval) => MatrixEntry(row, col, mval)}
    -    val retU = SparseMatrix(retUdata, m, sigma.length)
    -   
    -    MatrixSVD(retU, retS, retV)  
    +    if (computeU) {
    +      // Multiply A by VS^-1
    +      val aCols = data.map(entry => (entry.j, (entry.i, entry.mval)))
    +      val bRows = vsirdd.map(entry => (entry._1._1, (entry._1._2, entry._2)))
    +      val retUdata = aCols.join(bRows).map {
    +        case (key, ( (rowInd, rowVal), (colInd, colVal)) ) => 
    +          ((rowInd, colInd), rowVal * colVal)
    +      }.reduceByKey(_ + _).map{ case ((row, col), mval) => MatrixEntry(row, col, mval)}
    +      
    +      val retU = SparseMatrix(retUdata, m, sigma.length)
    +      MatrixSVD(retU, retS, retV)  
    +    } else {
    +      MatrixSVD(null, retS, retV)
    +    }
       }
     
    +/**
    + * Singular Value Decomposition for Tall and Skinny matrices.
    + * Given an m x n matrix A, this will compute matrices U, S, V such that
    + * A = U * S * V'
    + * 
    + * There is no restriction on m, but we require n^2 doubles to fit in memory.
    + * Further, n should be less than m.
    + * 
    + * The decomposition is computed by first computing A'A = V S^2 V',
    + * computing svd locally on that (since n x n is small),
    + * from which we recover S and V. 
    + * Then we compute U via easy matrix multiplication
    + * as U =  A * V * S^-1
    + * 
    + * Only the k largest singular values and associated vectors are found.
    + * If there are k such values, then the dimensions of the return will be:
    + *
    + * S is k x k and diagonal, holding the singular values on diagonal
    + * U is m x k and satisfies U'U = eye(k)
    + * V is n x k and satisfies V'V = eye(k)
    + *
    + * @param matrix dense matrix to factorize
    + * @param k Recover k singular values and vectors
    + * @param computeU gives the option of skipping the U computation
    + * @return Three dense matrices: U, S, V such that A = USV^T
    + */
    + def denseSVD(matrix: TallSkinnyDenseMatrix, k: Int,
    +              computeU: Boolean): TallSkinnyMatrixSVD = {
    +    val rows = matrix.rows
    +    val m = matrix.m
    +    val n = matrix.n
    +    val sc = matrix.rows.sparkContext
    +
    +    if (m < n || m <= 0 || n <= 0) {
    +      throw new IllegalArgumentException("Expecting a tall and skinny matrix")
    +    }
    +
    +    if (k < 1 || k > n) {
    +      throw new IllegalArgumentException("Must request up to n singular values")
    +    }
    +
    +    val rowIndices = matrix.rows.map(_.i)
    +
    +    // compute SVD
    +    val (u, sigma, v) = denseSVD(matrix.rows.map(_.data), k)
    +    
    +    // prep u for returning
    +    val retU = TallSkinnyDenseMatrix(u.zip(rowIndices).map{
    +                case (row, i) => MatrixRow(i, row) }, m, k)
    +    
    +    if(computeU) {
    +      TallSkinnyMatrixSVD(retU, sigma, v)
    +    } else {
    +      TallSkinnyMatrixSVD(null, sigma, v)
    +    }
    + }
    +
    +/**
    + * Singular Value Decomposition for Tall and Skinny matrices.
    + * Given an m x n matrix A, this will compute matrices U, S, V such that
    + * A = U * S * V'
    + * 
    + * There is no restriction on m, but we require n^2 doubles to fit in memory.
    + * Further, n should be less than m.
    + * 
    + * The decomposition is computed by first computing A'A = V S^2 V',
    + * computing svd locally on that (since n x n is small),
    + * from which we recover S and V. 
    + * Then we compute U via easy matrix multiplication
    + * as U =  A * V * S^-1
    + * 
    + * Only the k largest singular values and associated vectors are found.
    + * If there are k such values, then the dimensions of the return will be:
    + *
    + * S is k x k and diagonal, holding the singular values on diagonal
    + * U is m x k and satisfies U'U = eye(k)
    + * V is n x k and satisfies V'V = eye(k)
    + *
    + * @param matrix dense matrix to factorize
    + * @param k Recover k singular values and vectors
    + * @return Three matrices: U, S, V such that A = USV^T
    + */
    + def denseSVD(matrix: RDD[Array[Double]], k: Int) : 
    +     (RDD[Array[Double]], Array[Double], Array[Array[Double]])  = {
    +    val n = matrix.first.size
    +
    +    if (k < 1 || k > n) {
    +      throw new IllegalArgumentException("Must request up to n singular values")
    +    }
    +
    +    // Compute A^T A
    +    val fullata = matrix.map{
    +        row => 
    +          val miniata = Array.ofDim[Double](n, n)
    +          for(i <- 0 until n) for(j <- 0 until n) {
    +             miniata(i)(j) += row(i) * row(j)
    +          }
    +        miniata 
    +    }.fold(Array.ofDim[Double](n, n)){
    +      (a, b) =>
    +          for(i <- 0 until n) for(j <- 0 until n) {
    +             a(i)(j) += b(i)(j)
    +          }
    +      a
    +    }
    +
    +    // Construct jblas A^T A locally
    +    val ata = new DoubleMatrix(fullata)
    +
    +    // Since A^T A is small, we can compute its SVD directly
    +    val svd = Singular.sparseSVD(ata)
    +    val V = svd(0)
    +    val sigmas = MatrixFunctions.sqrt(svd(1)).toArray.filter(x => x > 1e-9)
    --- End diff --
    
    Done


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