Github user mengxr commented on a diff in the pull request:
https://github.com/apache/spark/pull/88#discussion_r10450573
--- Diff: mllib/src/main/scala/org/apache/spark/mllib/linalg/SVD.scala ---
@@ -142,17 +155,138 @@ 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)
+ *
+ * All input and output is expected in DenseMatrix format
+ *
+ * @param matrix sparse matrix to factorize
+ * @param k Recover k singular values and vectors
+ * @param computeU gives the option of skipping the U computation
+ * @return Three sparse matrices: U, S, V such that A = USV^T
+ */
+ def denseSVD(matrix: DenseMatrix, k: Int, computeU: Boolean):
DenseMatrixSVD = {
--- End diff --
Since the row indices are irrelevant to the computation, we should provide
users a simpler interface:
~~~
/** Returns (U, \Sigma, V) */
def tallAndSkinnySVD(data: RDD[Array[Double]]): (RDD[Array[Double]],
Array[Double], Array[Array[Double]]) = {
...
}
~~~
It is safe to always return U because it won't trigger a job until it is
used somewhere else.
In this way, the current interface can be implemented as a simple wrapper:
~~~
val svd = tallAndSkinnySVD(matrix.rows.map(row => row.data))
val U = svd.U.zip(matrix.rows.map(row => row.index)).map(...)
return ...
~~~
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