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cs525-sp18-g07
spark
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97dc5278
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97dc5278
authored
11 years ago
by
Reza Zadeh
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@@ -215,17 +215,18 @@ Available algorithms for gradient descent:
# Singular Value Decomposition
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^T
Given an
*m x n*
matrix
*A*
, this will compute matrices
*U, S, V*
such that
*A = U *
S
* V^T*
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^TA = V S^2 V^T,
The decomposition is computed by first computing
*
A^TA = V S^2 V^T
*
,
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
as
*
U = A *
V
* S^-1
*
Only singular vectors associated with singular values
greater or equal to MIN_SVALUE are recovered. If there are k
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