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Scientific Programming
/
2015
/
Article
/
Alg 2
Research Article
Parallel Framework for Dimensionality Reduction of Large-Scale Datasets
Algorithm 2
2D-Block Parallel Power Method.
Input
: Matrix
and the required numbed of eigenvalues
.
2D mesh of
processors.
Output
: Set of eigenvalues and eigenvectors of
,
=
and
.
(1)
Let
be a column-wise distributed vector in
.
(2)
for
do
(3)
Initialize
randomly. Processors within the same column use the same seed.
(4)
(5)
while
not converged
do
(6)
Compute
locally.
(7)
if
then
(8)
Perform column-wise all-reduce to obtain
.
(9)
else
(10) Perform row-wise all-reduce to obtain
.
(11)
end if
(12)
(13)
(14)
end while
(15) Compute
as in steps (6)–(11).
(16) Replicate entire vector
and
on each processor.
(17)
(18)
(19) Deflate local block of
:
.
(20)
end for