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