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