Parallel Nonnegative Matrix Factorization with Manifold Regularization

Algorithm 1

PNMF-M procedure.

Input: data matrix , reduced dimensionality , regularization parameter , tolerance , parallelism

Output: basis matrix , coefficient matrix

(1) Assign , , , and to as described in Figures 1 and 2

(2) Compute from

(3) Send to the other processes

(4) Receive from the other processes to obtain

(5) Merge all index sets to construct

(6) repeat

(7)  Apply (5) to update

(8)  Send to the other processes

(9)  Receive from the other processes to constitute

(10)  Apply (6) to update

(11)  Send to the other processes

(12)  Receive from the other processes to constitute

(13) until convergence

(14) return   and