  Matrix decomposition is ubiquitous and has applications in various fields
like speech processing, data mining and image processing to name a few. Under
matrix decomposition, nonnegative matrix factorization is used to decompose a
nonnegative matrix into a product of two nonnegative matrices which gives some
meaningful interpretation of the data. Thus, nonnegative matrix factorization
has an edge over the other decomposition techniques. In this paper, we propose
two novel iterative algorithms based on Majorization Minimization (MM)-in which
we formulate a novel upper bound and minimize it to get a closed form solution
at every iteration. Since the algorithms are based on MM, it is ensured that
the proposed methods will be monotonic. The proposed algorithms differ in the
updating approach of the two nonnegative matrices. The first
algorithm-Iterative Nonnegative Matrix Factorization (INOM) sequentially
updates the two nonnegative matrices while the second algorithm-Parallel
Iterative Nonnegative Matrix Factorization (PARINOM) parallely updates them. We
also prove that the proposed algorithms converge to the stationary point of the
problem. Simulations were conducted to compare the proposed methods with the
existing ones and was found that the proposed algorithms performs better than
the existing ones in terms of computational speed and convergence.
  KeyWords: Nonnegative matrix factorization, Majorization Minimization, Big
Data, Parallel, Multiplicative Update
