Non-negative Matrix Factorisation (NMF): Family of linear algebra
algorithms for identifying the latent structure in data represented
as a non-negative matrix.
Input: matrix A; rank k.
Output: Two k-dimensional factors W and H approximating A
So our Objective function looks like this :
There are several approaches inorder to solve this minimization Problem. I used Multiplicative Update Method
introduced by Lee and Seung in 1999. (This Paper)
As the Multiplicative Update is an iterative method, It is very senstive to initializations of W and H.
NNDSVD Method is a SVD based initialization, introduced by C. Boutsidis and E. Gallopoulos in 2007 (This Paper)