SVD Free Matrix Completion for Recommender System design

This is a demo for SVD free matrix recovery replacing Nuclear norm by Ky Fan norm

This is a demo for SVD free Low rank matrix recovery with application to Recommender System design.We simultaneously recover the user and item biases and interaction component of the rating matrix (assumed to be low rank) from the available rating data set. Usual Algorithms to solve for the same involve nuclear norm minimization which requires computationally intensive singular value decomposition at each iteration.
% In this formulation, nuclear norm is replaced by equivalent Ky-Fan norm
% This eliminates need for complex singular value decomposition at every
% iteration and just requires simple least squares at every step

% We solve
% min_X ||y-A(x+ bu+bi)||_2 + lambda_n||X||_ky-fan + lambda_b (||bu||_2 +||bi||_2)
% equivalent to
% min_X ||y-A(x+ bu+bi)||_2 + lambda_n[trace{(X'*X)_0.5}]+ lambda_b (||bu||_2 +||bi||_2)