Simple to use NMF/NTF with beta divergence

function [W,H,Q, Vhat] = betaNTF(V,K,varargin)
%------------------------------------------------------------------
% simple beta-NTF implementation
%
% Decomposes a tensor V of dimension FxTxI into a NTF model :
% V(f,t,i) = \sum_k W(f,k)H(t,k)Q(i,k)
%
% by minimizing a beta-divergence as a cost-functions.
% particular cases include :
% * beta = 2 : Euclidean cost function
% * beta = 1 : Kullback-Leibler costfunction
% * beta = 0 : Itakura-Saito cost function
%
% caution:
% The third dimension of V ought to be the smallest. permute
% your data to this purpose if needed.
%
%
% It is possible to weight the cost function by a weight factor P of
% the same size as V, and to fix some of the components for W, H,
% and Q
%
% inputs :
% * V : FxTxI non-negative data to approximate
% * K : number of NTF components
%
% * Optional arguments include :
% - W : FxKw spectral basis
% - H : TxKh temporal activations
% - Q : IxKq loading factors
%
% Note the if Kw,Kh or Kq < K, they are completed with random init.
%
% - P : FxTxI weighting matrix, permits to weight the cost function
% to optimize element-wise
% - fixedW : the first fixedW components of W are fixed (default=0)
% - fixedH : the first fixedH components of H are fixed (default=0)
% - fixedQ : the first fixedQ components of Q are fixed (default=0)
% - nIter : number of iterations, default=100
% - beta : beta divergence considered, default=0 (Itakura-Saito)
% - display : display plots during optimization (default=0)
%
%
% outputs
% * W,H,Q : NTF model parameters
% * Vhat : reconstruction
%
% Example :
% [W,H,Q, Vhat] = betaNTF(V,'W',myW,'fixedW',1)
%
% Reconstruct your data using:
% for j = 1:I, Vhat(:,:,j) = W * diag(Q(j,:)) * H'; end
%--------------------------------------------------------------------------
% Antoine Liutkus, Inria, 2015