Non-negative Matrix Factorization(NMF)

Non-negative Matrix Factorization(NMF) by multiplicative update & Greedy Coordinate Descent(GCD) written in Octave.

Features

You can execute NMF easily on Octave(of course MATLAB).

Using algorithm is multiplicative update rule on Euclid distance(EU), KL-divergence & IS(Itakura-Saito) divergence criterions.

Background of NMF

You should read the following articles.

• NMF: http://www.nature.com/nature/journal/v401/n6755/abs/401788a0.html

• Multiplicative Update:

  • EU,KL http://papers.nips.cc/paper/1861-algorithms-for-non-negative-matrix-factorization.pdf
  • others(beta-divergence) http://ieeexplore.ieee.org/abstract/document/5589233/

• Greedy Coordinate Descent(GCD) : This algorithm supports EU only.

  • https://www.cs.utexas.edu/~cjhsieh/nmf_kdd11.pdf

Usage

./exc_nmf.m

Default Setting

• This default program execute a simulation by real number. If you want to deal with real data, change codes, for example, "parameter_setting.m", "input_data.m" etc., for your use.

• size of random non-negative observation matrix: (18,30)

• numbers of basis vectors: 4

• numbers of iterations: 200

• initial value setting method of update rules: random non-negative values

You can change these default settings on "parameter_setting.m" like the following,

% size of observation matrix
I = 18; J = 30; 
% number of basis vectors
K = 4; 
% iteration numbers
itr = 200; 

Data that you want to use can be also changed on "input_data.m"

Initial value setting can be changed on each functions, "EU.m KL.m & IS.m"

% random initialization
T = abs(randn( I, K ));
V = abs(randn( K, J ));

Plans of additional features

• other algorithms

  • GCD( on EU )
  • HALS( on EU )
  • sBCD( on KL & IS )
  • CCD ( on KL )

• results visualization(ex. graph)

  • error with regard to time
  • final values of cost functions & relative error of NMF

• speed up

  • mex
  • brush up algorithms

This code is provided without liability and warranty.