Non-negative Matrix Factorization

This package implements four ways to compute a non-negative matrix factorization of a 2D non-negative numpy array.

1. Multiplicative update rules (MUR)
2. Alternating non-negative least squares (ANLS)
3. Alternating direction method of multipliers (ADMM)
4. Alternating optimization ADMM (AO-ADMM)

Usage

Compute factorization

Given non-negative data and the number of components you want the dataset to factorize into, you simply create an NMF instance and use the factorize method to compute the factorization.

$ from nmf import NMF
$ nmf = NMF(data, components)
$ nmf.factorize(method='mur', **method_args)

You can directly access the factors nmf.w and nmf.h.

Saving

If you want to save the results to a file, you can use the save_factorization method. The default folder to save is ./results and the default file name is constructed using the parameters used in the factorization.

Methods

MUR

Following the papers:

• Lee, Seung: Learning the parts of objects by non-negative matrix factorization, 1999
• Lee, Seung: Algorithms for non-negative matrix factorization, 2001

Accepts following method parameters:

• distance_type -- STRING: 'eu' for Euclidean, 'kl' for Kullback Leibler
• min_iter -- INT: minimum number of iterations
• max_iter -- INT: maximum number of iterations
• tol1 -- FLOAT: convergence tolerance
• tol2 -- FLOAT: convergence tolerance
• lambda_w -- FLOAT: regularization parameter for w-Update
• lambda_h -- FLOAT: regularization parameter for h-Update
• nndsvd_init -- Tuple(BOOL, STRING): if BOOL = True, use NNDSVD-type STRING
• save_dir -- STRING: folder to which to save

ANLS

Following the papers:

• Kim, Park: Non-negative matrix factorization based on alternating non-negativity constrained least squares and active set method

Accepts following method parameters:

• distance_type -- STRING: 'eu' for Euclidean, 'kl' for Kullback Leibler
• use_fcnnls -- BOOL: if true, use FCNNLS algorithm
• lambda_w -- FLOAT: regularization parameter for w-Update
• lambda_h -- FLOAT: regularization parameter for h-Update
• min_iter -- INT: minimum number of iterations
• max_iter -- INT: maximum number of iterations
• tol1 -- FLOAT: convergence tolerance
• tol2 -- FLOAT: convergence tolerance
• nndsvd_init -- Tuple(BOOL, STRING): if BOOL = True, use NNDSVD-type STRING
• save_dir -- STRING: folder to which to save

ADMM

Following the papers:

• Huang, Sidiropoulos, Liavas: A flexible and efficient algorithmic framework for constrained matrix and tensor factorization, 2015

Accepts following method parameters:

• rho -- FLOAT: ADMM dampening parameter
• distance_type -- STRING: 'eu' for Euclidean, 'kl' for Kullback Leibler
• reg_w -- Tuple(FLOAT, STRING): value und type of w-regularization
• reg_h -- Tuple(FLOAT, STRING): value und type of h-regularization
• min_iter -- INT: minimum number of iterations
• max_iter -- INT: maximum number of iterations
• tol1 -- FLOAT: convergence tolerance
• tol2 -- FLOAT: convergence tolerance
• nndsvd_init -- Tuple(BOOL, STRING): if BOOL = True, use NNDSVD-type STRING
• save_dir -- STRING: folder to which to save

AO-ADMM

Following the papers:

• Huang, Sidiropoulos, Liavas: A flexible and efficient algorithmic framework for constrained matrix and tensor factorization, 2015

Accepts following method parameters:

• distance_type -- STRING: 'eu' for Euclidean, 'kl' for Kullback Leibler
• reg_w -- Tuple(FLOAT, STRING): value und type of w-regularization
• reg_h -- Tuple(FLOAT, STRING): value und type of h-regularization
• min_iter -- INT: minimum number of iterations
• max_iter -- INT: maximum number of iterations
• admm_iter -- INT: maximum number of internal ADMM iterations
• tol1 -- FLOAT: convergence tolerance
• tol2 -- FLOAT: convergence tolerance
• nndsvd_init -- Tuple(BOOL, STRING): if BOOL = True, use NNDSVD-type STRING
• save_dir -- STRING: folder to which to save