This package includes Python implementations (with Numpy and Scipy) of numerical algorithms for computing nonnegative matrix factorization.

Numpy (http://www.numpy.org) and Scipy (http://www.scipy.org) need to be installed. Versions of Numpy and Scipy tested with this code were 1.6.1 and 0.9.0, respectively.

Use setup.py to install this package:

sudo python setup.py install

When A is a dense (numpy.array) or a sparse (scipy.sparse) matrix, the following code returns W and H as factor matrices of A with 10 as the lower rank.

from nonnegfac.nmf import NMF
W, H, info = NMF().run(A, 10)

Try to execute example.py to see simple usage. Function run() executes an NMF algorithm once, and Function run_repeat() executes an NMF algorithm for the specified number of times and returns the best result based on the norm of the error matrix. See nmf.py for the optional arguments and the return information of run() and run_repeat().

There are several algorithms implemented and included as separate classes. A specific algorithm can be used by creating an instance of one of the following classes. By default, NMF() creates an instance of NMF_ANLS_BLOCKPIVOT; another fast algorithm is NMF_HALS. Examples of using each of these algorithms are also included in example.py. See nmf.py and the following references for more information of algorithms.

• NMF_ANLS_BLOCKPIVOT - ANLS with block principal pivoting
• NMF_ANLS_AS_NUMPY - ANLS with scipy.optimize.nnls solver
• NMF_ANLS_AS_GROUP - ANLS with active-set method and column grouping
• NMF_HALS - Hierarchical alternating least squares
• NMF_MU - Multiplicative updating

1. Jingu Kim, Yunlong He, and Haesun Park. Algorithms for Nonnegative Matrix and Tensor Factorizations: A Unified View Based on Block Coordinate Descent Framework. Journal of Global Optimization, 58(2), pp. 285-319, 2014. http://link.springer.com/content/pdf/10.1007%2Fs10898-013-0035-4.pdf

2. Jingu Kim and Haesun Park. Fast Nonnegative Matrix Factorization: An Active-set-like Method And Comparisons. SIAM Journal on Scientific Computing (SISC), 33(6), pp. 3261-3281, 2011. https://sites.google.com/site/jingukim/2011_paper_sisc_nmf.pdf

Please send bug reports, comments, or questions to Jingu Kim. Contributions and extensions with new algorithms are welcome.