NMFLibrary 2.0 Release

NMFLibrary 2.0 Release (major update)

It is our pleasure to announce that a new version of NMFLibrary has been released. This is the first major update since the first version in April 2017. The featured updates include:

New NMF models are added.
New NMF solvers are added.
The code structure of solvers is refactored.
A solver/user-defined stopping function is supported.
The statistics display module is refined.
A python demonstration code is added.
Many bugs are fixed.

The software is available on GitHub.

The NMFLibrary is a pure-MATLAB library of a collection of algorithms of non-negative matrix factorization (NMF). Nonnegative matrix factorization (NMF) is a fundamental problem for discovering nonnegative latent factors and/or performing dimensionality reduction. NMF has been successfully applied in diverse technical fields, such as pattern recognition, image/video analysis, text mining, bioinformatics and Web analysis because non-negativity of the obtained factors gives understandable interpretations of data of interest. NMF approximates a nonnegative matrix ${\bf V}$ as a product of two nonnegative matrices ${\bf W}$ and ${\bf H}$ . More concretely, given ${\bf V}\in \mathbb{R}^{F \times N}_{+}$ , we calculate ${\bf W}\in \mathbb{R}^{F \times K}_{+}$ and ${\bf H}\in \mathbb{R}^{K \times N}_{+}$ as

$\displaystyle{\min_{\scriptsize {\bf W}, {\bf H}} \ \ \ D({\bf V} ,{\bf WH}),$ $\displaystyle{{\rm subject\ to} \ \ \ [{\bf W}]_{f,k} \geq 0, [{\bf H}]_{k,n} \geq 0, \ \ \ \ \ \forall f,n,k},$

where $D(\cdot, \cdot)$ is a distance measure between two matrices, and where $K$ is usually chosen such that $K \ll \min\{F, N\}$ , that is, ${\bf V}$ is approximately represented by the two low-rank matrices.