#### Introduction

A number of widely used machine learning methods, mainly clustering methods, can be accommodated into nonnegative matrix factorization framework with some variations. There are two purposes of applying matrix factorization to the user-item rating (or document-word frequency) matrix: to discover underling latent factors and/or to predict missing values of the matrix.

#### NMF

• Why non-negative? It enforces additive components. It encourages sparse representation. Its output is non-negative, which may make more sense for rating.

#### Software

• http://www.csie.ntu.edu.tw/~cjlin/libmf/
• http://www.libfm.org/ Factorization Machines
• https://github.com/JohnLangford/vowpal_wabbit/wiki/Matrix-factorization-example