Introduction to Non-Negative Matrix Factorization

• Activity Number: 120
• Type: Topic Contributed
• Date/Time: Monday, August 5, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): George Luta*+ and Fajwel Fogel and Douglas A. Marsteller and Joe Maisog
• Companies: Georgetown University and Ecole Polytechnique ParisTech and PepsiCo and Glotech, Inc.
• Keywords: non-negative matrix factorization ; NMF ; singular value decomposition ; SVD ; principal component analysis ; PCA

Abstract

Matrix factorization techniques are central to many statistical methods. The singular value decomposition method is often used to perform matrix factorizations although the interpretability of the elements of the factoring matrices may be problematic. We present an alternative method called non-negative matrix factorization (NMF) that has the potential to help with subject matter interpretability. The method is used when the matrix to be factored and the factoring matrices have non-negative elements. We present SAS JMP, R and Orange codes for computing NMF.