What is happening in non-negative matrix factorization?
Channel: Andersen Ang  
Date: 16/10/2018

Sparse Days 2018 at CERFACS, Toulouse, France
What is happening in non-negative matrix factorization?
Man Shun ANG, Andersen
Université de Mons, Belgium

Given a non-negative input matrix X, the goal of the Non-negative matrix factorization (NMF) is to decompose X into two (smaller) matrices W and H such that the product WH fits X under some metric distances such as the Frobenius norm and the Beta divergence. The non-negativity in NMF makes NMF finds many applications, due to the fact that the decomposed factors of NMF enjoy a more interpretability than the factors obtained by other methods. Despite the success of NMF in many applications, the NMF model itself is an ill-posed, underdetermined problem. Because of this, different new formulations of NMF are proposed in the past decade. This talk discuss what is going on NMF in this direction: from the classical separability condition, to the relaxed sufficiently scattered condition, minimum volume and the more.

September 27th 2018