# Informed Non-negative Matrix Factorization. Application on source pollution in the air

Robert Chreiky, doctorant au LISIC

jeudi 15 octobre 2015 à 13h30

B014

In this presentation, we provide the main topics in Non-negative Matrix Factorization. In the case of air pollution, the previous factorization is called receptor modeling and the factors are respectively called Contribution and Profile Matrix. It may be seen as a general optimization problem where the cost function is minimized according to some constraints such as non-negativity, Sum-to-1, set entries of one factor. The cost function is discussed through parametric robust divergences such as alpha-beta divergences. Then, we propose to deal with special constraints by using special parametrizations as given in Limem or Lantery’s work. We here combine both in order to derive new update rules for both factors. Simulations on synthetic data enable to emphasize the use of such new methods compared to the previous ones.