Andersen (Man Shun) Ang | University of Mons, Belgium
Non-negative Matrix Factorization: Applications, Theory and Computations
Given a non-negative matrix M, the goal of Non-negative Matrix Factorization (NMF) is to decompose M into two (smaller) matrices U and V such that their product fits M under some distance function. This talk gives a high-level general overview of what is happening in NMF across three topics: applications, theory and computation.
Due to the non-negativity, the decomposed factors of NMF enjoy a higher interpretability than the factors obtained by other methods, hence NMF finds many applications in machine learning and other areas. The first part of the talk will be on NMF in various application scenarios. Despite the success of NMF in many applications, the NMF model itself is an ill-posed, underdetermined problem. So different new NMF formulations have been proposed in the past decade.
The second part of this talk discusses what is going on with NMF in this direction: from the classical separability condition, to the sufficiently scattered condition, the minimum volume criterion, and the generalized separability.
Finally, the third part of this talk focuses on computational issues for NMF. In particular, an extrapolated block coordinate descent framework called Heuristic Extrapolation with Restarts (HER) will be introduced. Applying HER to Non-negative Tensor Factorization will also be discussed.