**Contact Info**

Department of Applied Mathematics

University of Waterloo

Waterloo, Ontario

Canada N2L 3G1

Phone: 519-888-4567, ext. 32700

Fax: 519-746-4319

PDF files require Adobe Acrobat Reader

Tuesday, August 20, 2019 — 2:30 PM EDT

MC 6460

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.

- Lecture (1)

**Contact Info**

Department of Applied Mathematics

University of Waterloo

Waterloo, Ontario

Canada N2L 3G1

Phone: 519-888-4567, ext. 32700

Fax: 519-746-4319

PDF files require Adobe Acrobat Reader

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1

The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is centralized within our Office of Indigenous Relations.