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Department of Applied Mathematics
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 5198884567, ext. 32700
Fax: 5197464319
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MC 6460
Andersen (Man Shun) Ang  University of Mons, Belgium
Nonnegative Matrix Factorization: Applications, Theory and Computations
Given a nonnegative matrix M, the goal of Nonnegative 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 highlevel general overview of what is happening in NMF across three topics: applications, theory and computation.
Due to the nonnegativity, 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 illposed, 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 Nonnegative Tensor Factorization will also be discussed.
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Contact Info
Department of Applied Mathematics
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 5198884567, ext. 32700
Fax: 5197464319
PDF files require Adobe Acrobat Reader