Conference abstracts

Session B7 - Numerical Linear Algebra

July 15, 15:30 ~ 16:00 - Room B5

Separable Nonnegative Matrix Factorization

Nicolas Gillis

University of Mons, Belgium   -

Nonnegative Matrix Factorization (NMF) is a linear dimensionality reduction technique for nonnegative data. NMF has become a very popular technique in data mining and machine learning because it automatically extracts meaningful features through a sparse and part-based representation. NMF consists in approximating a nonnegative data matrix with the product of two nonnegative matrices. In this talk, we first introduce NMF and illustrate its usefulness with some application examples. We then focus on the separability assumption that allows to provably solve the NMF problem (although it is NP-hard in general). We present several recent algorithms, including geometric algorithms and algorithms based on convex optimization. We illustrate the results with some numerical experiments.

Joint work with Robert Luce (EPFL, Switzerland) and Stephen Vavasis (University of Waterloo, Canada).

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FoCM 2017, based on a nodethirtythree design.