The why and how of nonnegative matrix factorization
The why and how of nonnegative matrix factorization Gillis, arXiv 2014 from: ‘Regularization, Optimization, Kernels, and Support Vector Machines.’
Last week we looked at the paper ‘Beyond news content,’ which made heavy use of nonnegative matrix factorisation. Today we’ll be looking at that technique in a little more detail. As the name suggests, ‘The Why and How of Nonnegative matrix factorisation’ describes both why NMF is interesting (the intuition for how it works), and how to compute an NMF. I’m mostly interested in the intuition (and also out of my depth for some of the how!), but I’ll give you a sketch of the implementation approaches.
Nonnegative matrix factorization (NMF) has become a widely used tool for the analysis of high dimensional data as it automatically extracts sparse and meaningful features from a set of nonnegative data vectors.
NMF was first introduced by Paatero andTapper in 1994, and popularised in a article by Lee and Seung in 1999. Since then, the number of publications referencing the technique has grown rapidly:

What is NMF?
NMF approximates a matrix with a low-rank matrix approximation such that
.
For the discussion in this paper, we’ll assume that is set Continue reading


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