Extension of NMF to 3D

Data Science Asked by Aleksejs Fomins on October 16, 2020

AFAIK, Non-Negative Matrix Factorization (NMF) is the procedure of looking for matrices $A$ and $B$ such that

$$Data_{ik} = sum_j A_{ij} B_{jk}$$

My data matrix is in fact 3D. I would like to fit the following model to my data

$$Data_{ikl} = sum_j A_{ij} B_{jk} C_{jl}$$

It would be great to know if this model has a name and is already implemented somewhere (preferably Python)

One Answer

Are you looking for something like this?

"Introduction to Tensor Decompositions and their Applications in Machine Learning"

I'm not sure if there are better papers for it, but from what I can tell tensor decomposition seems like what you're describing.

Answered by Andy M on October 16, 2020

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