Building intuition for tensors in machine learning

Question

I'm trying to understand tensors in the context of machine learning, but all the resources that mention tensors that I've found so far were building the intuitions through physics applications. As much as I would like to learn more about physics, it is not helping me build the intuitions that I need. Can you recommend a good materials about tensors that would help me with tensors in machine learning?

Thanks!

Answer 1

I get the feeling that the tensors they are referring to are most likely just multilinear maps, and not the tensor fields used in physics. I could have misjudged this, but even so it would be good to seek references that talk specifically about the technique they are applying. From the context, this is "tensor decomposition."

From the second link you posted, I found this:

Tensor decompositions have been used in signal processing and computational neuroscience for blind source separation and independent component analysis (ICA) [CJ10].

So a good place to start getting your hands on the technique they are using may be

[CJ10] P. Comon and C. Jutten. Handbook of Blind Source Separation: Independent Component Analysis and Applications. Academic Press. Elsevier, 2010.

I've been reading the Wikipedia hit for tensor decomposition and it does sound like the same topic. Note the pdf link on the page to A Survey of Multilinear Subspace Learning for Tensor Data and another potentially useful reference to Tensor Decompositions and applications.

From these sources, you'll just have to work your way down the chain of difficulty until you are at a level you understand, then work your way up to the concepts used in these surveys.