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This question is based on the now classical work: Collaborative filtering with implicit feedback. I'm mainly interested in finding references for the question below.

Suppose we are building a recommendation system from a two source dataset. As a concrete example, we can think of watching movies on Netflix on computer, vs watching Netflix on your phone. So this dataset has implicit feedback on computer watching and mobile watching for each customer.

The assumption here is that we see different behavior on computer vs mobile watching. For example, people might opt to watch movies on computer vs watching sports on mobile phones. The simplest approach toward recommending content to users would be to do collaborative filtering factorizations on mobile and computer separately. But this doesn't seem to take advantage of the fact that there might be links between user behavior in both datasets, along with issues of sparsity, particularly in the mobile dataset. Note that content-wise, the datasets are assumed to be the same: everything available on the web is also available on mobile. In other words, watching anything is fair game on either source.

What techniques exist for doing such collaborative filtering simultaneously on both datasets? I saw one possible reference here: http://ceur-ws.org/Vol-528/paper9.pdf

Here's how I was thinking about this, and I'm wondering if this is at all correct. So the implicit feedback matrix has components $r_{uk}$ for user $u$ and content $k$. I was thinking of instead writing it as: $r_{uk}+ir'_{uk}$, where the first term is implicit feedback from source $A$ and the second is implicit feedback from source $B$. Then, one does the collaborative filtering minimization, obtaining user $u$ recommendation vectors $x_u=(x_{u1},x_{u2},\cdots,x_{uK})$, so that the real part of $x_u$ gives content recommendation for source $A$ and the imaginary part gives content recommendation for source $B$. Does this make sense?

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