I'm implementing a simple user-based collaborative filtering. So, basically, I use a user vector $U$, and similarity matrix of the items, $H$. But I have extra data about my items, based on which I construct another similarity matrix, $E$. There's a hypothesis that combining $H$ and $E$ will improve the overall performance of collaborative filtering. So, what is the best way to combine them?
It's hard to straight up prescribe the best approach even when everything is known about the use case, the data, and the model (which is why this is an active research field). But given that we have absolutely no information about any of those, the only thing you can hope to get from an internet forum are some directions to explore.
- What happens when you straight up add the two?
- What happens if you assign some weights $\alpha$ and $\beta$ to each matrix, such that $\alpha + \beta = 1$?
- What happens if you implement every single method of combining the data from Table 3 of Hybrid Recommender Systems: Survey and Experiments?
Once you have done all of them, find the one that works the best. Use that.