# Extra data for similarity matrix in collaborative filtering algorithm

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?

• What happens if you assign some weights $\alpha$ and $\beta$ to each matrix, such that $\alpha + \beta = 1$?