I'm in the process of designing a website that is built around the concept of recommending various items to users based on their tastes. (i.e. items they've rated, items added to their favorites list, etc.) Some examples of this are Amazon, Movielens, and Netflix.
Now, my problem is, I'm not sure where to start in regards to the mathematical part of this system. I'm willing to learn the math that's required, it's just I don't know what type of math is required.
I've looked at a few of the publications over at Grouplens.org, specifically "Towards a Scalable kNN CF Algorithm: Exploring Effective Applications of Clustering." (pdf) I'm pretty good at understanding everything until page 5 "Prediction Generation"
p.s. I'm not exactly looking for an explanation of what's going on, though that might be helpful, but I'm more interested in the math I need to know. This way I can understand what's going on.