# Association Rules

Association rules presents a unique algorithm which does not perform like any others we worked with. We used an implementation described b Kim et. al .

## Fundamentals of Association Rules

Association rules try to connect the causal relationships between items. An association rule essentially is of the form A1, A2, A3, ... => B1, B2, B3, ... It attempts to show how a series of items can determine another series of items. For a more concrete example, if we said A => B, C, that would mean that the appearance of item A in someone's history would imply that B and C would be there as well.

It's not just the items that matter, however; another important factor is the confidence of a rule. Confidence is the intuitive idea of how applicable a rule is. It can range from 0 to 1. If the confidence is 1, then we know that the rule always applies - that is, every time we see A, we also see B and C. However, if the confidence is 0, it means it's never correct - A does not imply B and C.

## Association Rules for Recommendations

For our purposes we used association rules of the form A => B. This means that we looked at all single-item relationships. That is, what is the likelihood of the active user rating the item B, given that the active user has rated A?

We created a square matrix of all these single-item relationships and their associated confidence values between all n items in the dataset. Then, we treat the user as a vector in n-dimensional space. If you multiply the matrix by the vector, you get what is called a recommendation vector - the most likely items that the user will rate, given the ones they have rated in the past.

You can easily use is recommendation vector to order preferences of a user.