11.2. MODEL-BASED METHODS 377 We predict uSera should have a high preference for item4. This is not surprising as the three users who are similar to usera like the item, while the two users who are dissimilar to usera do not like it. An alternative measure to use for the weights is v e c t o r s i m i l a r i t y , which is discussed in [Breese et al., 1998]. Extensions to memory-based algorithms include default voting, inverse-user f r e q u e n c y , and case a m p l i f i c a t i o n . These extensions are also discussed in [Breese et al., 1998]. 11.2 Model-Based Methods The method discussed in the previous section is a heuristic method. In Chapter 1, Section 1.2, we distinguished heuristic methods from model-based methods. Next, we present model-based methods for doing collaborative filtering. 11.2.1 Probabilistic Collaborative Filtering In the framework of probability theory, we can use the expected value of the active user's (usera) vote for itemk as our prediction of that vote. That is, if the votes are integral values between 1 and r inclusive,