Memory-Based Weighted-Majority Prediction

In general, the task in Recommender Systems is to predict the
votes of a particular user (called the active user) over a given
subject or item, for deciding its recommendation. The prediction
is usually done from a database of user votes from a sample or
population of other users. In Memory-based collaborative filtering
algorithms [1], commonly used for Recommender Systems, the
vote prediction of an active user (indicated with a subscript a) is
done based on some partial information regarding the active user
and a set if weights calculated directly from the entire user-vote
database. It is assumed that the predicted vote of the active user
for item j, pa,j, is a weighted sum of the votes of the other users:
( , )( ) (1.1) , 1 , Σ= = + − n
a j a i i j i p v σ ws a i v v
where va , vi are the mean vote of user a and i respectively. And
n is the number of users in the database with non-zero weights

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that have voted over item j. The weights ws(a,i) express the
similarity between each user i and the active user a. σ is a
normalizing factor such that the absolute values of the weights
sum to unity.

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