Item-item collaborative filtering (CF) models are a well known and studied
family of recommender systems, however current literature does not provide any
theoretical explanation of the conditions under which item-based
recommendations will succeed or fail.
We investigate the existence of an ideal item-based CF method able to make
perfect recommendations. This CF model is formalized as an eigenvalue problem,
where estimated ratings are equivalent to the true (unknown) ratings multiplied
by a user-specific eigenvalue of the similarity matrix. Preliminary experiments
show that the magnitude of the eigenvalue is proportional to the accuracy of
recommendations for that user and therefore it can provide reliable measure of
confidence