  The purpose if this master's thesis is to study and develop a new algorithmic
framework for Collaborative Filtering to produce recommendations in the top-N
recommendation problem. Thus, we propose Lanczos Latent Factor Recommender
(LLFR); a novel "big data friendly" collaborative filtering algorithm for top-N
recommendation. Using a computationally efficient Lanczos-based procedure, LLFR
builds a low dimensional item similarity model, that can be readily exploited
to produce personalized ranking vectors over the item space. A number of
experiments on real datasets indicate that LLFR outperforms other
state-of-the-art top-N recommendation methods from a computational as well as a
qualitative perspective. Our experimental results also show that its relative
performance gains, compared to competing methods, increase as the data get
sparser, as in the Cold Start Problem. More specifically, this is true both
when the sparsity is generalized - as in the New Community Problem, a very
common problem faced by real recommender systems in their beginning stages,
when there is not sufficient number of ratings for the collaborative filtering
algorithms to uncover similarities between items or users - and in the very
interesting case where the sparsity is localized in a small fraction of the
dataset - as in the New Users Problem, where new users are introduced to the
system, they have not rated many items and thus, the CF algorithm can not make
reliable personalized recommendations yet.
