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The purpose if this master's thesis is to study and develop a new algorithmicframework for Collaborative Filtering to produce recommendations in the top-Nrecommendation problem. Thus, we propose Lanczos Latent Factor Recommender(LLFR); a novel "big data friendly" collaborative filtering algorithm for top-Nrecommendation. Using a computationally efficient Lanczos-based procedure, LLFRbuilds a low dimensional item similarity model, that can be readily exploitedto produce personalized ranking vectors over the item space. A number ofexperiments on real datasets indicate that LLFR outperforms otherstate-of-the-art top-N recommendation methods from a computational as well as aqualitative perspective. Our experimental results also show that its relativeperformance gains, compared to competing methods, increase as the data getsparser, as in the Cold Start Problem. More specifically, this is true bothwhen the sparsity is generalized - as in the New Community Problem, a verycommon problem faced by real recommender systems in their beginning stages,when there is not sufficient number of ratings for the collaborative filteringalgorithms to uncover similarities between items or users - and in the veryinteresting case where the sparsity is localized in a small fraction of thedataset - as in the New Users Problem, where new users are introduced to thesystem, they have not rated many items and thus, the CF algorithm can not makereliable personalized recommendations yet.

LLFR: A Lanczos-Based Latent Factor Recommender for Big Data Scenarios