On the Use of Lanczos Vectors for Efficient Latent Factor-Based Top-N Recommendation

In this work 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 at different density levels 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. This is true both when the sparsity is generalized -- as in the New Community Problem -- and in the very interesting case where the sparsity is localized in a small fraction of the dataset -- as in the New Users Problem.