Matrix and tensor decomposition in recommender systems

Abstract

This turorial offers a rich blend of theory and practice re- garding dimensionality reduction methods, to address the in- formation overload problem in recommender systems. This problem affects our everyday experience while searching for knowledge on a topic. Naive Collaborative Filtering can- not deal with challenging issues such as scalability, noise, and sparsity. We can deal with all the aforementioned chal- lenges by applying matrix and tensor decomposition meth- ods. These methods have been proven to be the most accu- rate (i.e., Netix prize) and efficient for handling big data. For each method (SVD, SVD++, timeSVD++, HOSVD, CUR, etc.) we will provide a detailed theoretical mathe- matical background and a step-by-step analysis, by using an integrated toy example, which runs throughout all parts of the tutorial, helping the audience to understand clearly the differences among factorisation methods.