Recommendation Systems

The purpose of a recommendation system is to predict how strong a user’s interest is in not yet consumed products. The user is then offered the most attractive product according to the prediction. Typical recommendation services include videos and movies as for Netflix, YouTube, and Spotify, consumption goods as for Amazon, pieces of social content as for Facebook and Twitter. Recommendation systems are supposed to contribute to the management of the information overload by suggesting a relevant subset from an unmanageable amount of products to the user. Aiming to generate appropriate predictions, mathematical methods of information retrieval are used. In this chapter, we discuss collaborative filtering techniques and apply them for the prediction of movie ratings, and for the analysis of latent semantics in the documents. The neighborhood- and model-based approaches of collaborative filtering are elaborated in detail. Within the neighborhood-based approach, similarity measures are introduced and the k-nearest neighbors algorithm is described. The model-based approach uses a linear-algebraic technique of singular value decomposition. Singular value decomposition allows to reveal hidden patterns of users’ choice behavior. After imposing a low-rank model on the latter, the prediction becomes optimization-driven. For solving the corresponding low-rank approximation problem, we apply the well-known optimization algorithm of gradient descent. An efficient application of gradient descent is enabled by matrix factorization of the low-rank approximation.