The recommender problem with convex hulls

Abstract

We introduce a novel approach for the user-based, collaborative filtering, recommender problem for selecting neighbors and weighting their ratings to make a prediction. The proposed approach is based on computational geometry using convex hulls and linear programming (LP). Computational testing is used to compare our approach with one of the current standard methods based on Pearson correlations using three data sets: Jester, Yahoo! Music User Ratings of Musical Artists (Yahoo!Artists), and MovieLens. The comparisons reveal that the method based on convex hulls and LPs can reduce the RMSE for predicted ratings to up to onethird of that of Pearson’s correlations. The results make a new method based on polyhedral geometry available to attack other machine learning problems.