Efficient Rectangular Maximal-Volume Algorithm for Rating Elicitation in Collaborative Filtering
KAUST DepartmentKing Abdullah University of Science and Technology, Thuwal, Kingdom of Saudi Arabia
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AbstractCold start problem in Collaborative Filtering can be solved by asking new users to rate a small seed set of representative items or by asking representative users to rate a new item. The question is how to build a seed set that can give enough preference information for making good recommendations. One of the most successful approaches, called Representative Based Matrix Factorization, is based on Maxvol algorithm. Unfortunately, this approach has one important limitation - a seed set of a particular size requires a rating matrix factorization of fixed rank that should coincide with that size. This is not necessarily optimal in the general case. In the current paper, we introduce a fast algorithm for an analytical generalization of this approach that we call Rectangular Maxvol. It allows the rank of factorization to be lower than the required size of the seed set. Moreover, the paper includes the theoretical analysis of the method's error, the complexity analysis of the existing methods and the comparison to the state-of-the-art approaches.
CitationFonarev A, Mikhalev A, Serdyukov P, Gusev G, Oseledets I (2016) Efficient Rectangular Maximal-Volume Algorithm for Rating Elicitation in Collaborative Filtering. 2016 IEEE 16th International Conference on Data Mining (ICDM). Available: http://dx.doi.org/10.1109/ICDM.2016.0025.
SponsorsWork on problem setting and numerical examples was supported by Russian Science Foundation grant 14-11-00659. Work on theoretical estimations of approximation error and practical algorithm was supported by Russian Foundation for Basic Research 16-31-00351 mol_a. Also we thank Evgeny Frolov for helpful discussions.