Efficient retrieval of recommendations in a matrix factorization framework

Noam Koenigstein*, Parikshit Ram, Yuval Shavitt

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


Low-rank Matrix Factorization (MF) methods provide one of the simplest and most effective approaches to collaborative filtering. This paper is the first to investigate the problem of efficient retrieval of recommendations in a MF framework. We reduce the retrieval in a MF model to an apparently simple task of finding the maximum dot-product for the user vector over the set of item vectors. However, to the best of our knowledge the problem of efficiently finding the maximum dot-product in the general case has never been studied. To this end, we propose two techniques for efficient search - (i) We index the item vectors in a binary spatial-partitioning metric tree and use a simple branch and-bound algorithm with a novel bounding scheme to efficiently obtain exact solutions. (ii) We use spherical clustering to index the users on the basis of their preferences and pre-compute recommendations only for the representative user of each cluster to obtain extremely efficient approximate solutions. We obtain a theoretical error bound which determines the quality of any approximate result and use it to control the approximation. Both these simple techniques are fairly independent of each other and hence are easily combined to further improve recommendation retrieval efficiency. We evaluate our algorithms on real-world collaborative-filtering datasets, demonstrating more than ×7 speedup (with respect to the naive linear search) for the exact solution and over ×250 speedup for approximate solutions by combining both techniques.

Original languageEnglish
Title of host publicationCIKM 2012 - Proceedings of the 21st ACM International Conference on Information and Knowledge Management
Number of pages10
StatePublished - 2012
Event21st ACM International Conference on Information and Knowledge Management, CIKM 2012 - Maui, HI, United States
Duration: 29 Oct 20122 Nov 2012

Publication series

NameACM International Conference Proceeding Series


Conference21st ACM International Conference on Information and Knowledge Management, CIKM 2012
Country/TerritoryUnited States
CityMaui, HI


  • collaborative filtering
  • fast retrieval
  • inner-product


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