TY - GEN
T1 - Efficient retrieval of recommendations in a matrix factorization framework
AU - Koenigstein, Noam
AU - Ram, Parikshit
AU - Shavitt, Yuval
PY - 2012
Y1 - 2012
N2 - 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.
AB - 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.
KW - collaborative filtering
KW - fast retrieval
KW - inner-product
UR - http://www.scopus.com/inward/record.url?scp=84871067909&partnerID=8YFLogxK
U2 - 10.1145/2396761.2396831
DO - 10.1145/2396761.2396831
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AN - SCOPUS:84871067909
SN - 9781450311564
T3 - ACM International Conference Proceeding Series
SP - 535
EP - 544
BT - CIKM 2012 - Proceedings of the 21st ACM International Conference on Information and Knowledge Management
T2 - 21st ACM International Conference on Information and Knowledge Management, CIKM 2012
Y2 - 29 October 2012 through 2 November 2012
ER -