Computational geometry: an introduction
Computational geometry: an introduction
Approximate nearest neighbors: towards removing the curse of dimensionality
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Similarity estimation techniques from rounding algorithms
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Google news personalization: scalable online collaborative filtering
Proceedings of the 16th international conference on World Wide Web
Lessons from the Netflix prize challenge
ACM SIGKDD Explorations Newsletter - Special issue on visual analytics
Collaborative filtering via euclidean embedding
Proceedings of the fourth ACM conference on Recommender systems
Yahoo! music recommendations: modeling music ratings with temporal dynamics and item taxonomy
Proceedings of the fifth ACM conference on Recommender systems
Maximum inner-product search using cone trees
Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining
Proceedings of the sixth ACM conference on Recommender systems
Towards scalable and accurate item-oriented recommendations
Proceedings of the 7th ACM conference on Recommender systems
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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.