Existence and Construction of Edge-Disjoint Pathson Expander Graphs
SIAM Journal on Computing
Communications of the ACM
Analysis of recommendation algorithms for e-commerce
Proceedings of the 2nd ACM conference on Electronic commerce
Item-based collaborative filtering recommendation algorithms
Proceedings of the 10th international conference on World Wide Web
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Competitive recommendation systems
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Amazon.com Recommendations: Item-to-Item Collaborative Filtering
IEEE Internet Computing
Latent Class Models for Collaborative Filtering
IJCAI '99 Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence
Convergent algorithms for collaborative filtering
Proceedings of the 4th ACM conference on Electronic commerce
Recommendation Systems: A Probabilistic Analysis
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
On the use of linear programming for unsupervised text classification
Proceedings of the eleventh ACM SIGKDD international conference on Knowledge discovery in data mining
PolyLens: a recommender system for groups of users
ECSCW'01 Proceedings of the seventh conference on European Conference on Computer Supported Cooperative Work
Manipulation-resistant collaborative filtering systems
Proceedings of the third ACM conference on Recommender systems
Computing a nonnegative matrix factorization -- provably
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Mining contextual movie similarity with matrix factorization for context-aware recommendation
ACM Transactions on Intelligent Systems and Technology (TIST) - Special section on twitter and microblogging services, social recommender systems, and CAMRa2010: Movie recommendation in context
Unifying rating-oriented and ranking-oriented collaborative filtering for improved recommendation
Information Sciences: an International Journal
Learning mixtures of arbitrary distributions over large discrete domains
Proceedings of the 5th conference on Innovations in theoretical computer science
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A collaborative filtering system at an e-commerce site or similar service uses data about aggregate user behavior to make recommendations tailored to specific user interests. We develop recommendation algorithms with provable performance guarantees in a probabilistic mixture model for collaborative filtering proposed by Hofmann and Puzicha. We identify certain novel parameters of mixture models that are closely connected with the best achievable performance of a recommendation algorithm; we show that for any system in which these parameters are bounded, it is possible to give recommendations whose quality converges to optimal as the amount of data grows. All our bounds depend on a new measure of independence that can be viewed as an L"1-analogue of the smallest singular value of a matrix. Using this, we introduce a technique based on generalized pseudoinverse matrices and linear programming for handling sets of high-dimensional vectors. We also show that standard approaches based on L"2 spectral methods are not strong enough to yield comparable results, thereby suggesting some inherent limitations of spectral analysis.