efficient retrieval of recommendations in a matrix factorization framework
DESCRIPTION
Efficient Retrieval of Recommendations in a Matrix Factorization Framework. Motivation. In the field of Recommender System , Matrix Factorization (MF) models have shown superior accuracy for recommendation tasks. E.g., The Netflix Prize, KDD-Cup’11, etc. - PowerPoint PPT PresentationTRANSCRIPT
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Efficient Retrieval of Recommendationsin a Matrix Factorization Framework
Noam Koenigstein Parikshit Ram Yuval ShavittSchool of Electrical
Engineering
Tel Aviv University
Computational Science &Engineering
Georgia Institute ofTechnology
School of ElectricalEngineering
Tel Aviv University
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Motivation• In the field of Recommender System, Matrix Factorization
(MF) models have shown superior accuracy for recommendation tasks.E.g., The Netflix Prize, KDD-Cup’11, etc.
• Training is fast. Computing test scores is fast.But… Retrieval of Recommendations (RoR) is s--l--o--w !
• This problem is well known in the industry, yet never been approached before in academia!
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22
45
3 32
. . . .
4 12
25
I T E M S
USERS
Yahoo! Music:
1M Users625K Items
6 Tera elements ~300 multiplications ~5 days CPU
Naïve Multithreading: High latency + wasteful
Yahoo! Music:
1M Users625K Items
6 Tera elements ~300 multiplications ~5 days CPU
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Reduction to Inner Product
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�̂�𝑢𝑖=𝐩𝑢𝑇 𝐪𝑖=‖𝐩𝑢
❑‖‖𝐪𝑖‖cos𝜃𝑢𝑖
Core problem:
Given a user vector and a set of item, find an item vector that will maximize
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Best Matches Algorithms
• Metric Space
• Cosine Similarity
• Locality Sensitive Hashing
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Metric TreesR
R
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Branch-and-bound Algorithm
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Bounding Inner Product Similarity
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Approximate Solution
Users vectors can be normalized Users can be clustered based on their spherical angle!
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Relative Error Bound
What is the error when recommendations are retrieved based on an approximate user vector?
|𝑒𝑟𝑟𝑜𝑝𝑡|=|𝑝𝑐❑𝑇𝑞𝑖
❑−𝑝𝑢❑𝑇𝑞𝑖
❑||𝑝𝑐❑
𝑇 𝑞𝑖❑|
≤1−cos (𝜃𝑝𝑐𝑞 𝑖
+Δ )cos (𝜃𝑝𝑐𝑞 𝑖 )
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Adaptive Approximate Solution
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Experimentations Set-up MovieLens Netflix Yahoo!
MusicRatings 1,000,206 100,480,507 252,800,275
Users 6,040 480,189 1,000,990
Items 3,952 17,770 624,961
Sparsity 95.81% 98.82% 99.96%
Yahoo! Music Recommendations: Modeling Music Ratings with Temporal Dynamics and Item TaxonomyGideon Dror, Noam Koenigstein, Yehuda Koren(RecSys-11`)
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Exact Alg. Speedup
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Approximate Alg. Speedup
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Speedup vs. Precision
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Speedup vs. MedianRank
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Conclusions
• We introduce a new and relevant research problem
• An exact solution with limited speedup
• An approximate solution with a tradeoff between accuracy and speedup
• Much room for further research…