Abstract
Matrix factorization has been widely utilized as a latent factor model for solving the recommender system problem using collaborative filtering. For a recommender system, all the ratings in the rating matrix are bounded within a pre-determined range. In this paper, we propose a new improved matrix factorization approach for such a rating matrix, called Bounded Matrix Factorization (BMF), which imposes a lower and an upper bound on every estimated missing element of the rating matrix. We present an efficient algorithm to solve BMF based on the block coordinate descent method. We show that our algorithm is scalable for large matrices with missing elements on multicore systems with low memory. We present substantial experimental results illustrating that the proposed method outperforms the state of the art algorithms for recommender system such as stochastic gradient descent, alternating least squares with regularization, SVD++ and Bias-SVD on real-world datasets such as Jester, Movielens, Book crossing, Online dating and Netflix.
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Notes
Throughout this paper, we might use rows and users, columns and items, reduced rank and hidden latent features, values and ratings, low-rank factors and user/item-feature matrix, interchangeably and appropriately chosen for better understanding of the idea.
In our notation, if the inequality is between a vector/matrix and a scalar, every element in the vector/matrix should satisfy the inequality against the scalar.
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Acknowledgments
This work is supported in part by the National Science Foundation (NSF) Grants CCF-0808863, Defense Advanced Research Projects Agency (DARPA) XDATA program Grant FA8750-12-2-0309 and ERC Grant 258581 (under FP7/2007-2013) “Structured low-rank approximation”; the Research Foundation Flanders (FWO-Vlaanderen); the Flemish Government (Methusalem Fund, METH1); the Belgian Federal Government (IAP VII / DYSCO). Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundations and DARPA. Part of this research was carried out while the second author was with Georgia Institute of Technology.
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Kannan, R., Ishteva, M. & Park, H. Bounded matrix factorization for recommender system. Knowl Inf Syst 39, 491–511 (2014). https://doi.org/10.1007/s10115-013-0710-2
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DOI: https://doi.org/10.1007/s10115-013-0710-2