Matrix Decomposition for Recommendation System

Jie Zhu; Yiming Wei; Binbin Fu

doi:doi:10.11648/j.ajsea.20150404.11

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Matrix Decomposition for Recommendation System

Jie Zhu, Yiming Wei, Binbin Fu

Published in American Journal of Software Engineering and Applications (Volume 4, Issue 4)

Received: 11 June 2015 Accepted: 24 June 2015 Published: 4 July 2015

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Abstract

Matrix decomposition, when the rating matrix has missing values, is recognized as an outstanding technique for recommendation system. In order to approximate user-item rating matrix, we construct loss function and append regularization constraint to prevent overfitting. Thus, the solution of matrix decomposition becomes an optimization problem. Alternating least squares (ALS) and stochastic gradient descent (SGD) are two popular approaches to solve optimize problems. Alternating least squares with weighted regularization (ALS-WR) is a good parallel algorithm, which can perform independently on user-factor matrix or item-factor matrix. Based on the idea of ALS-WR algorithm, we propose a modified SGD algorithm. With experiments on testing dataset, our algorithm outperforms ALS-WR. In addition, matrix decompositions based on our optimization method have lower RMSE values than some classic collaborate filtering algorithms.

Published in	American Journal of Software Engineering and Applications (Volume 4, Issue 4)
DOI	10.11648/j.ajsea.20150404.11
Page(s)	65-70
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Matrix Decomposition, Regularization, Collaborative Filtering, Optimization

References

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[3]	ALI K, WIJNAND V S. TiVo: Making show recommendations using a distributed collaborative filtering architecture[C]//KDD'04: Proceedings of the 10th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. New York: ACM, 2004:394- 401．
[4]	GOLDBERG K Y，ROEDER T，GUPTA D，et al. Eigentaste: A constant time collaborative filtering algorithm [J]. Information Retrieval, 2001, 4( 2): 133－151．
[5]	SALAKHUTDINOV R，MNIH A，HINTON G．Restricted Boltzmann machines for collaborative filtering[C]//Proceedings of the 24th International Conference on Machine Learning．New York: ACM, 2007:791－798．
[6]	HOFMANN T. Latent semantic models for collaborative filtering [J]. ACM Transactions on Information Systems，2004, 22(1) : 89－115．
[7]	BLEI D，NG A，JORDAN M．Latent Dirichlet allocation [J]. Journal of Machine Learning Research, 2003, 3: 993－1022．
[8]	DaWei C, Zhao Y, HaoYan L. The overfitting phenomenon of SVD series algorithms in rating matrix [J]. Journal of Shandong university (engineering science), 2014，44(3): 15-21
[9]	XiaoFeng H, Xin L, Qingsheng Z. A parallel improvements based on regularized matrix factorization of collaborative filtering model [J]. Journal of electronics and information, 2013，35(6):1507-1511.
[10]	Zhou Y, Wilkinson D, Schreiber R, et al. Large-scale parallel collaborative filtering for the Netflix prize [M]//Algorithmic Aspects in Information and Management. Springer Berlin Heidelberg, 2008: 337-348.
[11]	I.Pil´aszy,D. Zibriczky, and D.Tikk. Fast ALS-based matrix factorization for explicit and implicit feedback datasets. In Proceedings of the Fourth ACM Conference on Recommender Systems, pages71–78, 2010.

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APA Style

Jie Zhu, Yiming Wei, Binbin Fu. (2015). Matrix Decomposition for Recommendation System. American Journal of Software Engineering and Applications, 4(4), 65-70. https://doi.org/10.11648/j.ajsea.20150404.11

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ACS Style

Jie Zhu; Yiming Wei; Binbin Fu. Matrix Decomposition for Recommendation System. Am. J. Softw. Eng. Appl. 2015, 4(4), 65-70. doi: 10.11648/j.ajsea.20150404.11

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AMA Style

Jie Zhu, Yiming Wei, Binbin Fu. Matrix Decomposition for Recommendation System. Am J Softw Eng Appl. 2015;4(4):65-70. doi: 10.11648/j.ajsea.20150404.11

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@article{10.11648/j.ajsea.20150404.11,
  author = {Jie Zhu and Yiming Wei and Binbin Fu},
  title = {Matrix Decomposition for Recommendation System},
  journal = {American Journal of Software Engineering and Applications},
  volume = {4},
  number = {4},
  pages = {65-70},
  doi = {10.11648/j.ajsea.20150404.11},
  url = {https://doi.org/10.11648/j.ajsea.20150404.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajsea.20150404.11},
  abstract = {Matrix decomposition, when the rating matrix has missing values, is recognized as an outstanding technique for recommendation system. In order to approximate user-item rating matrix, we construct loss function and append regularization constraint to prevent overfitting. Thus, the solution of matrix decomposition becomes an optimization problem. Alternating least squares (ALS) and stochastic gradient descent (SGD) are two popular approaches to solve optimize problems. Alternating least squares with weighted regularization (ALS-WR) is a good parallel algorithm, which can perform independently on user-factor matrix or item-factor matrix. Based on the idea of ALS-WR algorithm, we propose a modified SGD algorithm. With experiments on testing dataset, our algorithm outperforms ALS-WR. In addition, matrix decompositions based on our optimization method have lower RMSE values than some classic collaborate filtering algorithms.},
 year = {2015}
}

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TY  - JOUR
T1  - Matrix Decomposition for Recommendation System
AU  - Jie Zhu
AU  - Yiming Wei
AU  - Binbin Fu
Y1  - 2015/07/04
PY  - 2015
N1  - https://doi.org/10.11648/j.ajsea.20150404.11
DO  - 10.11648/j.ajsea.20150404.11
T2  - American Journal of Software Engineering and Applications
JF  - American Journal of Software Engineering and Applications
JO  - American Journal of Software Engineering and Applications
SP  - 65
EP  - 70
PB  - Science Publishing Group
SN  - 2327-249X
UR  - https://doi.org/10.11648/j.ajsea.20150404.11
AB  - Matrix decomposition, when the rating matrix has missing values, is recognized as an outstanding technique for recommendation system. In order to approximate user-item rating matrix, we construct loss function and append regularization constraint to prevent overfitting. Thus, the solution of matrix decomposition becomes an optimization problem. Alternating least squares (ALS) and stochastic gradient descent (SGD) are two popular approaches to solve optimize problems. Alternating least squares with weighted regularization (ALS-WR) is a good parallel algorithm, which can perform independently on user-factor matrix or item-factor matrix. Based on the idea of ALS-WR algorithm, we propose a modified SGD algorithm. With experiments on testing dataset, our algorithm outperforms ALS-WR. In addition, matrix decompositions based on our optimization method have lower RMSE values than some classic collaborate filtering algorithms.
VL  - 4
IS  - 4
ER  -

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Author Information

Jie Zhu

School of Information, Beijing Wuzi University, Beijing, China
Yiming Wei

School of Information, Beijing Wuzi University, Beijing, China
Binbin Fu

School of Information, Beijing Wuzi University, Beijing, China

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APA Style

Jie Zhu, Yiming Wei, Binbin Fu. (2015). Matrix Decomposition for Recommendation System. American Journal of Software Engineering and Applications, 4(4), 65-70. https://doi.org/10.11648/j.ajsea.20150404.11

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ACS Style

Jie Zhu; Yiming Wei; Binbin Fu. Matrix Decomposition for Recommendation System. Am. J. Softw. Eng. Appl. 2015, 4(4), 65-70. doi: 10.11648/j.ajsea.20150404.11

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AMA Style

Jie Zhu, Yiming Wei, Binbin Fu. Matrix Decomposition for Recommendation System. Am J Softw Eng Appl. 2015;4(4):65-70. doi: 10.11648/j.ajsea.20150404.11

Copy | Download

@article{10.11648/j.ajsea.20150404.11,
  author = {Jie Zhu and Yiming Wei and Binbin Fu},
  title = {Matrix Decomposition for Recommendation System},
  journal = {American Journal of Software Engineering and Applications},
  volume = {4},
  number = {4},
  pages = {65-70},
  doi = {10.11648/j.ajsea.20150404.11},
  url = {https://doi.org/10.11648/j.ajsea.20150404.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajsea.20150404.11},
  abstract = {Matrix decomposition, when the rating matrix has missing values, is recognized as an outstanding technique for recommendation system. In order to approximate user-item rating matrix, we construct loss function and append regularization constraint to prevent overfitting. Thus, the solution of matrix decomposition becomes an optimization problem. Alternating least squares (ALS) and stochastic gradient descent (SGD) are two popular approaches to solve optimize problems. Alternating least squares with weighted regularization (ALS-WR) is a good parallel algorithm, which can perform independently on user-factor matrix or item-factor matrix. Based on the idea of ALS-WR algorithm, we propose a modified SGD algorithm. With experiments on testing dataset, our algorithm outperforms ALS-WR. In addition, matrix decompositions based on our optimization method have lower RMSE values than some classic collaborate filtering algorithms.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Matrix Decomposition for Recommendation System
AU  - Jie Zhu
AU  - Yiming Wei
AU  - Binbin Fu
Y1  - 2015/07/04
PY  - 2015
N1  - https://doi.org/10.11648/j.ajsea.20150404.11
DO  - 10.11648/j.ajsea.20150404.11
T2  - American Journal of Software Engineering and Applications
JF  - American Journal of Software Engineering and Applications
JO  - American Journal of Software Engineering and Applications
SP  - 65
EP  - 70
PB  - Science Publishing Group
SN  - 2327-249X
UR  - https://doi.org/10.11648/j.ajsea.20150404.11
AB  - Matrix decomposition, when the rating matrix has missing values, is recognized as an outstanding technique for recommendation system. In order to approximate user-item rating matrix, we construct loss function and append regularization constraint to prevent overfitting. Thus, the solution of matrix decomposition becomes an optimization problem. Alternating least squares (ALS) and stochastic gradient descent (SGD) are two popular approaches to solve optimize problems. Alternating least squares with weighted regularization (ALS-WR) is a good parallel algorithm, which can perform independently on user-factor matrix or item-factor matrix. Based on the idea of ALS-WR algorithm, we propose a modified SGD algorithm. With experiments on testing dataset, our algorithm outperforms ALS-WR. In addition, matrix decompositions based on our optimization method have lower RMSE values than some classic collaborate filtering algorithms.
VL  - 4
IS  - 4
ER  -

Copy | Download