Skip to main content

GWMF: Gradient Weighted Matrix Factorisation for Recommender Systems

  • Conference paper
  • 4594 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 7808))

Abstract

In this paper, we developed a new algorithm, Gradient Weighted Matrix Factorisation (GWMF), for matrix factorisation. GWMF uses weights to focus the approximation in the matrix factorisation to the higher approxmation residual. Therefore, it improves the matrix factorisation accuracy and increases the speed of convergence. We also introduce a regularisation parameter to control overfitting. We applied our algorithm to a movie recommendation problem and GWMF performs better than ordinal gradient descent-based matrix factorisation (GMF) on Movielens dataset. GWMF converges faster than GMF and it guarantees lower root mean square error (RMSE) at earlier iterations on both training and testing.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. The size of the World Wide Web, http://www.worldwidewebsize.com/

  2. The Size of Internet to Double Every 5 Years, http://www.labnol.org/internet/internet-size-to-double-every-5-years/6569/

  3. Adomavicius, G., Tuzhilin, A.: Toward the Next Generation of Recommender Systems: A Survey of the State-of-the-Art and Possible Extensions. In: IEEE Transaction of Knowledge and Data Engineering, pp. 734–749 (2005)

    Google Scholar 

  4. Pazzani, M., Billsus, D.: Learning and Revising User Profiles: The identification of Interesting web sites. J. Mac. Lea. 27, 313–331 (1997)

    Article  Google Scholar 

  5. Jannach, D., Friedrich, G.: Tutorial: Recommender Systems. In: Joint Conference on Artificial Intelligence, Barcelona (2011)

    Google Scholar 

  6. Salakhutdinov, R., Mnih, A.: Probabilistic Matrix Factorization. In: Neural Information Processing Systems (2008)

    Google Scholar 

  7. Hubert, L., Meulman, J., Heiser, W.: Two Purposes for Matrix Factorization: A Historical Appraisal. Society for Industrial and Applied Mathematics 42, 68–82 (2000)

    MathSciNet  MATH  Google Scholar 

  8. Koren, Y., Bell, R.M., Volinsky, C.: Matrix Factorization Techniques for Recommender Systems. IEEE Computer 42(8), 30–37 (2009)

    Article  Google Scholar 

  9. Salakhutdinov, R., Mnih, A.: Bayesian Probabilistic Matrix Factorization using Markov Chain Monte Carlo. In: 25th International Conference on Machine Learning (ICML), Helsinki (2008)

    Google Scholar 

  10. Zhang, S., Wang, W., Ford, J., Makedon, F.: Learning from Incomplete Ratings Using Non-negative Matrix Factorization. In: Proceedings of the SIAM International Conference on Data Mining, SDM (2006)

    Google Scholar 

  11. Gu, A., Zhou, J., Ding, C.: Collaborative Filtering: Weighted Nonnegative Matrix Factorization Incorporating User and Item Graphs. In: 10th SIAM International Conference on Data Mining (SDM), USA (2010)

    Google Scholar 

  12. Chen, G., Wang, F., Zhang, C.: Collaborative Filtering Using Orthogonal Nonnegative Matrix Trifactorization. J. of Inf. Pro. and Man. 45, 368–379 (2009)

    Google Scholar 

  13. Wu, M.: Collaborative Filtering via Ensembles of Matrix Factorizations. In: Proceedings of KDD Cup and Workshop, pp. 43–47 (2007)

    Google Scholar 

  14. Lee, D.D., Seung, H.S.: Algorithms for Non-Negative Matrix Factorization. In: Advances in Neural Information Processing, pp. 556–562 (2000)

    Google Scholar 

  15. Jin, R., Liu, Y., Si, L., Carbonell, J., Hauptmann, A.G.: A New Boosting Algorithm Using Input-Dependent Regularizer. In: Proceedings of the 20th International Conference on Machine Learning, Washington (2003)

    Google Scholar 

  16. MovieLens Data Sets, http://www.grouplens.org/node/73

  17. Netflix Prize, http://www.netflixprize.com/

  18. Gentle, J.: 6.8.1 Solutions that Minimize Other Norms of the Residuals. In: Matrix Algebra. Springer, New York (2007)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Chowdhury, N., Cai, X. (2013). GWMF: Gradient Weighted Matrix Factorisation for Recommender Systems. In: Ishikawa, Y., Li, J., Wang, W., Zhang, R., Zhang, W. (eds) Web Technologies and Applications. APWeb 2013. Lecture Notes in Computer Science, vol 7808. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37401-2_73

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-37401-2_73

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-37400-5

  • Online ISBN: 978-3-642-37401-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics