Comparison Between Stochastic Gradient Descent and VLE Metaheuristic for Optimizing Matrix Factorization

  • Juan A. Gómez-PulidoEmail author
  • Enrique Cortés-Toro
  • Arturo Durán-Domínguez
  • José M. Lanza-Gutiérrez
  • Broderick Crawford
  • Ricardo Soto
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 1173)


Matrix factorization is used by recommender systems in collaborative filtering for building prediction models based on a couple of matrices. These models are usually generated by stochastic gradient descent algorithm, which learns the model minimizing the error done. Finally, the obtained models are validated according to an error criterion by predicting test data. Since the model generation can be tackled as an optimization problem where there is a huge set of possible solutions, we propose to use metaheuristics as alternative solving methods for matrix factorization. In this work we applied a novel metaheuristic for continuous optimization, which works inspired by the vapour-liquid equilibrium. We considered a particular case were matrix factorization was applied: the prediction student performance problem. The obtained results surpassed thoroughly the accuracy provided by stochastic gradient descent.


Matrix factorization Gradient descent Metaheuristics 



The authors would like to thank the grants given as follows: PhD. Juan A. Gomez-Pulido is supported by grant IB16002 (Junta Extremadura, Spain). MSc. Enrique Cortés-Toro is supported by grant INF-PUCV 2015. PhD. Broderick Crawford is supported by grant Conicyt/Fondecyt/Regular/1171243. PhD. Ricardo Soto is supported by grant Conicyt/Fondecyt/Regular/1160455.


  1. 1.
    Alpaydin, E.: Introduction to Machine Learning. The Massachusetts Institute of Technology Press, Cambridge (2010)zbMATHGoogle Scholar
  2. 2.
    Angra, S., Ahuja, S.: Machine learning and its applications: a review. In: 2017 International Conference on Big Data Analytics and Computational Intelligence, pp. 57–60 (2017)Google Scholar
  3. 3.
    Bottou, L.: Large-scale machine learning with stochastic gradient descent. In: Lechevallier, Y., Saporta, G. (eds.) Proceedings of COMPSTAT 2010, pp. 177–186. Springer, Heidelberg (2010). Scholar
  4. 4.
    Cortes-Toro, E.M., Crawford, B., Gomez-Pulido, J.A., Soto, R., Lanza-Gutierrez, J.M.: A new metaheuristic inspired by the vapour-liquid equilibrium for continuous optimization. Appl. Sci. 8(11), 2080 (2018)CrossRefGoogle Scholar
  5. 5.
    Dorigo, M., Maniezzo, V., Colorni, A.: Ant system: optimization by a colony of cooperating agents. IEEE Trans. Syst. Man Cybern. Part B 26(1), 29–41 (1996)CrossRefGoogle Scholar
  6. 6.
    Feo, T.A., Resende, M.G.C.: Greedy randomized adaptive search procedures. J. Glob. Optim. 6(2), 109–133 (1995)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Gansterer, M., Almeder, C., Hartl, R.F.: Simulation-based optimization methods for setting production planning parameters. Int. J. Prod. Econ. 151, 206–213 (2014)CrossRefGoogle Scholar
  8. 8.
    Gendreau, M., Potvin, J.E.: Handbook of Metaheuristics. Springer, Heidelberg (2010). Scholar
  9. 9.
    Glover, F.: Tabu search - part II. INFORMS J. Comput. 2(1), 4–32 (1990)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Holland, J.H.: Genetic Algorithms and Adaptation. In: Selfridge, O.G., Rissland, E.L., Arbib, M.A. (eds.) Adaptive Control of Ill-Defined Systems. NATO Conference Series (II Systems Science), vol. 16, pp. 317–333. Springer, Boston (1984). Scholar
  11. 11.
    Jannach, D., Zanker, M., Felfernig, A., Friedrich, G.: Recommender Systems: An Introduction. Cambridge University Press, Cambridge (2011)Google Scholar
  12. 12.
    Karaboga, D.: Artificial bee colony algorithm. Scholarpedia 5(3), 6915 (2010)CrossRefGoogle Scholar
  13. 13.
    Kennedy, J., Eberhart, R.: Particle swarm optimization. In: IEEE International Conference on Neural Networks (1995)Google Scholar
  14. 14.
    Kirkpatrick, S., Gelatt Jr., D., Vecchi, M.P.: Optimization by simmulated annealing. Science 220(4598), 671–680 (1983)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Koren, Y., Bell, R., Volinsky, C.: Matrix factorization techniques for recommender systems. Computer 42(8), 30–37 (2009)CrossRefGoogle Scholar
  16. 16.
    Masoumeh, R., Reza, B.: Using the genetic algorithm to enhance nonnegative matrix factorization initialization. Expert Syst. 31(3), 213–219 (2013)Google Scholar
  17. 17.
    McCabe, W.L., Smith, J.C., Harriot, P.: Unit Operations of Chemical Engineering. The McGraw-Hill Companies, Inc., New York (2007)Google Scholar
  18. 18.
    Melville, P., Sindhwani, V.: Recommender systems. In: Encyclopedia of Machine Learning, pp. 829–838 (2010)Google Scholar
  19. 19.
    Mladenovic, N., Drazic, M., Kovacevic-Vujcic, V., Cangalovic, M.: General variable neighborhood search for the continuous optimization. Eur. J. Oper. Res. 191(3), 753–770 (2008)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Morse, G., Stanley, K.O.: Simple evolutionary optimization can rival stochastic gradient descent in neural networks. In: GECCO, pp. 477–484. ACM (2016)Google Scholar
  21. 21.
    Murphy, K.: Machine Learning. A Probabilistic Perspective. The Massachusetts Institute of Technology Press, Cambridge (2012)zbMATHGoogle Scholar
  22. 22.
    Rana, S., Jasola, S., Kumar, R.: A review on particle swarm optimization algorithms and their applications to data clustering. Artif. Intell. Rev. 35(3), 211–222 (2011)CrossRefGoogle Scholar
  23. 23.
    Rashedi, E., Nezamabadi-pour, H., Saryazdi, S.: GSA: a gravitational search algorithm. Inf. Sci. 179(13), 2232–2248 (2009)CrossRefGoogle Scholar
  24. 24.
    Rendle, S., Schmidt-Thieme, L.: Online-updating regularized kernel matrix factorization models for large-scale recommender systems. In: Proceedings of the 2008 ACM Conference on Recommender Systems, pp. 251–258 (2008)Google Scholar
  25. 25.
    Ricci, F., Rokach, L., Shapira, B., Kantor, P.B. (eds.): Recommender Systems Handbook. Springer, Heidelberg (2011). Scholar
  26. 26.
    Smith, J., Van Ness, H., Abbott, M., Borgnakke, C.: Introduction to Chemical Engineering Thermodynamics, 7th edn. The McGraw-Hill Companies, Inc., New York (2005)Google Scholar
  27. 27.
    Smith, R.: Chemical Process Design and Integration. Wiley, Hoboken (2005)Google Scholar
  28. 28.
    Sonntag, R.E., Borgnakke, C., Wylen, G.J.V.: Fundamentals of Thermodynamics, 6th edn. Wiley, Hoboken (2003)Google Scholar
  29. 29.
    Soto, M., Rossi, A., Sevaux, M.: Two iterative metaheuristic approaches to dynamic memory allocation for embedded systems. In: Merz, P., Hao, J.-K. (eds.) EvoCOP 2011. LNCS, vol. 6622, pp. 250–261. Springer, Heidelberg (2011). Scholar
  30. 30.
    Sun, J., Garibaldi, J.M., Hodgman, C.: Parameter estimation using metaheuristics in systems biology: a comprehensive review. IEEE/ACM Trans. Comput. Biology Bioinform. 9(1), 185–202 (2012)CrossRefGoogle Scholar
  31. 31.
    Talbi, E.G.: Metaheuristics: From Design to Implementation. Wiley, Hoboken (2009)CrossRefGoogle Scholar
  32. 32.
    Tan, Y.: FWA application on non-negative matrix factorization. In: Tan, Y. (ed.) Fireworks Algorithm, pp. 247–262. Springer, Heidelberg (2015). Scholar
  33. 33.
    Thai-Nghe, N., Drumond, L., Horvath, T., Krohn-Grimberghe, A., Nanopoulos, A., Schmidt-Thieme, L.: Factorization techniques for predicting student performance. In: Educational Recommender Systems and Technologies: Practices and Challenges, pp. 129–153. IGI-Global (2012)Google Scholar
  34. 34.
    Yoo, D., Kim, J., Geem, Z.: Overview of harmony search algorithm and its applications in civil engineering. Evol. Intell. 7(1), 3–16 (2014)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Universidad de ExtremaduraBadajozSpain
  2. 2.Universidad de Playa AnchaValparaísoChile
  3. 3.Universidad Carlos III de MadridMadridSpain
  4. 4.Pontificia Universidad Católica de ValparaísoValparaísoChile

Personalised recommendations