Abstract
The column subset selection problem is a well-known complex optimization problem that has a number of appealing real-world applications including network and data sampling, dimension reduction, and feature selection. There are a number of traditional deterministic and randomized heuristic algorithms for this problem. Recently, it has been tackled by a variety of bio-inspired and evolutionary methods. In this work, differential evolution, a popular and successful real-parameter optimization algorithm, adapted for fixed-length subset selection, is used to find solutions to the column subset selection problem. Its results are compared to a recent genetic algorithm designed for the same purpose.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Affenzeller, M., Winkler, S., Wagner, S., Beham, A.: Genetic Algorithms and Genetic Programming: Modern Concepts and Practical Applications. Chapman & Hall/CRC, Boca Raton (2009)
Avron, H., Boutsidis, C.: Faster subset selection for matrices and applications. SIAM J. Matrix Anal. Appl. 34(4), 1464–1499 (2013)
Balzano, L., Nowak, R., Bajwa, W.U.: Column subset selection with missing data. In: NIPS workshop on low-rank methods for large-scale machine learning (2010)
Boutsidis, C., Mahoney, M.W., Drineas, P.: An improved approximation algorithm for the column subset selection problem. In: Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 968–977. SODA ’09. Society for Industrial and Applied Mathematics, Philadelphia (2009)
Cai, D., He, X., Han, J.: Spectral regression for efficient regularized subspace learning. In: Proceedings of the International Confeence on Computer Vision (ICCV’07) (2007)
Çivril, A.: Column subset selection problem is UG-hard. J. Comput. Syst. Sci. 80(4), 849–859 (2014)
Çivril, A., Magdon-Ismail, M.: Column subset selection via sparse approximation of SVD. Theoret. Comput. Sci. 421, 1–14 (2012)
Couvreur, C., Bresler, Y.: On the optimality of the backward greedy algorithm for the subset selection problem. SIAM J. Matrix Anal. Appl. 21(3), 797–808 (2000)
Deshpande, A., Rademacher, L.: Efficient volume sampling for row/column subset selection. In: Proceedings of the 2010 IEEE 51st Annual Symposim on Foundations of Computer Science, pp. 329–338. FOCS ’10. IEEE Computer Society, Washington (2010)
dos S. Santana, L.E.A., de Paula Canuto, A.M.: Filter-based optimization techniques for selection of feature subsets in ensemble systems. Expert Syst. Appl. 41(4, Part 2), 1622–1631 (2014)
Farahat, A.K., Elgohary, A., Ghodsi, A., Kamel, M.S.: Distributed column subset selection on mapreduce. In: 2013 IEEE 13th International Conference on Data Mining (ICDM), pp. 171–180, December 2013
Farahat, A.K., Elgohary, A., Ghodsi, A., Kamel, M.S.: Greedy column subset selection for large-scale data sets. CoRR abs/1312.6838 (2013)
Farahat, A.K., Ghodsi, A., Kamel, M.S.: A fast greedy algorithm for generalized column subset selection. CoRR abs/1312.6820 (2013)
Friedberg, S.: Linear Algebra, 4th edn. Prentice-Hall Of India Pvt Limited, New Delhi (2003)
Golub, G., Van Loan, C.: Matrix Computations. Johns Hopkins Studies in the Mathematical Sciences, 3rd edn. Johns Hopkins University Press, Baltimore (1996)
Kromer, P., Platos, J.: Solving the p-median problem by a simple differential evolution. In: 2014 IEEE International Conference on Systems, Man and Cybernetics (SMC), pp. 3503–3507, October 2014
Kromer, P., Platos, J.: Genetic algorithm for sampling from scale-free data and networks. In: Proceedings of the 2014 Conference on Genetic and Evolutionary Computation, pp. 793–800. GECCO ’14. ACM, New York (2014)
Krömer, P., Platoš, J.: New genetic algorithm for the p-median problem. In: Pan, J.-S., Snasel, V., Corchado, E.S., Abraham, A., Wang, S.-L. (eds.) Intelligent Data Analysis and Its Applications, Volume II. Advances in Intelligent Systems and Computing, vol. 298, pp. 35–44. Springer, Heidelberg (2014)
Kromer, P., Snasel, V., Platos, J., Abraham, A.: Many-threaded implementation of differential evolution for the cuda platform. In: Proceedings of the 13th Annual Conference on Genetic and Evolutionary Computation, pp. 1595–1602. GECCO ’11. ACM, New York (2011)
Kromer, P., Platos, J., Snasel, V.: Genetic algorithm for the column subset selection problem. In: 2014 Eighth International Conference on Complex, Intelligent and Software Intensive Systems (CISIS), pp. 16–22, July 2014
Price, K.V., Storn, R.M., Lampinen, J.A.: Differential Evolution A Practical Approach to Global Optimization. Natural Computing Series. Springer, Berlin (2005)
Storn, R., Price, K.: Differential evolution- a simple and efficient adaptive scheme for global optimization over continuous spaces. Technical report (1995)
Tan, C.J., Lim, C.P., Cheah, Y.: A multi-objective evolutionary algorithm-based ensemble optimizer for feature selection and classification with neural network models. Neurocomputing 125, 217–228 (2014)
Acknowledgments
This work was supported by the IT4Innovations Centre of Excellence project (CZ.1.05/1.1.00/02.0070), funded by the European Regional Development Fund and the national budget of the Czech Republic via the Research and Development for Innovations Operational Programme and by Project SP2015/146 of the Student Grant System, VŠB - Technical University of Ostrava.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Krömer, P., Platoš, J. (2016). A Comparison of Differential Evolution and Genetic Algorithms for the Column Subset Selection Problem. In: Burduk, R., Jackowski, K., Kurzyński, M., Woźniak, M., Żołnierek, A. (eds) Proceedings of the 9th International Conference on Computer Recognition Systems CORES 2015. Advances in Intelligent Systems and Computing, vol 403. Springer, Cham. https://doi.org/10.1007/978-3-319-26227-7_21
Download citation
DOI: https://doi.org/10.1007/978-3-319-26227-7_21
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-26225-3
Online ISBN: 978-3-319-26227-7
eBook Packages: EngineeringEngineering (R0)