Skip to main content
SpringerLink
Log in

Reduction of Dimension and Size of Data Set by Parallel Fast Simulated Annealing

  • Chapter
  • First Online:
Issues and Challenges of Intelligent Systems and Computational Intelligence

Part of the book series: Studies in Computational Intelligence ((SCI,volume 530))

  • 575 Accesses

Abstract

A universal method of dimension and sample size reduction, designed for exploratory data analysis procedures, constitutes the subject of this paper. The dimension is reduced by applying linear transformation, with the requirement that it has the least possible influence on the respective locations of sample elements. For this purpose an original version of the heuristic Parallel Fast Simulated Annealing method was used. In addition, those elements which change the location significantly as a result of the transformation, may be eliminated or assigned smaller weights for further analysis. As well as reducing the sample size, this also improves the quality of the applied methodology of knowledge extraction. Experimental research confirmed the usefulness of the procedure worked out in a broad range of problems of exploratory data analysis such as clustering, classification, identification of outliers and others.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover 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

Institutional subscriptions

Notes

  1. 1.

    Particular coordinates of a random variable of course constitute one-dimensional random variables and if the probabilistic aspects are not the subject of research, then in data analysis these variables are given the terms “feature” or “attribute”.

References

  1. Gendreau, M., Potvin, J.-Y.: Handbook of Metaheuristics. Springer, New York (2010)

    Book  MATH  Google Scholar 

  2. Francois, D., Wertz, V., Verleysen, M.: The concentration of fractional distances. IEEE Trans. Knowl. Data Eng. 19, 873–886 (2007)

    Article  Google Scholar 

  3. Xu, R., Wunsch, D.C.: Clustering. Wiley, New Jersey (2009)

    Google Scholar 

  4. van der Maaten, L.J.P.: Feature extraction from visual data. Ph.D. thesis, Tilburg University (2009)

    Google Scholar 

  5. Bartenhagen, C., Klein, H.-U., Ruckert, C., Jiang, X., Dugas, M.: Comparative study of unsupervised dimension reduction techniques for the visualization of microarray gene expression data. BMC Bioinformatics, 11, paper no 567 (2010)

    Google Scholar 

  6. Yan, S., Xu, D., Zhang, B., Zhang, H.-J., Yang, Q., Lin, S.: Graph embedding and extensions: a general framework for dimensionality reduction. IEEE Trans. Pattern Anal. Mach. Intell. 29, 40–51 (2007)

    Article  Google Scholar 

  7. Rodriguez-Martinez, E., Goulermas, J.Y., Tingting, M., Ralph, J.F.: Automatic induction of projection pursuit indices. IEEE Trans. Neural Netw. 21, 1281–1295 (2010)

    Article  Google Scholar 

  8. Han, J., Kamber, M.: Data Mining: Concepts and Techniques. Morgan Kaufmann, San Francisco (2006)

    Google Scholar 

  9. Kulczycki, P., Kowalski, P.A.: Bayes classification of imprecise information of interval type. Control Cybern. 40, 101–123 (2011)

    MathSciNet  Google Scholar 

  10. Wilson, D.R., Martinez, T.R.: Reduction techniques for instance-based learning algorithms. Mach. Learn. 38, 257–286 (2000)

    Article  MATH  Google Scholar 

  11. Kulczycki, P.: Estymatory jadrowe w analizie systemowej. WNT, Warsaw (2005)

    Google Scholar 

  12. Wand, M.P., Jones, M.C.: Kernel Smoothing. Chapman and Hall, London (1995)

    Book  MATH  Google Scholar 

  13. Deng, Z., Chung, F.-L., Wang, S.: FRSDE: fast reduced set density estimator using minimal enclosing ball approximation. Pattern Recogn. 41, 1363–1372 (2008)

    Article  MATH  Google Scholar 

  14. Saxena, A., Pal, N.R., Vora, M.: Evolutionary methods for unsupervised feature selection using Sammon’s stress function. Fuzzy Inform. Eng. 2, 229–247 (2010)

    Article  Google Scholar 

  15. Sammon, J.W.: A nonlinear mapping for data structure analysis. IEEE Trans. Comput. 18, 401–409 (1969)

    Article  Google Scholar 

  16. Strickert, M., Teichmann, S., Sreenivasulu, N., Seiffert, U.: ‘DIPPP’ online self-improving linear map for distance-preserving data analysis. 5th Workshop on Self-Organizing Maps (WSOM), Paris, 5–8 September 2005, pp. 661–668 (2005)

    Google Scholar 

  17. Vanstrum, M.D., Starks, S.A.: An algorithm for optimal linear maps. Southeastcon Conference, Huntsville, 5–8 April 1981, pp. 106–110 (1981)

    Google Scholar 

  18. Cox, T.F., Cox, M.A.A.: Multidimensional Scaling. Chapman and Hall, Boca Raton (2000)

    Google Scholar 

  19. Pal, S.K., Mitra, P.: Pattern Recognition Algorithms for Data Mining. Chapman and Hall, Boca Raton (2004)

    Book  MATH  Google Scholar 

  20. Mitra, P., Murthy, C.A., Pal, S.K.: Density-based multiscale data condensation. IEEE Trans. Pattern Anal. Mach. Intell. 24, 734–747 (2002)

    Article  Google Scholar 

  21. Geman, S., Geman, D.: Stochastic relaxation, Gibbs distribution and the Bayesian restoration in images. IEEE Trans. Pattern Anal. Mach. Intell. 6, 721–741 (1984)

    Article  MATH  Google Scholar 

  22. Szu, H., Hartley, R.: Fast simulated annealing. Phys. Lett. A 122, 157–162 (1987)

    Article  Google Scholar 

  23. Ingber, L.: Adaptive simulated annealing (ASA): lessons learned. Control Cybern. 25, 33–54 (1996)

    MATH  Google Scholar 

  24. Nam, D., Lee, J.-S., Park, C.H.: N-dimensional Cauchy neighbor generation for the fast simulated annealing. IEICE Trans. Inf. Syst. E87–D, 2499–2502 (2004)

    Google Scholar 

  25. Aarts, E.H.L., Korst, J.H.M., van Laarhoven, P.J.M.: Simulated annealing. In: Aarts, E.H.L., Lenstra, J.K. (eds.) Local Search in Combinatorial Optimization. Wiley, Chichester (1997)

    Google Scholar 

  26. Ben-Ameur, W.: Computing the initial temperature of simulated annealing. Comput. Optim. Appl. 29, 367–383 (2004)

    Article  MathSciNet  Google Scholar 

  27. Kuo, Y.: Using simulated annealing to minimize fuel consumption for the time-dependent vehicle routing problem. Comput. Ind. Eng. 59, 157–165 (2010)

    Article  Google Scholar 

  28. Mesgarpour, M., Kirkavak, N., Ozaktas, H.: Bicriteria scheduling problem on the two-machine flowshop using simulated annealing. Lect. Notes Comput. Sci. 6022, 166–177 (2010)

    Article  MathSciNet  Google Scholar 

  29. Sait, S.M., Youssef, H.: Iterative Computer Algorithms with Applications in Engineering: Solving Combinatorial Optimization Problems. IEEE Computer Society Press, Los Alamitos (2000)

    Google Scholar 

  30. Bartkute, V., Sakalauskas, L.: Statistical inferences for termination of Markov type random search algorithms. J. Optim. Theory Appl. 141, 475–493 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  31. David, H.A., Nagaraja, H.N.: Order Statistics. Wiley, New York (2003)

    Book  MATH  Google Scholar 

  32. Zhigljavsky, A., Zilinskas, A.: Stochastic Global Optimization. Springer-Verlag, Berlin (2008)

    MATH  Google Scholar 

  33. Azencott, R.: Simulated Annealing: Parallelization Techniques. Wiley, New York (1992)

    MATH  Google Scholar 

  34. Alba, E.: Parallel Metaheuristics: A New Class of Algorithms. Wiley, New York (2005)

    Book  Google Scholar 

  35. Kendall, M.G., Stuart, A.: The Advanced Theory of Statistics; Vol. 2: Inference and Relationship. Griffin, London (1973)

    MATH  Google Scholar 

  36. Borg, I., Groenen, P.J.F.: Modern Multidimensional Scaling. Theory and Applications. Springer-Verlag, Berlin (2005)

    MATH  Google Scholar 

  37. Camastra, F.: Data dimensionality estimation methods: a survey. Pattern Recogn. 36, 2945–2954 (2003)

    Article  MATH  Google Scholar 

  38. Kerdprasop, K., Kerdprasop, N., Sattayatham, P.: Weighted k-means for density-biased clustering. Lect. Notes Comput. Sci. 3589, 488–497 (2005)

    Article  Google Scholar 

  39. Parvin, H., Alizadeh, H., Minati, B.: A modification on k-nearest neighbor classifier. Glob. J. Comput. Sci. Technol. 10, 37–41 (2010)

    Google Scholar 

  40. Łukasik, S.: Algorytm redukcji wymiaru i licznosci proby dla celow procedur eksploracyjnej analizy danych. Ph.D. thesis, Systems Research Institute, Polish Academy of Sciences (2012)

    Google Scholar 

  41. Kulczycki, P., Łukasik, S.: An algorithm for reducing dimension and size of sample for data exploration procedures. In press (2014)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Systems Research Institute, Centre of Information Technology for Data Analysis Methods, Polish Academy of Sciences, Warsaw, Poland

    Piotr Kulczycki & Szymon Łukasik

  2. Department of Automatic Control and Information Technology, Cracow University of Technology, Cracow, Poland

    Piotr Kulczycki & Szymon Łukasik

Authors
  1. Piotr Kulczycki
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Szymon Łukasik
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Piotr Kulczycki .

Editor information

Editors and Affiliations

  1. Department of Automation, Széchenyi István University, Győr, Hungary

    László T. Kóczy

  2. Department of Information Technology, Széchenyi István University, Győr, Hungary

    Claudiu R. Pozna

  3. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Janusz Kacprzyk

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Kulczycki, P., Łukasik, S. (2014). Reduction of Dimension and Size of Data Set by Parallel Fast Simulated Annealing. In: Kóczy, L., Pozna, C., Kacprzyk, J. (eds) Issues and Challenges of Intelligent Systems and Computational Intelligence. Studies in Computational Intelligence, vol 530. Springer, Cham. https://doi.org/10.1007/978-3-319-03206-1_19

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-03206-1_19

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-03205-4

  • Online ISBN: 978-3-319-03206-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation