Genetic Algorithm for Multidimensional Scaling over Mixed and Incomplete Data

  • P. Tecuanhuehue-Vera
  • Jesús Ariel Carrasco-Ochoa
  • José Fco. Martínez-Trinidad
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7329)

Abstract

Multidimensional scaling maps a set of n-dimensional objects into a lower-dimension space, usually the Euclidean plane, preserving the distances among objects in the original space. Most algorithms for multidimensional scaling have been designed to work on numerical data, but in soft sciences, it is common that objects are described using quantitative and qualitative attributes, even with some missing values. For this reason, in this paper we propose a genetic algorithm especially designed for multidimensional scaling over mixed and incomplete data. Some experiments using datasets from the UCI repository, and a comparison against a common algorithm for multidimensional scaling, shows the behavior of our proposal.

Keywords

Multidimensional scaling Mixed and incomplete data Genetic algorithms 

References

  1. 1.
    Cox, T.F., Cox, M.A.A.: Multidimensional Scaling. Chapman & Hall, London (1994)MATHGoogle Scholar
  2. 2.
    Kruskal, J.B.: Non metric multidimensional scaling: A numerical method. Psychometrika 29(2), 115–129 (1964)MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Tenenbaum, J.B., de Silva, V., Langford, J.C.: A global geometric framework for nonlinear dimensionality reduction. Science 290, 2319–2323 (2000)CrossRefGoogle Scholar
  4. 4.
    Roweis, S.T., Lawrence, K.S.: Nonlinear dimensionality reduction by locally linear embedding. Science 290, 2323–2326 (2000)CrossRefGoogle Scholar
  5. 5.
    An, J., Xu, Y.J., Ratanamahatana, C.A., Chen, Y.P.P.: A dimensionality reduction algorithm and its application for interactive visualization. Journal of Visual Languages and Computing 18, 48–70 (2006)MATHCrossRefGoogle Scholar
  6. 6.
    Faloutsos, C., Lin, K.L.: FastMap: A Fast Algorithm for Indexing, Data-Mining and Visualization of Traditional and Multimedia Datasets. In: ACM SIGMOD International Conference on Management of Data, pp. 163–174 (1995)Google Scholar
  7. 7.
    Shepard, R.N.: The analysis of proximities: Multidimensional scaling with an unknown distance function. Psychometrika 27(2), 125–140 (1962)MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Dijkstra, E.W.: A note on two problems in connection with graphs. Numerische Mathematik 1, 269–271 (1959)MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Kruskal, J.B.: Multidimensional scaling by optimizing goodness of fit to a non metric hypothesis. Psychometrika 29(1), 1–27 (1964)MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Takane, Y., Young, F.W., de Leeuw, J.: Non metric individual differences multidimensional scaling: An alternating least squares method with optimal scaling features. Psychometrika 42, 7–67 (1977)MATHCrossRefGoogle Scholar
  11. 11.
    Wilson, D.R., Martinez, T.: Improved heterogeneous Distance Functions. Journal of Artificial Intelligence Research (JAIR) 6(1), 1–34 (1997)MathSciNetMATHGoogle Scholar
  12. 12.
    Merz, C., Murphy, P.: UCI repository of machine learning databases. Technical report, Univ. of California at Irvine, Department of Information and Computer Science (1998)Google Scholar
  13. 13.
    Schaffer, J.D., Caruana, A.R., Eshelman, L.J., Das, R.: A Study of Control Parameters Affecting Online Performance of Genetic Algorithms for Function Optimization. In: Proceedings of the Third International Conference on Genetic Algorithms, pp. 51–60. Morgan Kaufmann Publishers, San Mateo (1989)Google Scholar
  14. 14.
    Holland, J.H.: Adaptation in Natural and Artificial Systems. MIT Press, Cambridge (1992)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • P. Tecuanhuehue-Vera
    • 1
  • Jesús Ariel Carrasco-Ochoa
    • 1
  • José Fco. Martínez-Trinidad
    • 1
  1. 1.Optics and ElectronicsNational Institute for AstrophysicsPueblaMexico

Personalised recommendations