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Complex Function Sets Improve Symbolic Discriminant Analysis of Microarray Data

  • David M. Reif
  • Bill C. White
  • Nancy Olsen
  • Thomas Aune
  • Jason H. Moore
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2724)

Abstract

Our ability to simultaneously measure the expression levels of thousands of genes in biological samples is providing important new opportunities for improving the diagnosis, prevention, and treatment of common diseases. However, new technologies such as DNA microarrays are generating new challenges for variable selection and statistical modeling. In response to these challenges, a genetic programming-based strategy called symbolic discriminant analysis (SDA) for the automatic selection of gene expression variables and mathematical functions for statistical modeling of clinical endpoints has been developed. The initial development and evaluation of SDA has focused on a function set consisting of only the four basic arithmetic operators. The goal of the present study is to evaluate whether adding more complex operators such as square root to the function set improves SDA modeling of microarray data. The results presented in this paper demonstrate that adding complex functions to the terminal set significantly improves SDA modeling by reducing model size and, in some cases, reducing classification error and runtime. We anticipate SDA will be an important new evolutionary computation tool to be added to the repertoire of methods for the analysis of microarray data.

Keywords

Systemic Lupus Erythematosus Linear Discriminant Analysis Complex Function Classification Error Multifactor Dimensionality Reduction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Schena, M., Shalon, D., Davis, R.W., Brown, P.O.: Quantitative monitoring of gene expression patterns with a complementary DNA microarray. Science 270 (1995) 467–470CrossRefGoogle Scholar
  2. 2.
    Moore, J.H., Parker, J.S., Hahn, L.W.: Symbolic discriminant analysis for mining gene expression patterns. In: De Raedt, L., Flach, P. (eds) Lecture Notes in Artificial Intelligence 2167, pp 372–81, Springer-Verlag, Berlin (2001)Google Scholar
  3. 3.
    Moore, J.H., Parker, J.S., Olsen, N., Aune, T. Symbolic discriminant analysis of microarray data in autoimmune disease. Genetic Epidemiology 23 (2002) 57–69CrossRefGoogle Scholar
  4. 4.
    Koza, J.R.: Genetic Programming: On the Programming of Computers by Means of Natural Selection. The MIT Press, Cambridge London (1992)zbMATHGoogle Scholar
  5. 5.
    Moore, J.H., Parker, J.S.: Evolutionary computation in microarray data analysis. In: Lin, S. and Johnson, K. (eds): Methods of Microarray Data Analysis. Kluwer Academic Publishers, Boston (2001)Google Scholar
  6. 6.
    Templeton, A.R.: Epistasis and complex traits. In: Wade, M., Brodie III, B., Wolf, J. (eds.): Epistasis and Evolutionary Process. Oxford University Press, New York (2000)Google Scholar
  7. 7.
    Moore, J.H., Williams, S.M.: New strategies for identifying gene-gene interactions in hypertension. Annals of Medicine 34 (2002) 88–95CrossRefGoogle Scholar
  8. 8.
    Moore, J.H.: Cross validation consistency for the assessment of genetic programming results in microarray studies. In: Raidl, G. et al. (eds) Lecture Notes in Computer Science 2611, in press, Springer-Verlag, Berlin (2003).Google Scholar
  9. 9.
    Hastie, T., Tibshirani, R., Friedman, J.: The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer, New York (2001)zbMATHGoogle Scholar
  10. 10.
    Devroye, L., Gyorfi, L., Lugosi, G.: A Probabilistic Theory of Pattern Recognition. Springer-Verlag, New York (1996)zbMATHGoogle Scholar
  11. 11.
    Ritchie, M.D., Hahn, L.W., Roodi, N., Bailey, L.R., Dupont, W.D., Plummer, W.D., Parl, F.F. and Moore, J.H.: Multifactor dimensionality reduction reveals high-order interactions among estrogen metabolism genes in sporadic breast cancer. American Journal of Human Genetics 69 (2001) 138–147CrossRefGoogle Scholar
  12. 12.
    Fisher, R.A.: The Use of Multiple Measurements in Taxonomic Problems. Ann. Eugen. 7 (1936) 179–188Google Scholar
  13. 13.
    Johnson, R.A., Wichern, D.W.: Applied Multivariate Statistical Analysis. Prentice Hall, Upper Saddle River (1998)Google Scholar
  14. 14.
    Huberty, C.J.: Applied Discriminant Analysis. John Wiley & Sons, Inc., New York (1994)zbMATHGoogle Scholar
  15. 15.
    Neter, J., Wasserman, W., Kutner, M.H.: Applied Linear Statistical Models, Regression, Analysis of Variance, and Experimental Designs. 3rd edn. Irwin, Homewood (1990)Google Scholar
  16. 16.
    Langley, P.: Elements of Machine Learning. Morgan Kaufmann Publishers, Inc., San Francisco (1996)Google Scholar
  17. 17.
    Cantu-Paz, E.: Efficient and Accurate Parallel Genetic Algorithms. Kluwer Academic Publishers, Boston (2000)zbMATHGoogle Scholar
  18. 18.
    http://garage.cps.msu.edu/software/software-index.htmlGoogle Scholar
  19. 19.
    Fogel, G.B., Corne, D.W.: Evolutionary Computation in Bioinformatics. Morgan Kaufmann Publishers, Inc., San Francisco (2003)Google Scholar
  20. 20.
    Maas, K., Chan, S., Parker, J., Slater, A., Moore, J.H., Olsen, N., and Aune, T.M.: Cutting edge: molecular portrait of human autoimmunity. Journal of Immunology 169 (2002) 5–9Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • David M. Reif
    • 1
  • Bill C. White
    • 1
  • Nancy Olsen
    • 2
  • Thomas Aune
    • 2
  • Jason H. Moore
    • 1
  1. 1.Program in Human Genetics, Department of Molecular Physiology and BiophysicsVanderbilt UniversityNashvilleUSA
  2. 2.Program in Human Genetics, Department of MedicineVanderbilt UniversityNashvilleUSA

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