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Signomial Classification Method with 0-regularization

L0-정규화를 이용한 Signomial 분류 기법

  • Lee, Kyung-Sik (Department of Industrial and Management Engineering, Hankuk University of Foreign Studies)
  • 이경식 (한국외국어대학교 산업경영공학과)
  • Received : 2011.02.06
  • Accepted : 2011.02.21
  • Published : 2011.06.01

Abstract

In this study, we propose a signomial classification method with 0-regularization (0-)which seeks a sparse signomial function by solving a mixed-integer program to minimize the weighted sum of the 0-norm of the coefficient vector of the resulting function and the $L_1$-norm of loss caused by the function. $SC_0$ gives an explicit description of the resulting function with a small number of terms in the original input space, which can be used for prediction purposes as well as interpretation purposes. We present a practical implementation of $SC_0$ based on the mixed-integer programming and the column generation procedure previously proposed for the signomial classification method with $SL_1$-regularization. Computational study shows that $SC_0$ gives competitive performance compared to other widely used learning methods for classification.

Keywords

References

  1. Brieman, L., Friedman, J., Olshen, R., and Stone, C. (1984), Classication and Regression Trees, Chapman and Hall.
  2. Burges, C. J. C. (1998), A Tutorial on Support Vector Machines for Pattern Recognition, Data Mining and Knowledge Discovery, 2, 121-167. https://doi.org/10.1023/A:1009715923555
  3. Chang, C. C. and Lin, C. J. (2001), LIBSVM : a library for support vector machines, http://www.csie.ntu.edu.tw/-cjlin/libsvm.
  4. Chavatal, V. (1993), Linear Programming, W. H. Freeman and Company.
  5. Gunn, S. R. (1998), Support Vector Machines for Classification and Regression, Technical Report of School of Electronics and Computer Science, University of Southampton.
  6. Hosmer, T. and Lemeshow, S. (2000), Applied logistic regression, John Wiley and Sons.
  7. Jeong, Y., Lee, C., Kim, N., and Lee, K. (2010), Remote health monitoring Parkinson's disease severity using signomial regression model, IE Interfaces, 23, 365-371.
  8. Kim, H. and Loh, W. Y. (2001), Classification tree with unbiased multiway splits, Journal of American Stattistical Association, 96, 598-604.
  9. Lee, K., Kim, N., and Jeong, M. (2010), Sparse Signomial Classification and Regression, RUTCOR Research Reports.
  10. Matlab statistics toolbox (2008), http://www.mathworks.com.
  11. Murphy, P. M. and Aha, D. W. (1992), UCI Machine Learning Repository, http://archive.ics.uci.edu/ml/.
  12. Vapnik, V. N. (1995), The Nature of Statistical Learning Theory, Springer.
  13. Xpress (2010), http://www.fico.com.