Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
권호 표지
DOI QR코드

DOI QR Code

Geographically weighted least squares-support vector machine

  • Received : 2016.12.26
  • Accepted : 2017.01.10
  • Published : 2017.01.31
Download PDF
⟨ Previous Next ⟩

Abstract

When the spatial information of each location is given specifically as coordinates it is popular to use the geographically weighted regression to incorporate the spatial information by assuming that the regression parameters vary spatially across locations. In this paper, we relax the linearity assumption of geographically weighted regression and propose a geographically weighted least squares-support vector machine for estimating geographically weighted mean by using the basic concept of kernel machines. Generalized cross validation function is induced for the model selection. Numerical studies with real datasets have been conducted to compare the performance of proposed method with other methods for predicting geographically weighted mean.

Keywords

References

  1. Anselin, L. (1992). Spatial econometrics: Method and models, Kluwer Academic Publishers, Boston.
  2. Brunsdon, C. and Fotheringham, A. S. (1999). Some notes on Parametric signi cance tests for geographically weighted regression. Journal of Regional Science, 39, 497-524. https://doi.org/10.1111/0022-4146.00146
  3. Fotheringham, A. S., Brunsdon, C. and Charlton, M. (2002). Geographically weighted regressio, John Wiley and Sons, Chichester, UK.
  4. Fotheringham, A. S., Charlton, M. E. and Brunsdon, C. (1996). The geography of parameter space: An investigation of spatial non-stationarity. International Journal of Geographical Information Science, 10, 605-627 https://doi.org/10.1080/02693799608902100
  5. Hwang, C. and Shim, J. (2016). Deep LS-SVM for regression. Journal of the Korean Data & Information Science Society, 27 827-833. https://doi.org/10.7465/jkdi.2016.27.3.827
  6. Hwang, C., Bae, J. and Shim, J. (2016). Robust varying coecient model using L1 penalized locally weighted regression. Journal of the Korean Data & Information Science Society, 27, 1059-1066. https://doi.org/10.7465/jkdi.2016.27.4.1059
  7. Kimeldorf, G. and Wahba, G. (1971). Some results on Tchebychean spline functions. Journal of Mathe-matical Analysis and Applications, 33, 82-95. https://doi.org/10.1016/0022-247X(71)90184-3
  8. Mika, S., Ratsch, G., Weston, J., Schddoto lkopf, B. and Muller, K. R. (1999). Fisher discriminant analysis with kernels. IEEE International Workshop on Neural Networks for Signal Processing IX, Madison, WI, August, 41-48.
  9. Rosenblatt, F. (1958). The perceptron: A probabilistic model for information storage and organization in the brain. Psychological Review, 65, 386-408. https://doi.org/10.1037/h0042519
  10. Salvati, N., Ranalli, M. G. and Pratesi, M. (2011). Small area estimation of the mean using non-parametric M-quantile regression: A comparison when a linear mixed model does not hold. Journal of Statistical Computation and Simulation, 81, 945-964. https://doi.org/10.1080/00949650903575237
  11. Saunders, C., Gammerman, A. and Vork, V. (1998). Ridge regression learning algorithm in dual variable. Proceedings of the 15th International Conference on Machine Learning, San Fransisco, CA, Morgan Kaufmann, 515-521.
  12. Shim, J. Kim, C. and Hwang, C. (2011). Semiparametric least squares support vector machine for accelerated failure time model. Journal of Korean Statistical Society, 40, 75-83. https://doi.org/10.1016/j.jkss.2010.05.002
  13. Smola, A. J., Friess, T. T. and Schlkopf, B. (1998). Semiparametric support vector and linear programming machines. Proceedings of the 1998 Conference on Advances in Neural Information Processing Systems, Cambridge, MA, MIT Press, 585-591.
  14. Suykens, J. A. K. and Vandewalle, J. (1999). Least squares support vector machine classiers. Neural Pro-cessing Letters, 9, 293-300. https://doi.org/10.1023/A:1018628609742
  15. Suykens, J. A. K., Vandewalle, J. and DeMoor, B. (2001). Optimal control by least squares support vector machines. Neural Networks, 14, 23-35. https://doi.org/10.1016/S0893-6080(00)00077-0
  16. Vapnik, V. (1995). The nature of statistical learning theory, Springer, Berlin.
  17. Wahba, G. (1990). Spline models for observational data, CMMS-NSF Regional Conference Series in Applied Mathematics, 59, SIAM, Philadelphia.
  18. Xu, J., Zhang, X. and Li, Y. (2001). Kernel MSE algorithm: A uni ed framework for KFD, LS-SVM. Proceedings of the International Joint Conference on Neural Networks, IJCNN 2001, Washington, DC, IEEE, 1486-1491.
  19. Zhang, L. J. (2004). Modeling spatial variation in tree diameter-height relationships. Forest Ecology and Management, 189, 317-329. https://doi.org/10.1016/j.foreco.2003.09.004

Cited by

  1. 통계적 기계학습에서의 ADMM 알고리즘의 활용 vol.28, pp.6, 2017, https://doi.org/10.7465/jkdi.2017.28.6.1229
  2. Adaptive ridge procedure for L0-penalized weighted support vector machines vol.28, pp.6, 2017, https://doi.org/10.7465/jkdi.2017.28.6.1271
  3. R의 Shiny를 이용한 시각화 분석 활용 사례 vol.28, pp.6, 2017, https://doi.org/10.7465/jkdi.2017.28.6.1279