Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Arrow Diagrams for Kernel Principal Component Analysis

  • Received : 2013.02.06
  • Accepted : 2013.04.08
  • Published : 2013.05.31
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Abstract

Kernel principal component analysis(PCA) maps observations in nonlinear feature space to a reduced dimensional plane of principal components. We do not need to specify the feature space explicitly because the procedure uses the kernel trick. In this paper, we propose a graphical scheme to represent variables in the kernel principal component analysis. In addition, we propose an index for individual variables to measure the importance in the principal component plane.

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References

  1. Gabriel, K. R. (1971). The biplot display of matrices with the application to principal component analysis, Biometrika, 58, 453-467. https://doi.org/10.1093/biomet/58.3.453
  2. Hastie, T., Tibshirani, R. and Friedman, J. (2009). The Elements of Statistical Learning, Second Edition, Springer, New York.
  3. Karatzoglou, A., Smola, A., Hornik, K. and Zeileis, A. (2004). 'kernlab' - An S4 package for kernel methods in R, Journal of Statistical Software, 11, 1-20.
  4. Karatzoglou, A., Smola, A. and Hornik, K. (2012). R Package 'kernlab' (Version 0.9-15), http://cran.r-project.org/
  5. Scholkopf, B., Smola, A. and Muller, K. R. (1998). Nonlinear component analysis as a kernel eigenvalue problem, Neural Computation, 10, 1299-1319. https://doi.org/10.1162/089976698300017467

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  1. SVM-Guided Biplot of Observations and Variables vol.20, pp.6, 2013, https://doi.org/10.5351/CSAM.2013.20.6.491
  2. Global and Local Views of the Hilbert Space Associated to Gaussian Kernel vol.21, pp.4, 2014, https://doi.org/10.5351/CSAM.2014.21.4.317