Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

A Penalized Principal Component Analysis using Simulated Annealing

  • Published : 2003.12.01
Download PDF
⟨ Previous Next ⟩

Abstract

Variable selection algorithm for principal component analysis using penalty function is proposed. We use the fact that usual principal component problem can be expressed as a maximization problem with appropriate constraints and we will add penalty function to this maximization problem. Simulated annealing algorithm is used in searching for optimal solutions with penalty functions. Comparisons between several well-known penalty functions through simulation reveals that the HARD penalty function should be suggested as the best one in several aspects. Illustrations with real and simulated examples are provided.

Keywords

References

  1. Simulated Annealing and Boltzmann Machines Aarts,E.;Korst,J.
  2. Journal of the Italian Statistical Association v.6 Wavelets in Statistics : A Review Antoniadis,A. https://doi.org/10.1007/BF03178905
  3. Journal of Applied Statistics v.22 Loadings and Correlations in the Interpretation of Principal Components Cadima,J.;Jolliffe,I.T. https://doi.org/10.1080/757584614
  4. Journal of the American Statistical Association v.96 Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties Fan,J.;Li,R. https://doi.org/10.1198/016214501753382273
  5. Annals of Eugenics v.7 The use of multiple measurements in taxonomic problems Fisher,R.A. https://doi.org/10.1111/j.1469-1809.1936.tb02137.x
  6. Optimisation in Statistics Constrained Multivariate Analysis Hausman,R.;Zanckis,S.H.(ed.);Rustagi,J.S.(ed.)
  7. Applied Multivariate Statistical Analysis Johnson,R.A.;Wichern,D.W.
  8. Applied Statistics v.38 Rotation of Ill-defined Principal Components Jolliffe,I.T. https://doi.org/10.2307/2347688
  9. Journal of Applied Statistics v.22 Rotation of Principal Components: Choice of Normalization Constraints Jolliffe,I.T. https://doi.org/10.1080/757584395
  10. A Modified Principal Components Technique Based on the LASSO Jolliffe,I.T.;Uddin,M.
  11. principal component analysis Jolliffe,I.T.
  12. Science v.220 no.Issue 4598 Optimization by Simulated Annealing Kirkpatrick,S.;Gelatt,C.D.;Vecchi,M.P.
  13. A Modified Principal Component Technique Based on the LASSO Jolliffe,I.T.;Uddin,M.
  14. Applied Statistics v.21 Discarding variables in a Principal Component Analysis I : Artificial Data Jolliffe,I.T. https://doi.org/10.2307/2346488
  15. Applied Statistics v.22 Discarding variables in a Principal Component Analysis II-Real Data Jolliffe,I.T. https://doi.org/10.2307/2346300
  16. Technometrics v.26 Principal Variables McCabe,G.P. https://doi.org/10.2307/1268108
  17. Applied Statistics v.49 Simple Principal Components Vines,S.K.