Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

Functional Data Classification of Variable Stars

  • Park, Minjeong (Statistical Research Institute, Statistics Korea) ;
  • Kim, Donghoh (Department of Applied Mathematics, Sejong University) ;
  • Cho, Sinsup (Department of Statistics, Seoul National University) ;
  • Oh, Hee-Seok (Department of Statistics, Seoul National University)
  • Received : 2013.02.27
  • Accepted : 2013.07.12
  • Published : 2013.07.31
Download PDF
⟨ Previous Next ⟩

Abstract

This paper considers a problem of classification of variable stars based on functional data analysis. For a better understanding of galaxy structure and stellar evolution, various approaches for classification of variable stars have been studied. Several features that explain the characteristics of variable stars (such as color index, amplitude, period, and Fourier coefficients) were usually used to classify variable stars. Excluding other factors but focusing only on the curve shapes of variable stars, Deb and Singh (2009) proposed a classification procedure using multivariate principal component analysis. However, this approach is limited to accommodate some features of the light curve data that are unequally spaced in the phase domain and have some functional properties. In this paper, we propose a light curve estimation method that is suitable for functional data analysis, and provide a classification procedure for variable stars that combined the features of a light curve with existing functional data analysis methods. To evaluate its practical applicability, we apply the proposed classification procedure to the data sets of variable stars from the project STellar Astrophysics and Research on Exoplanets (STARE).

Keywords

References

  1. Akerlof, C., Alcock, C., Allsman, R., Axelrod, T., Bennett, D. P., Cook, K. H., Freeman, K., Griest, K., Marshall, S., Park, H.-S., Perlmutter, S., Peterson, B., Quinn, P., Reimann, J., Rodgers, A., Stubbs, C. W. and Sutherland, W. (1994). Application of cubic splines to the spectral analysis of unequally spaced data, The Astrophysical Journal, 436, 787-794. https://doi.org/10.1086/174954
  2. Biau, G., Bunea, F. and Wegkamp, M. H. (2005). Functional classification in Hilbert spaces, IEEE Transactions on Information Theory, 51, 2163-2172. https://doi.org/10.1109/TIT.2005.847705
  3. Blomme, J., Debosscher, J., De Ridder, J., Aerts, C., Gilliand, R. L., Christensen-Dalsgaard, J., Kjeldsen, H., Brown, T. M., Borucki,W. J., Koch, D., Jenkins, J. M., Kurtz, D.W., Stello, D., Stevens, I. R. and Suran, M. D. (2010). Automated classification of variable stars in the asteroseismology program of the Kepler space mission, The Astrophysical Journal Letters, 713, L204-L207. https://doi.org/10.1088/2041-8205/713/2/L204
  4. Clarkson, D., Fraley, C., Gu, C. C. and Ramsay, J. O. (2005). S+ Functional Data Analysis: User's Manual for Windows, Springer.
  5. Deb, S. and Singh, H. P. (2009). Light curve analysis of variable stars using Fourier decomposition and principal component analysis, Astronomy & Astrophysics, 507, 1729-1737. https://doi.org/10.1051/0004-6361/200912851
  6. Debosscher, J., Sarro, L. M., Aerts, C., Cuypers, J., Vandenbussche, B., Garrido, R. and Solano, E. (2008). Automated supervised classification of variable stars I. Methodology, Astronomy & Astrophysics Manuscript No. 7638.
  7. Deeming, T. J. (1975). Fourier analysis with unequally-spaced data, Astrophysical and Space Science, 36, 137-158. https://doi.org/10.1007/BF00681947
  8. Dwortesky, M. M. (1983). A period-finding method for sparse randomly spaced observations or "How long is a piece of string ?", Monthly Notices of the Royal Astronomical Society, 203, 917-924. https://doi.org/10.1093/mnras/203.4.917
  9. Ferraty, F. and Vieu, P. (2003). Curves discrimination: A nonparametric functional approach, Com-putational Statistics and Data Analysis, 44, 161-173. https://doi.org/10.1016/S0167-9473(03)00032-X
  10. Friedman, J. H. (1984). A variable span smoother, Technical report No. 5. Laboratory for Computa-tional Statistics, Department of Statistics, Stanford University.
  11. Hall, P., Reimann, J. and Rice, J. (2000). Nonparametric estimation of a periodic function, Biometrika, 87, 545-557. https://doi.org/10.1093/biomet/87.3.545
  12. Hall, P., Poskitt, D. S. and Presnell, B. (2001). A functional data-analytic approach to signal discrimination, Technometircs, 43, 1-9. https://doi.org/10.1198/00401700152404273
  13. Hegland, M., Clarke, W. and Kahn, M. (2001). Mining the MACHO dataset, Computer Physics Communications, 142, 22-28. https://doi.org/10.1016/S0010-4655(01)00307-1
  14. Lafler, J. and Kinman, T. D. (1965). An RR Lyrae survey with the Lick 20-inch astrograph II. The cal-culation of RR Lyrae periods by electronic computer, Astrophysical Journal Supplement Series, 11, 216-222. https://doi.org/10.1086/190116
  15. Lomb, N. R. (1976). Least-squares frequency analysis of unequally spaced data, Astrophysical and Space Science, 39, 447-462. https://doi.org/10.1007/BF00648343
  16. Oh, H.-S., Nychka, D., Brown, T. and Charbonneau, P. (2004). Period analysis of variable stars by robust smoothing, Journal of the Royal Statistical Society Series C, 53, 15-30. https://doi.org/10.1111/j.1467-9876.2004.00423.x
  17. Ramsay, J. O. and Silverman, B. W. (2002). Applied Functional Data Analysis, Springer, New York.
  18. Ramsay, J. O. and Silverman, B. W. (2005). Functional Data Analysis, 2nd ed, Springer, New York.
  19. Ramsay, J. O., Hooker, G. and Graves, S. (2009). Functional Data Analysis with R and MATLAB, Springer, Dordrecht.
  20. Reimann, J. D. (1994). Frequency Estimation Using Unequally-Spaced Astronomical Data, Ph.D. thesis, Department of Statistics, University of California at Berkeley.
  21. Rossi, F. and Villa, N. (2006). Support vector machine for functional data classification, Neurocomputing, 69, 730-742. https://doi.org/10.1016/j.neucom.2005.12.010
  22. Sarro, L., Debosscher, J. M., Lopez, M. and Aerts, C. (2009). Automated supervised classification of variable stars II. Application to the OGLE database, Astronomy & Astrophysics, 494, 739-768. https://doi.org/10.1051/0004-6361:200809918
  23. Scargle, J. D. (1982). Studies in astronomical time series analysis II. Statistical aspects of spectral analysis of unevenly spaced data, Astrophysical Journal, 263, 835-853. https://doi.org/10.1086/160554
  24. Stellingwerf, R. F. (1978). Period determination using phase dispersion minimization, Astrophysical Journal, 224, 953-960. https://doi.org/10.1086/156444
  25. Usatov, M. and Nosulchik, A. (2008). The extended catalog of red AGB variable stars found in the NSVS database, Open European Journal of Variable Stars.
  26. Willemsen, P. G. and Eyer, L. (2005). A study of supervised classification of Hipparcos variable stars using PCA and support vector machines, Manuscript.
  27. Wozniak, P. R., Williams, S. J., Vestrand, W. T. and Gupta, V. (2004). Identifying red variables in the northern sky variability survey, The Astronomical Journal, 128, 2965-2976. https://doi.org/10.1086/425526