Dimension Reduction and Selection of Landmarks

A Monte Carlo Experiment
  • Dmitri A. Rusakov
Part of the NATO ASI Series book series (NSSA, volume 284)


A methodology of discarding landmarks that convey little shape and size information and is based on principal component analysis is considered. A sample of 100 two-dimensional “forms” described by five landmarks (three independent and two linearly dependent, with an independent perturbation component) is simulated. It is shown that the essential dimensionality of such data sets can be revealed by comparing eigenvalues of the data correlation matrix (PC values). A simple criterion to select the optimal landmark subset that uses raw data and minimizes the variance between PCs values is suggested.


Dimension Reduction Simple Criterion Size Information Landmark Position Fitted Form 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bookstein, F. L. 1984. A statistical method for biological shape comparison. Journal of Theoretical Biology 107: 475–520.PubMedCrossRefGoogle Scholar
  2. Bookstein, F. L. 1986. Size and shape spaces for landmark data in two dimensions (with discussion and rejoinder). Statistical Science 1: 181–242.CrossRefGoogle Scholar
  3. Bookstein, F. L. 1991. Morphometric tools for landmark data: Geometry and biology. Cambridge University Press: Cambridge.Google Scholar
  4. Bliss, T. V. P. and G. Collingridge. 1993. A synaptic model of memory: long-term potentiation in the hippocampus. Nature 361: 31–39.PubMedCrossRefGoogle Scholar
  5. Dryden, I. L. and K. V. Mardia. 1992. Size and shape analysis of landmark data. Biometrika 79: 57–68.CrossRefGoogle Scholar
  6. Goodall, C. 1991. Procrustes methods in the statistical analysis of shape (with discussion and rejoinder). Journal of the Royal Statistical Society, Series B, 53: 285–339.Google Scholar
  7. Goodall,C. R. and K. V. Mardia. 1991. A geometrical derivation of the shape density. Advances in Applied Probability 23: 496–514.CrossRefGoogle Scholar
  8. Goodwin, B. C., S. Kauffman, and J. D. Murray. 1993. Is morphogenesis an intrinsically robust process? Journal of Theoretical Biology 163: 135–144.PubMedCrossRefGoogle Scholar
  9. Jolliffe, I. T. 1972. Discarding variables in a principal component analysis. I: Artificial data. Applied Statistics 21: 160–173.CrossRefGoogle Scholar
  10. Kendall, D. G. 1989. A survey of the statistical theory of shape. Statistical Science 4: 87–120.CrossRefGoogle Scholar
  11. Krzanowski, W. J. I987a. Cross-validation in principal component analysis. Biometrics 43: 575–584.CrossRefGoogle Scholar
  12. Krzanowski, W. J. 1987b. Selection of variables to preserve multivariate data structure, using principal components. Applied Statistics 36: 22–33.CrossRefGoogle Scholar
  13. McCabe, G. P. 1984. Principal variables. Technometrics 26: 137–144.CrossRefGoogle Scholar
  14. Mardia, K. V., J. T. Kent and J. M. Bibby. 1979. Multivariate analysis. Academic press: London:Google Scholar
  15. Reyment, R. A. 1990. Reification of classical multivariate statistical analysis in morphometry. Pages 123–144 in F. J. Rohlf and F. L. Bookstein, (eds.), Proceeding of the Michigan morphometric workshop. University of Michigan Museum of Zoology Special Publication 2.Google Scholar
  16. Reyment, R. A. 1991. Multidimensional palaeobiology. Pergamon Press: Oxford.Google Scholar
  17. Rohlf, F. J. 1990. Morphometrics. Annual Review of Ecology and Systematics 21: 299–3 16.CrossRefGoogle Scholar
  18. Rohlf, F. J. and L. F. Marcus. 1993. A revolution in morphometrics. Trends in Ecology and Evolution 8: 129–132.CrossRefGoogle Scholar
  19. Rusakov, D. A. 1993a. Estimation of the size distribution of closed cell elements from analysis of their plane random sections. Biometrics 49: 141–149.CrossRefGoogle Scholar
  20. Rusakov, D. A. 1993b. Quantal behaviour of synaptic transmission can be statistically examined using the Fourier line spectrum of the histogram of synaptic potentials. Neuroscience Letters 163: 231–234.PubMedCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • Dmitri A. Rusakov
    • 1
  1. 1.The Open UniversityMilton KeynesUK

Personalised recommendations