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Burning Sage: Reversing the Curse of Dimensionality in the Visualization of High-Dimensional Data

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Listed:
  • Ursula Laa
  • Dianne Cook
  • Stuart Lee

Abstract

In high-dimensional data analysis the curse of dimensionality reasons that points tend to be far away from the center of the distribution and on the edge of highdimensional space. Contrary to this, is that projected data tends to clump at the center. This gives a sense that any structure near the center of the projection is obscured, whether this is true or not. A transformation to reverse the curse, is defined in this paper, which uses radial transformations on the projected data. It is integrated seamlessly into the grand tour algorithm, and we have called it a burning sage tour, to indicate that it reverses the curse. The work is implemented into the tourr package in R. Several case studies are included that show how the sage visualizations enhance exploratory clustering and classification problems.

Suggested Citation

  • Ursula Laa & Dianne Cook & Stuart Lee, 2020. "Burning Sage: Reversing the Curse of Dimensionality in the Visualization of High-Dimensional Data," Monash Econometrics and Business Statistics Working Papers 36/20, Monash University, Department of Econometrics and Business Statistics.
    • Handle: RePEc:msh:ebswps:2020-36
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    File URL: https://www.monash.edu/business/ebs/research/publications/ebs/wp36-2020.pdf
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    References listed on IDEAS

    as
    1. Peter Hall & J. S. Marron & Amnon Neeman, 2005. "Geometric representation of high dimension, low sample size data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(3), pages 427-444, June.
    2. Wickham, Hadley & Cook, Dianne & Hofmann, Heike & Buja, Andreas, 2011. "tourr: An R Package for Exploring Multivariate Data with Projections," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 40(i02).
    3. Jeongyoun Ahn & J. S. Marron, 2010. "The maximal data piling direction for discrimination," Biometrika, Biometrika Trust, vol. 97(1), pages 254-259.
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