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Measuring the Local Dimension of Point Clouds

In: Computing Science and Statistics

Author

Listed:
  • Steven P. Ellis

    (University of Rochester, Department of Statistics)

  • Maria J. Girard

    (University of Rochester, Department of Statistics)

Abstract

A technique which measures the dimension of a point cloud in the vicinity of each observation in a multivariate data set is discussed. The basic idea is as follows. First, each observation is taken in turn as the center of a ball. A formula inspired by a stochastic model is applied to the observations contained in the ball. The result is a “raw” local dimension for the observation at the center. The raw dimensions are then smoothed, either by kernel smoothing or recursive partitioning. By measuring dimension locally, low-dimensional structure in the data can be recognized even if it is nonlinear.

Suggested Citation

  • Steven P. Ellis & Maria J. Girard, 1992. "Measuring the Local Dimension of Point Clouds," Springer Books, in: Connie Page & Raoul LePage (ed.), Computing Science and Statistics, pages 328-331, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-2856-1_47
    DOI: 10.1007/978-1-4612-2856-1_47
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