Measuring the Local Dimension of Point Clouds

Steven P. Ellis and Maria J. Girard
Additional contact information
Steven P. Ellis: University of Rochester, Department of Statistics
Maria J. Girard: University of Rochester, Department of Statistics

A chapter in Computing Science and Statistics, 1992, pp 328-331 from Springer

Abstract: 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.

Keywords: Recursive partitioning; kernel smoother (search for similar items in EconPapers)
Date: 1992
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-2856-1_47

Ordering information: This item can be ordered from
http://www.springer.com/9781461228561

DOI: 10.1007/978-1-4612-2856-1_47

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().