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PP Index Menu
This menu allows you to select among various projection pursuit
functions.
The "Natural Hermite" index is by constructed by comparing the
projected data density with a normal density by an L2-distance wrt
Normal measure. The projected data density and the normal density is
expanded using Hermite polynomials.
The "Holes" index is responsive to projections containing very few
data points in the center.
The "Central Mass" index is responsive to projections containing a
heavy concentration of mass in the center.
The "Skewness" index is responsive to projections exhibiting skewness.
See Cook, Buja, Cabrera (JCGS, 1993a,b) for more details on the above
indices.
The "Legendre" index is constructed by inverting the density through a
normal cdf, and then comparing the resultant density with that of a
Unif[-1,1] using an L2-distance. Legendre polynomials are used to
expand the unknown data density. This is a good general index, and
fast to compute. This index was proposed by Friedman (JASA, 1987).
The "Hermite" index is constructed using Hermite polynomials for the
expansion. The data density is compared to a standard normal density
using an L2-distance wrt Lebesgue measure. This index works best when
few terms are used in the expansion. The idea of using Hermite
polynomials instead of Legendre was proposed by Hall (Ann. Stat.,
1989).
The "Friedman-Tukey" index is similar to the original projection
pursuit index proposed by Friedman and Tukey in 1974. It is based on
an L2-norm of a local kernel density estimate.
The "Entropy" index is an extension of the Friedman-Tukey index in
that it is constructed by the negative entropy of a kernel density
estimate. This index was proposed by Jones, in his PhD thesis, Bath,
1983.
"Binned Friedman-Tukey" and "Binned Entropy" are the same as the last
two indices except they are computed faster because binning is used for
the kernel density estimate.
In the indices based on kernel methods the size of the bandwidth is
drawn in relation to the data on the plot window when the tour is
paused.
For further information we'll direct you to "Direction and Motion
Control in the Grand Tour," by Cook, Buja, and Cabrera, available as a
Bellcore Technical Memorandum or in the proceedings of the 1991
Interface conference. Also there is an Iowa State University preprint
"Grand Tour and Projection Pursuit" by Cook, Buja, Cabrera (1993), and a
forthcoming Institute of Statistics, Catholic University of Louvain,
Belgium, Technical Report "Improvement of Computational Speed for
Kernel-based Indices in XGobi" by Klinke and Cook.
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