ider: convU – R documentation

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convU

Intrinsic Dimension Estimation with Convergence Property of a U-statistics.

Description

convU estimates intrinsic dimension of given dataset based on the convergence property of Ustatistics(smoothed correlation dimension) w.r.t. kernel bandwidth

Usage

convU(x, maxDim = 5, DM = FALSE)

Arguments

`x`	data matrix or distance matrix given by as.matrix(dist(x)).
`maxDim`	maximum of the candidate dimension.
`DM`	whether `'x'` is distance matrix or not. logical.

Details

A variant of fractal dimension called the correlation dimension is considered. The correlation dimension is defined by the notion of the correlation integral, which is calculated by counting the number of pairs closer than certain threshold epsilon. The counting operation is replaced with the kernel smoothed version, and based on the convergence property of the resulting U-statistics, an intrinsic dimension estimator is derived.

Value

Estimated global intrinsic dimension.

Author(s)

Hideitsu Hino hideitsu.hino@gmail.com

References

M. Hein and J-Y. Audibert. Intrinsic dimensionality estimation of submanifolds in Rd. International Conference on Machine Learning, 2005.

Examples

x <- gendata(DataName='SwissRoll',n=300)
estconvU <- convU(x=x)
print(estconvU)

ider

Various Methods for Estimating Intrinsic Dimension

v0.1.0

GPL-2

Authors

Hideitsu Hino

Initial release

2017-04-24