ider (version 0.1.1)

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)

Value

Estimated global intrinsic dimension.

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.

Author

Hideitsu Hino

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.

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)