estimate_Ustat: ID Estimation with Convergence Rate of U-statistic on...

In Rdimtools: Dimension Reduction and Estimation Methods

ID Estimation with Convergence Rate of U-statistic on Manifold

Description

U-statistic is built upon theoretical arguments with the language of smooth manifold. The convergence rate of the statistic is achieved as a proxy for the estimated dimension by, at least partially, considering the scale and influence of extrinsic curvature. The method returns integer valued estimate in that there is no need for rounding the result for practical usage.

Usage

est.Ustat(X, maxdim = min(ncol(X), 15))

Arguments

X	an (n\times p) matrix or data frame whose rows are observations.
maxdim	maximum possible dimension allowed for the algorithm to investigate.

Value

a named list containing containing

estdim

estimated intrinsic dimension.

Author(s)

Kisung You

References

\insertRef

hein_intrinsic_2005Rdimtools

Examples

## create 3 datasets of intrinsic dimension 2.
X1 = aux.gensamples(dname="swiss")
X2 = aux.gensamples(dname="ribbon")
X3 = aux.gensamples(dname="saddle")

## acquire an estimate for intrinsic dimension
out1 = est.Ustat(X1)
out2 = est.Ustat(X2)
out3 = est.Ustat(X3)

## print the results
line1 = paste0("* est.Ustat : 'swiss'  gives ",round(out1$estdim,2))
line2 = paste0("* est.Ustat : 'ribbon' gives ",round(out2$estdim,2))
line3 = paste0("* est.Ustat : 'saddle' gives ",round(out3$estdim,2))
cat(paste0(line1,"\n",line2,"\n",line3))

Rdimtools documentation built on Nov. 5, 2025, 5:28 p.m.