Intrinsic Dimension Estimation by a Minimal Neighborhood Information

Unlike many intrinsic dimension (ID) estimation methods, est.twonn only requires two nearest datapoints from a target point and their distances. This extremely minimal approach is claimed to redue the effects of curvature and density variation across different locations in an underlying manifold.

est.twonn(X)

Arguments

X

an \((n\times p)\) matrix or data frame whose rows are observations.

Value

a named list containing containing

estdim

estimated intrinsic dimension.

References

Facco E, d'Errico M, Rodriguez A, Laio A (2017). “Estimating the Intrinsic Dimension of Datasets by a Minimal Neighborhood Information.” Scientific Reports, 7(1).

Author

Kisung You

Examples

# \donttest{
## 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.twonn(X1)
out2 = est.twonn(X2)
out3 = est.twonn(X3)

## print the results
line1 = paste0("* est.twonn : 'swiss'  gives ",round(out1$estdim,2))
line2 = paste0("* est.twonn : 'ribbon' gives ",round(out2$estdim,2))
line3 = paste0("* est.twonn : 'saddle' gives ",round(out3$estdim,2))
cat(paste0(line1,"\n",line2,"\n",line3))
#> * est.twonn : 'swiss'  gives 1.96
#> * est.twonn : 'ribbon' gives 2.27
#> * est.twonn : 'saddle' gives 2.09
# }