Authors argue that the approach proposed in est.mle1 is empirically bias-prone in that the averaging of sample statistics over all data points is taken to be a harmonic manner.

est.mle2(X, k1 = 10, k2 = 20)

## Arguments

X

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

k1

minimum neighborhood size, larger than 1.

k2

maximum neighborhood size, smaller than $$n$$.

## Value

a named list containing containing

estdim

estimated intrinsic dimension.

## References

MacKay DJC, Ghahramani Z (2005). “Comments on 'Maximum Likelihood Estimation of Intrinsic Dimension' by E. Levina and P. Bickel (2004).” https://www.inference.org.uk/mackay/dimension/.

Kisung You

## Examples

# \donttest{
## create example data sets with intrinsic dimension 2
X1 = aux.gensamples(dname="swiss")
X2 = aux.gensamples(dname="ribbon")

## acquire an estimate for intrinsic dimension
out1 = est.mle2(X1)
out2 = est.mle2(X2)
out3 = est.mle2(X3)

line1 = paste0("* est.mle2 : dimension of 'swiss'  data is ",round(out1$estdim,2)) line2 = paste0("* est.mle2 : dimension of 'ribbon' data is ",round(out2$estdim,2))
line3 = paste0("* est.mle2 : dimension of 'saddle' data is ",round(out3\$estdim,2))
cat(paste0(line1,"\n",line2,"\n",line3))
#> * est.mle2 : dimension of 'swiss'  data is 1.99
#> * est.mle2 : dimension of 'ribbon' data is 2
#> * est.mle2 : dimension of 'saddle' data is 2.19
# }