Assuming the density in a hypersphere is constant, authors proposed to build
a likelihood structure based on modeling local spread of information via Poisson Process.
est.mle1 requires two parameters that model the reasonable range of neighborhood size
to reflect inhomogeneity of distribution across data points.
est.mle1(X, k1 = 10, k2 = 20)an \((n\times p)\) matrix or data frame whose rows are observations.
minimum neighborhood size, larger than 1.
maximum neighborhood size, smaller than \(n\).
a named list containing containing
estimated intrinsic dimension.
Levina E, Bickel PJ (2005). “Maximum Likelihood Estimation of Intrinsic Dimension.” In Saul LK, Weiss Y, Bottou L (eds.), Advances in Neural Information Processing Systems 17, 777--784. MIT Press.
# \donttest{
## create example data sets with 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.mle1(X1)
out2 = est.mle1(X2)
out3 = est.mle1(X3)
## print the estimates
line1 = paste0("* est.mle1 : 'swiss' estiamte is ",round(out1$estdim,2))
line2 = paste0("* est.mle1 : 'ribbon' estiamte is ",round(out2$estdim,2))
line3 = paste0("* est.mle1 : 'saddle' estiamte is ",round(out3$estdim,2))
cat(paste0(line1,"\n",line2,"\n",line3))
#> * est.mle1 : 'swiss' estiamte is 2.19
#> * est.mle1 : 'ribbon' estiamte is 2.31
#> * est.mle1 : 'saddle' estiamte is 2.52
# }