pack {ider}

Intrinsic Dimension Estimation Using Packing Numbers.

Description

pack estimates intrinsic dimension of given dataset based on the packing number.

Usage

pack(x, k1 = NULL, k2 = NULL, greedy = TRUE, eps = 0.01, DM = FALSE)

Arguments

x

data matrix or distance matrix given by as.matrix(dist(x)).

k1

first radius parameter. If one of k1 or k2 is NULL, then both are automatically determined from the input data.

k2

second radius parameter.

greedy

logical. If TRUE, then a greedy algorithm is used for estimating the packing number. If FALSE, then a hierarchical clustering algorithm is used instead.

eps

accuracy parameter.

DM

whether 'x' is distance matrix or not. logical.

Details

A variant of fractal dimension called the capacity dimension is considered. The capacity dimension is defined by using the notion of covering number, which is hard to calculate in general. In this function, the packing number of the data space is used as the surrogate of the covering number. The packing number is estimated by greedy manner or by hierarchical clustering.

Value

Estimated global intrinsic dimension.

Author(s)

Hideitsu Hino [e-mail]

References

B. Kegl. Intrinsic dimension estimation using packing numbers. Advances in Neural Information Processing Systems 15, 2002.

B. Eriksson and M. Crovella. Estimating intrinsic dimension via clustering. IEEE Statistical Signal Processing Workshop, 2012.

Examples

x <- gendata(DataName='SwissRoll',n=300)
estpackG <- pack(x=x,greedy=TRUE)  ## estimate the packing number by greedy method
print(estpackG)
estpackC <- pack(x=x,greedy=FALSE) ## estimate the packing number by cluttering
print(estpackC)