mada {ider}

Manifold-Adaptive Local Dimension Estimation.

Description

mada estimates local information dimension of given dataset based on the first order expansion of probability mass function.

Usage

mada(x, k = NULL, comb = "average", DM = FALSE, local = FALSE, maxDim = 5)

Arguments

x

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

k

k-NN parameter.

comb

'average', 'median' or 'vote' for combining local estimates when global estimate is required.

DM

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

local

logical. If TRUE, a vector of local dimensions at each sample point is returned.

maxDim

maximum of the candidate dimensions.

Details

A variant of fractal dimension called the local information dimension is considered. The local information dimension is estimated by using the probability mass function. The function mada considers first order expansion of the probability mass around the inspection point, and it estimates the local information dimension by using two different radii from the inspection point.

Value

Estimated local or global intrinsic dimension.

Author(s)

Hideitsu Hino [e-mail]

References

A. M. Farahmand, C. Szepesvari and J-Y. Audibert. Manifold-adaptive dimension estimation. International Conference on Machine Learning, 2007.

Examples

## local intrinsic dimension estimate
tmp <- gendata(DataName='ldbl',n=300)
x <- tmp$x
estmada <- mada(x=x,local=TRUE)
head(estmada)  ## estimated local intrinsic dimensions by mada
head(tmp$tDim) ## true local intrinsic dimensions