ider (version 0.1.1)

side: Higher-order Local Information Dimension Estimator.

Description

side is a Higher-order Information Dimension Estimator, which estimates local information dimension of given dataset based on the polynomial regression with Poisson error structure.

Usage

side(
  x,
  maxDim = 5,
  DM = FALSE,
  local = FALSE,
  method = "disc",
  comb = "average"
)

Value

Estimated local or global intrinsic dimension.

Arguments

x

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

maxDim

maximum of the candidate dimensions.

DM

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

local

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

method

algorithm to estimate intrinsic dimension. 'disc' for discrite dimension estimation. 'cont' for continuous dimension estimation with MLE by Newton-method.

comb

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

Author

Hideitsu Hino

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 side considers higher-order expansion of the probability mass around the inspection point, and it estimates the local information dimension by fitting a generalized linear model with Poisson error structure and an identity link function. There are two methods for dimension estimation: the first method tries different dimensions and adopt the one with maximum likelihood, while the second method directly maximises the likelihood with respect to the intrinsic dimension. The former returns an integer-valued dimension estimate, and the latter returns a real-valued estimate. The result of the former method is used as an initial value for the latter method in numerical optimization. Slow but more accurate than mada in some cases.

References

H. Hino, J. Fujiki, S. Akaho, and N. Murata, 'Local Intrinsic Dimension Estimation by Generalized Linear Modeling', Neural Computation, 2017

Examples

## local intrinsic dimension estimate
tmp <- gendata(DataName='ldbl', n=300)
x <- tmp$x
set.seed(999)
idx <- c(sample(which(tmp$tDim==1)[1:10],3), sample(which(tmp$tDim==2)[1:30],3))
estmada <- mada(x=x[1:100,], local=TRUE)
estmada[idx]  ## estimated local intrinsic dimensions by mada
tmp$tDim[idx] ## true local intrinsic dimensions
estside <- side(x=x[1:100,], local=TRUE)
estside[idx] ## estimated local intrinsic dimensions by side