gride_evolution {intRinsic}

Gride evolution based on Maximum Likelihood Estimation

Description

The function allows the study of the evolution of the id estimates as a function of the scale of a dataset. A scale-dependent analysis is essential to identify the correct number of relevant directions in noisy data. To increase the average distance from the second NN (and thus the average neighborhood size) involved in the estimation, the function computes a sequence of Gride models with increasing NN orders, n1 and n2. See also Denti et al., 2022 for more details.

Usage

gride_evolution(X, vec_n1, vec_n2, upp_bound = 50)

## S3 method for class 'gride_evolution'
print(x, ...)

## S3 method for class 'gride_evolution'
plot(x, ...)

Arguments

X

data matrix with n observations and D variables.

vec_n1

vector of integers, containing the smaller NN orders considered in the evolution.

vec_n2

vector of integers, containing the larger NN orders considered in the evolution.

upp_bound

upper bound for the interval used in the numerical optimization (via optimize). Default is set to 50.

x

an object of class gride_evolution.

...

other arguments passed to specific methods.

Value

list containing the Gride evolution, the corresponding NN distance ratios, the average n2-th NN order distances, and the NN orders considered.

the function prints a summary of the Gride evolution to console.

References

Denti F, Doimo D, Laio A, Mira A (2022). "The generalized ratios intrinsic dimension estimator." Scientific Reports, 12(20005). ISSN 20452322, doi:10.1038/s41598-022-20991-1.

Examples

X       <-  replicate(5,rnorm(10000,0,.1))
gride_evolution(X = X,vec_n1 = 2^(0:5),vec_n2 = 2^(1:6))