compute_mus {intRinsic}

Compute the ratio statistics needed for the intrinsic dimension estimation

Description

The function compute_mus computes the ratios of distances between nearest neighbors (NNs) of generic order, denoted as mu(n_1,n_2). This quantity is at the core of all the likelihood-based methods contained in the package.

Usage

compute_mus(X = NULL, dist_mat = NULL, n1 = 1, n2 = 2, Nq = FALSE, q = 3)

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

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

## S3 method for class 'mus'
plot(x, range_d = NULL, ...)

Arguments

X

a dataset with n observations and D variables.

dist_mat

a distance matrix computed between n observations.

n1

order of the first NN considered. Default is 1.

n2

order of the second NN considered. Default is 2.

Nq

logical indicator. If TRUE, it provides the N^q matrix needed for fitting the Hidalgo model.

q

integer, number of NN considered to build N^q.

x

object of class mus, obtained from the function compute_mus().

...

ignored.

range_d

a sequence of values for which the generalized ratios density is superimposed to the histogram of mus.

Value

the principal output of this function is a vector containing the ratio statistics, an object of class mus. The length of the vector is equal to the number of observations considered, unless ties are present in the dataset. In that case, the duplicates are removed. Optionally, if Nq is TRUE, the function returns an object of class mus_Nq, a list containing both the ratio statistics mus and the adjacency matrix NQ.

References

Facco E, D'Errico M, Rodriguez A, Laio A (2017). "Estimating the intrinsic dimension of datasets by a minimal neighborhood information." Scientific Reports, 7(1). ISSN 20452322, doi:10.1038/s41598-017-11873-y.

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(2,rnorm(1000))
mu          <- compute_mus(X, n1 = 1, n2 = 2)
mudots      <- compute_mus(X, n1 = 4, n2 = 8)
pre_hidalgo <- compute_mus(X, n1 = 4, n2 = 8, Nq = TRUE, q = 3)