Type:	Package
Title:	Geometric Analysis of Configurations in High-Dimensional Spaces
Version:	0.1.0
Description:	Tools for analysing the geometry of configurations in high-dimensional spaces using the Average Membership Degree (AMD) framework and synthetic configuration generation. The package supports a domain-agnostic approach to studying the shape, dispersion, and internal structure of point clouds, with applications across biological and ecological datasets, including those derived from deep-time records. The AMD framework builds on the idea that strongly coupled systems may occupy a limited set of recurrent regimes in state space, producing high-occupancy regions separated by sparsely populated transitional configurations. The package focuses on detecting these concentration patterns and quantifying their geometric definition without assuming any underlying dynamical model. It provides AMD curve computation, cluster assignment, and sigma-equivalent estimation, together with S3 methods for plotting, printing, and summarising AMD and sigma-equivalent objects. Mendoza (2025) https://mmendoza1967.github.io/AMDconfigurations/.
License:	MIT + file LICENSE
URL:	https://github.com/mmendoza1967/AMDconfigurations, https://mmendoza1967.github.io/AMDconfigurations/
BugReports:	https://github.com/mmendoza1967/AMDconfigurations/issues
Encoding:	UTF-8
RoxygenNote:	7.3.3
Depends:	R (≥ 4.1)
Imports:	e1071, stats
Suggests:	testthat (≥ 3.0.0), knitr, rmarkdown, pkgdown
VignetteBuilder:	knitr
Config/testthat/edition:	3
NeedsCompilation:	no
Packaged:	2026-03-12 04:30:56 UTC; Manuel Mendoza
Author:	Manuel Mendoza [aut, cre]
Maintainer:	Manuel Mendoza <mmendoza@mncn.csic.es>
Repository:	CRAN
Date/Publication:	2026-03-17 18:10:03 UTC

Ecological dataset used in the example

Description

The dataset Fulldata contains the ecological data used in the example script inst/examples/example_ecology.R. It is included in the package to provide a complete reproducible workflow for the ecological case study.

Usage

data("Fulldata")

Format

A data frame with multiple variables (see example script for details).

Source

Internal dataset prepared by the authors.

Reduced transcriptomic dataset (1000 variables)

Description

This dataset contains the 1000 variables with highest variance from the original transcriptomic dataset used in the AMDconfigurations package.

Usage

data("Transcdata_small")

Format

A numeric matrix with 933 rows and 1000 columns.

Details

The full cleaned dataset (~58,000 variables) is available at Zenodo (DOI: https://doi.org/10.5281/zenodo.18604443).

Source

Original dataset cleaned and processed by the authors.

Fuzzy c-means clustering with multiple random initializations

Description

This function performs fuzzy c-means clustering on a dataset using multiple random initializations. For each initialization, the algorithm is run using e1071::cmeans(), and the solution with the smallest within-cluster objective function is retained.

Usage

assign_configurations(
  data,
  c,
  its = 50,
  iter_max = 100,
  m = 2,
  scale_data = FALSE,
  verbose = TRUE
)

Arguments

Details

The function is independent from the AMD workflow. It simply provides a robust fuzzy clustering procedure by selecting the best solution across several random seeds.

Value

A list of class "amd_assignment" containing:

c_opt

The number of clusters used.

cluster

A vector of hard cluster assignments (1..c).

membership

The fuzzy membership matrix.

centers

Cluster centers from the best solution.

objective

The minimum within-cluster objective value.

Examples

X <- matrix(rnorm(2000), ncol = 10)
res <- assign_configurations(X, c = 4)
table(res$cluster)

Compute the Average Membership Degree (AMD) curve

Description

This function computes the Average Membership Degree (AMD) curve for fuzzy c-means clustering across a sequence of cluster numbers. For each value of k, the algorithm is run multiple times and AMD summarises how sharply samples are assigned to clusters across iterations. The function returns the AMD values (raw, mean, max) and the estimated optimal number of configurations c_opt.

Usage

compute_amd_curve(
  data,
  its,
  nin,
  nsp,
  seeds = NULL,
  verbose = TRUE,
  plot_curve = FALSE,
  open_device = TRUE,
  scale_data = FALSE,
  iter_max = 100,
  m = 2,
  preselect_top_sd = NULL
)

Arguments

Details

AMD is computed as the mean maximum membership across samples minus 1/k, which corrects for the expected value under random assignment.

Value

An object of class "amd_curve" with components:

k_opt

Estimated optimal number of configurations c_opt.

max

Vector of maximum AMD values across iterations for each k.

mean

Vector of mean AMD values across iterations for each k.

raw

Matrix of AMD values (iterations × k).

coordinates

Final membership matrix for k = c_opt.

Estimate the sigma-equivalent value from an AMD curve

Description

This function computes the sigma-equivalent value associated with a given AMD curve. It generates a synthetic sigma-AMDmax sweep, interpolates the relationship between sigma and AMDmax, and finds the sigma value whose AMDmax matches the observed peak in the real data.

Usage

estimate_sigma_equivalent(
  real_data,
  its = 10,
  nin = 2,
  nsp = 12,
  c_opt = NULL,
  c_synth = NULL,
  sigmas,
  iter_max = 100,
  make_plot = TRUE,
  return_plot = TRUE,
  quiet = FALSE
)

Arguments

Value

A list containing:

sigma_equivalent

Numeric value of the estimated sigma-equivalent.

sweep

Data frame with sigma values and corresponding AMDmax values.

plot

A ggplot object, returned only if return_plot = TRUE.

Examples

# Synthetic dataset
X <- matrix(rnorm(2000), ncol = 10)

# Compute AMD curve with small, fast settings
res <- compute_amd_curve(
  data = X,
  its  = 5,
  nin  = 2,
  nsp  = 5
)

# Sigma‑equivalent estimation
estimate_sigma_equivalent(
  real_data = X,
  its       = 5,
  nin       = 2,
  nsp       = 5,
  c_opt     = res$c_opt,
  sigmas    = seq(0.1, 2, length.out = 10),
  iter_max  = 10,
  quiet     = TRUE
)

Plot method for AMD curve objects

Description

This method provides a convenient interface to plot AMD curves returned by compute_amd_curve(). It forwards the call to plot_AMD(), allowing users to simply call plot(res).

Usage

## S3 method for class 'amd_curve'
plot(x, type = c("mean", "max"), open_device = TRUE, ...)

Arguments

Value

Invisibly returns NULL.

Plot method for sigma-equivalent objects

Description

Plots the relationship between tested sigma values and the corresponding synthetic AMD peaks, marking the real AMD peak and the estimated sigma-equivalent value \sigma_{eq}.

Usage

## S3 method for class 'amd_sigma'
plot(x, open_device = TRUE, ...)

Arguments

Details

This method is automatically invoked when calling plot(x) on an object returned by estimate_sigma_equivalent().

Value

Invisibly returns NULL.

Plot the AMD curve

Description

This function plots the Average Membership Degree (AMD) curve from an object returned by compute_amd_curve(). It visualises either the mean AMD values or the maximum AMD values across iterations, and marks the optimal number of configurations c_opt.

Usage

plot_AMD(amd_object, type = c("mean", "max"), open_device = TRUE, ...)

Arguments

Value

Invisibly returns NULL. The function is called for its side effect of producing a plot.

Examples

X <- matrix(rnorm(2000), ncol = 10)
res <- compute_amd_curve(X, its = 10, nin = 2, nsp = 8)
plot_AMD(res)
plot_AMD(res, type = "max")

Print method for AMD curve objects

Description

Provides a concise summary of an AMD curve object returned by compute_amd_curve(). Displays the optimal number of configurations c_opt, the AMD peak, and the evaluated range of k.

Usage

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

Arguments

Value

Invisibly returns x.

Print method for sigma-equivalent objects

Description

Provides a concise summary of an object returned by estimate_sigma_equivalent(), including the real AMD peak, the estimated sigma-equivalent value sigma_eq, and the tested sigma range.

Usage

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

Arguments

Value

Invisibly returns x.

Summary method for AMD curve objects

Description

Provides a detailed summary of an AMD curve object, including mean and maximum AMD values, the optimal number of configurations, and the evaluated range of k.

Usage

## S3 method for class 'amd_curve'
summary(object, ...)

Arguments

Value

Invisibly returns object.

Summary method for sigma-equivalent objects

Description

Provides a detailed summary of an object returned by estimate_sigma_equivalent(), including the real AMD peak, the tested sigma values, the corresponding synthetic AMD peaks, and the estimated sigma-equivalent value \sigma_{eq}.

Usage

## S3 method for class 'amd_sigma'
summary(object, ...)

Arguments

Value

Invisibly returns object.

Summary method for sigma_equivalent objects

Description

Summary method for sigma_equivalent objects

Usage

## S3 method for class 'sigma_equivalent'
summary(object, ...)

Arguments

Value

Invisibly returns the object.