Compute the AMD curve across a range of cluster numbers

This function computes the Average Membership Deviation (AMD) curve for fuzzy c-means clustering across a sequence of cluster numbers k. For each k, multiple random initialisations are performed and the AMD value is computed as:

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

data

A numeric matrix or data frame of samples (rows) × features (columns).

its

Number of random initialisations per value of k.

nin

Minimum number of clusters to evaluate.

nsp

Maximum number of clusters to evaluate.

seeds

Optional numeric vector of seeds for deterministic behaviour. Must have length its * (nsp - nin + 1). If NULL, random seeds are drawn.

verbose

Logical; print progress messages.

plot_curve

Logical; if TRUE, plot the AMD curve.

open_device

Logical; if TRUE, open a new graphics device for the plot.

scale_data

Logical; if TRUE, standardise features before clustering.

iter_max

Maximum number of iterations for fuzzy c-means.

m

Fuzziness parameter for fuzzy c-means (default 2).

preselect_top_sd

Optional integer; if provided, only the top-SD features are retained before clustering (useful for very high-dimensional data).

Value

A list with components:

k_opt

The optimal number of clusters (maximising AMD peak).

max

Vector of AMD peak values for each k.

mean

Vector of mean AMD values across repetitions.

raw

Matrix of AMD values (rows = repetitions, columns = k).

Details

$$ \mathrm{AMD}(k) = \mathrm{mean}(\max_i u_{i}) - 1/k $$

where \(u_i\) is the membership vector of sample \(i\). The optimal number of clusters is selected as the k that maximises the AMD peak across repetitions.

Examples

if (FALSE) { # \dontrun{
set.seed(1)
X <- matrix(rnorm(2000), nrow = 100, ncol = 20)
res <- compute_amd_curve(X, its = 10, nin = 2, nsp = 6)
res$k_opt
} # }