gmeans: G-means Clustering

In gmeans: G-means Clustering

G-means Clustering

Description

Perform G-means clustering on a data matrix.

Usage

gmeans(x, k_init = 2L, k_max = 10L, level = 0.05, ...)

Arguments

x	(matrix()) Numeric matrix of data, or a data frame with all numeric columns. Logical input is coerced to a 0/1 matrix. Missing and infinite values are not allowed and the matrix must have at least one row and one column.
k_init	(integer(1)) Initial amount of centers. Default is 2L.
k_max	(integer(1)) Maximum amount of centers. Must be greater than or equal to k_init. Default is 10L.
level	(numeric(1)) Significance level for the Anderson-Darling test. Default is 0.05. See ad.test() for more information.
...	(any) Additional arguments passed to stats::kmeans(). nstart has no effect since the initial centers are always given as a matrix.

Details

The G-means clustering algorithm is an extension of the traditional k-means algorithm that automatically determines the number of clusters by iteratively testing the Gaussianity of data within clusters. The process begins with a specified initial number of clusters (k_init) and iteratively increases the number of clusters until it reaches the specified maximum (k_max) or the data within clusters is determined to be Gaussian at the specified significance level (level).

The algorithm is outlined as follows:

1. Let C be the initial set of centers (usually C \leftarrow \{\bar{x}\}).

2. Perform k-means clustering on the dataset X using the current set of centers C, i.e., C \leftarrow \text{kmeans}(C, X).

3. For each center c_j, identify the set of data points \{x_i \mid \text{class}(x_i) = j\} that are assigned to c_j.

4. Use the Anderson-Darling test to check if the set of data points \{x_i \mid \text{class}(x_i) = j\} follows a Gaussian distribution at the confidence level \alpha.

5. If the data points appear Gaussian, keep c_j. Otherwise, replace c_j with two new centers.

6. Repeat from step 2 until no more centers are added.

Value

An object of class c("gmeans", "kmeans"). See stats::kmeans() for details.

References

Hamerly, Greg, Elkan, Charles (2003). “Learning the k in k-means.” In Thrun S, Saul L, Schölkopf B (eds.), Advances in Neural Information Processing Systems, volume 16. https://proceedings.neurips.cc/paper_files/paper/2003/file/234833147b97bb6aed53a8f4f1c7a7d8-Paper.pdf.

Examples

set.seed(123)
x <- rbind(
  matrix(rnorm(100, sd = 0.3), ncol = 2),
  matrix(rnorm(100, mean = 1, sd = 0.3), ncol = 2)
)
colnames(x) <- c("x", "y")
cl <- gmeans(x)

gmeans documentation built on Sept. 12, 2026, 1:06 a.m.