Package 'bfcluster'

R² for Cluster Solutions after Buttler & Fickel (1995)

Description

Computes the proportion of explained distance variation (R²) for a given clustering solution using a distance matrix derived from the Buttler-Fickel distance. The statistic reflects how well the clustering partitions the total pairwise distance structure.

Usage

bf_R2(D, cluster)

Arguments

D	A distance object of class dist, usually computed via buttler_fickel_dist().
cluster	An integer or factor vector of cluster assignments, typically obtained from cutree() or another clustering method.

Details

The R² is defined as:

$R^2 = 1 - \frac{D_{\text{within}}}{D_{\text{total}}}$

where $D_{\text{total}}$ is the sum of all pairwise distances and $D_{\text{within}}$ is the sum of distances within clusters.

Value

A numeric value between 0 and 1 indicating the proportion of explained distance variation. Higher values represent better cluster fit.

Examples

df <- data.frame(
  sex    = factor(c("m","f","m","f")),
  height = c(180, 165, 170, 159),
  age    = c(25, 32, 29, 28)
)

types <- c("nominal", "metric", "metric")

D <- buttler_fickel_dist(df, types)
hc <- hclust(D)
cl <- cutree(hc, k = 2)

bf_R2(D, cl)

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Buttler-Fickel Distance Matrix

Description

Computes a distance matrix following Buttler & Fickel (1995) for mixed-scale variables. Each variable-specific distance matrix is normalized by its mean pairwise distance (Gini mean difference), ensuring equal contribution of all variables to the overall distance.

Usage

buttler_fickel_dist(df, types)

Arguments

df	A data.frame where rows are cases and columns are variables.
types	A character vector of the same length as ncol(df), indicating the scale level of each variable. Allowed values are "metric", "ordinal", or "nominal".

Value

An object of class dist.

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