Compute Calculate of All Possible Silhouette Methods

Computes all possible silhouette indices from available functions in the package and returns a summary data frame comparing crisp, fuzzy, and median silhouette values across different methods.

Usage

calSilhouette(
  prox_matrix = NULL,
  proximity_type = c("dissimilarity", "similarity"),
  prob_matrix = NULL,
  a = 2,
  print.summary = FALSE,
  clust_fun = NULL,
  ...
)

Arguments

prox_matrix: A numeric matrix where rows represent observations and columns represent proximity measures (e.g., distances or similarities) to clusters. Typically, this is a membership or dissimilarity matrix from clustering results. If clust_fun is provided, prox_matrix should be the name of the matrix component as a string (e.g., if clust_fun = fcm from ppclust package the prox_matrix = "d").
proximity_type: Character string specifying the type of proximity measure in prox_matrix. Options are "similarity" (higher values indicate closer proximity) or "dissimilarity" (lower values indicate closer proximity). Defaults to "dissimilarity".
prob_matrix: A numeric matrix of cluster membership probabilities, where rows represent observations and columns represent clusters (depending on prob_type). If clust_fun is provided, prob_matrix can be given as the name of the matrix component (e.g., "u" for the fcm function). Defaults to NULL.
a: Numeric value controlling the fuzzifier or weight scaling in fuzzy silhouette averaging. Higher values increase the emphasis on strong membership differences. Must be positive. Defaults to 2.
print.summary: Logical; if TRUE, prints a summary table of average silhouette widths and sizes for each cluster. Defaults to FALSE.
clust_fun: Optional S3 or S4 function object or function as character string specifying a clustering function that produces the proximity measure matrix. For example, fcm or "fcm". If provided, prox_matrix must be the name of the matrix component in the clustering output (e.g., "d" for fcm when proximity_type = "dissimilarity"). Defaults to NULL.
...: Additional arguments passed to clust_fun, such as x,centers for fcm.

Value

A data frame with the following columns:

Method: Character vector of method names
Crisp_Silhouette: Numeric vector of crisp (unweighted) average silhouette values
Fuzzy_Silhouette: Numeric vector of fuzzy (weighted) average silhouette values (NA if prob_matrix is not available for the method)
Median_Silhouette: Numeric vector of median silhouette values

Details

This function computes all available silhouette methods from the package and returns a comparative summary. The methods included depend on the available input matrices:

If prox_matrix is available:

medoid - Medoid-based silhouette using Silhouette
pac - PAC-based silhouette using Silhouette

If prob_matrix is available:

pp_pac - Posterior probabilities silhouette with PAC method using softSilhouette
pp_medoid - Posterior probabilities silhouette with Medoid method using softSilhouette
nlpp_pac - Negative log posterior probabilities silhouette with PAC method using softSilhouette
nlpp_medoid - Negative log posterior probabilities silhouette with Medoid method using softSilhouette
pd_pac - Probability distribution silhouette with PAC method using softSilhouette
pd_medoid - Probability distribution silhouette with Medoid method using softSilhouette
cer - Certainty-based silhouette using cerSilhouette
db - Density-based silhouette using dbSilhouette

At least one of prox_matrix or prob_matrix must be provided.

Examples

if (requireNamespace("ppclust", quietly = TRUE)) {
  # Example with FCM clustering
  library(ppclust)
  data(iris)
  fcm_result <- fcm(iris[, -5], centers = 3)

  # Using matrices directly
  summary_result <- calSilhouette(
    prox_matrix = fcm_result$d,
    prob_matrix = fcm_result$u,
    proximity_type = "dissimilarity",
    print.summary = TRUE
  )
}
#> 
#> Summary of All Silhouette Methods
#> ========================================== 
#>       Method     Crisp     Fuzzy    Median
#>       medoid 0.8288288 0.9297577 0.9179945
#>          pac 0.7541271 0.8799106 0.8484197
#>       pp_pac 0.7541271 0.8799106 0.8484197
#>    pp_medoid 0.8288288 0.9297577 0.9179945
#>     nlpp_pac 0.8185224 0.9304926 0.9261387
#>  nlpp_medoid 0.8749545 0.9604788 0.9616532
#>       pd_pac 0.7469894 0.8786105 0.8562152
#>    pd_medoid 0.8196600 0.9280044 0.9225377
#>          cer 0.8572481 0.9248327 0.9041529
#>           db 0.3303585 0.4206051 0.3097745

if (requireNamespace("ppclust", quietly = TRUE)) {
  # Using clustering function
  summary_result2 <- calSilhouette(
    prox_matrix = "d",
    prob_matrix = "u",
    proximity_type = "dissimilarity",
    clust_fun = ppclust::fcm,
    x = iris[, -5],
    centers = 3,
    print.summary = TRUE
  )
}
#> 
#> Summary of All Silhouette Methods
#> ========================================== 
#>       Method     Crisp     Fuzzy    Median
#>       medoid 0.8288288 0.9297577 0.9179945
#>          pac 0.7541271 0.8799106 0.8484197
#>       pp_pac 0.7541271 0.8799106 0.8484197
#>    pp_medoid 0.8288288 0.9297577 0.9179945
#>     nlpp_pac 0.8185224 0.9304926 0.9261387
#>  nlpp_medoid 0.8749545 0.9604788 0.9616532
#>       pd_pac 0.7469894 0.8786105 0.8562152
#>    pd_medoid 0.8196600 0.9280044 0.9225377
#>          cer 0.8572481 0.9248327 0.9041529
#>           db 0.3303585 0.4206051 0.3097745