qcluster (version 1.2.1)

qscore: Clustering Quadratic Score

Description

Computes both the hard and the smooth quadratic score of a clustering. Handles both

Usage

qscore(data, params, type = "both")

Value

A numeric vector with both the hard and the smooth score, or only one of them depending on the argument type.

Arguments

data

a numeric vector, matrix, or data frame of observations. Rows correspond to observations and columns correspond to variables/features. Let N=nrows(data) and P=ncol(data). Categorical variables and NA values are not allowed.

params

a list containing cluster parameters (size, mean, cov). Let K=number of clusters. The elements of the list are as follows: $prop=vector of clusters' proportions; $mean=matrix of dimension (P x K) containing the clusters' mean parameters; $cov=array of size (P x P x K) containing the clusters' covariance matrices.

type

the type of score, a character in the set c("both", "smooth", "hard"). The default value is set to "booth". See Details.

Details

The function calculates quadratic scores as defined in equation (22) in Coraggio and Coretto (2023).

References

Coraggio, Luca and Pietro Coretto (2023). Selecting the number of clusters, clustering models, and algorithms. A unifying approach based on the quadratic discriminant score. Journal of Multivariate Analysis, Vol. 196(105181), 1-20. DOI: tools:::Rd_expr_doi("10.1016/j.jmva.2023.105181")

See Also

clust2params

Examples

# --- load and split data
data("banknote")
set.seed(345)
idx   <- sample(1:nrow(banknote), size = 25, replace = FALSE)
dat_f <- banknote[-idx, -1] ## training data set  
dat_v <- banknote[ idx, -1] ## validation data set 


# --- Gaussian model-based clustering, K=3
# fit clusters 
fit1 <- gmix(dat_f, K=3)
## compute quadratic scores using fitted mixture parameters
s1 <- qscore(dat_v , params = fit1$params)
s1


# --- k-means clustering, K=3
# obtain the k-means partition 
cl_km <- kmeans(dat_f, centers = 3, nstart = 1)$cluster
## convert k-means hard assignment into  cluster parameters 
par_km <- clust2params(dat_f, cl_km)
# compute quadratic scores 
s2 <- qscore(dat_v, params = par_km)
s2