qscore: Clustering Quadratic Score

In qcluster: Clustering via Quadratic Scoring

Clustering Quadratic Score

Description

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

Usage

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

Arguments

data	a numeric vector, matrix, or data frame of observations. Rows correspond to observations and columns correspond to variables/features. Let N=nrow(data) and P=ncol(data). Categorical variables and NA values are not allowed.
params	a list containing cluster parameters (proportion, mean, cov). Let K=number of clusters. The elements of the list are as follows: $proportion= 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. These parameters must be conformable with data; see also clust2params.
type	the type of score, a character in the set c("both", "smooth", "hard"). The default value is set to "both". See Details.

Details

The function calculates quadratic scores as defined in equation (22) in Coraggio and Coretto (2023). The score is computed from a Gaussian parameterization supplied in params.

Value

A named numeric vector with components hard and smooth. When only one score is requested through type, the other component is returned as NA.

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: \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.jmva.2023.105181")}

See Also

clust2params, gmix

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

qcluster documentation built on June 5, 2026, 5:07 p.m.