fsml_kmeans Interface

public interface fsml_kmeans

The procedure implements the K-means clustering algorithm using the Mahalanobis distance as the similarity measure. It accepts initial centroids (cm_in), refines them iteratively, and returns the final centroids (cm).

The input matrix (x) holds observations in rows (nd) and variables in columns (nv). The number of clusters (nc) must be at least 1 and not greater than the number of data points. The procedure assigns each observation to the nearest centroid using the Mahalanobis distance, recomputes centroids from cluster memberships, and iterates until convergence or the iteration limit is reached. Final centroids are sorted by the first variable, and assignments are updated accordingly.

If the covariance matrix (cov_in) is passed, it will be used to calculate the Mahalanobis distance. If it is not passed, the variables are standardised before computing the covariance matrix on the transformed data.

The global mean (gm), cluster centroids (cm), membership assignments (cl), and cluster sizes (cc), the covariance matrix (cov - either cov_in or internally calculated) and standard deviations (sigma) used in the distance calculations are returned.

Calls

interface~~fsml_kmeans~~CallsGraph interface~fsml_kmeans fsml_kmeans proc~s_nlp_kmeans s_nlp_kmeans interface~fsml_kmeans->proc~s_nlp_kmeans proc~s_err_print s_err_print proc~s_nlp_kmeans->proc~s_err_print proc~s_err_warn s_err_warn proc~s_nlp_kmeans->proc~s_err_warn proc~s_nlp_kmeans_core s_nlp_kmeans_core proc~s_nlp_kmeans->proc~s_nlp_kmeans_core proc~f_utl_r2c f_utl_r2c proc~s_err_print->proc~f_utl_r2c proc~s_err_warn->proc~f_utl_r2c proc~f_lin_mahalanobis_core f_lin_mahalanobis_core proc~s_nlp_kmeans_core->proc~f_lin_mahalanobis_core proc~f_sts_cov_core f_sts_cov_core proc~s_nlp_kmeans_core->proc~f_sts_cov_core proc~f_sts_mean_core f_sts_mean_core proc~s_nlp_kmeans_core->proc~f_sts_mean_core proc~f_sts_var_core f_sts_var_core proc~s_nlp_kmeans_core->proc~f_sts_var_core proc~s_utl_sort s_utl_sort proc~s_nlp_kmeans_core->proc~s_utl_sort proc~f_lin_mahalanobis_core->proc~f_sts_cov_core proc~s_utl_cholesky_solve s_utl_cholesky_solve proc~f_lin_mahalanobis_core->proc~s_utl_cholesky_solve proc~f_sts_cov_core->proc~f_sts_mean_core proc~f_sts_var_core->proc~f_sts_mean_core chol chol proc~s_utl_cholesky_solve->chol

Module Procedures

public impure subroutine s_nlp_kmeans(x, nd, nv, nc, cm_in, gm, cm, cl, cc, cov, sigma, cov_in)

Impure wrapper procedure for s_nlp_kmeans_core.

Arguments

Type IntentOptional Attributes Name
real(kind=wp), intent(in) :: x(nd,nv)

raw data (samples, variables)
integer(kind=i4), intent(in) :: nd

number of data points
integer(kind=i4), intent(in) :: nv

number of variables
integer(kind=i4), intent(in) :: nc

number of clusters
real(kind=wp), intent(in) :: cm_in(nv,nc)

initial centroids (raw, not standardised)
real(kind=wp), intent(out) :: gm(nv)

global means
real(kind=wp), intent(out) :: cm(nv,nc)

centroids (refined, standardised)
integer(kind=i4), intent(out) :: cl(nd)

cluster assignments
integer(kind=i4), intent(out) :: cc(nc)

cluster sizes
real(kind=wp), intent(out) :: cov(nv,nv)

covariance matrix
real(kind=wp), intent(out) :: sigma(nv)

standard deviations per variable
real(kind=wp), intent(in), optional :: cov_in(nv,nv)

optional covariance matrix