fsml_hkmeans Interface

public interface fsml_hkmeans

The procedure implements a hybrid clustering approach combining agglomerative hierarchical clustering and k-means clustering, both using the Mahalanobis distance as the similarity measure. The hierarchical step first partitions the data into nc clusters by iteratively merging the most similar clusters. The resulting centroids from are then used as initial centroids (cm_in) for the k-means procedure, which refines them iteratively.

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. In the hierarchical clustering step, variables are standardised before computing the covariance matrix on the transformed data. The covariance matrix is passed to the k-means clustering procedure along with the initial cluster centroids. The k-means clustering step then assigns each observation to the nearest centroid, 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.

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

Note: This procedure uses the pure procedure for calculating the Mahalanobis distance f_lin_mahalanobis_core, which useschol from the stdlib_linalg module.

Calls

interface~~fsml_hkmeans~~CallsGraph interface~fsml_hkmeans fsml_hkmeans proc~s_nlp_hkmeans s_nlp_hkmeans interface~fsml_hkmeans->proc~s_nlp_hkmeans proc~s_err_print s_err_print proc~s_nlp_hkmeans->proc~s_err_print proc~s_err_warn s_err_warn proc~s_nlp_hkmeans->proc~s_err_warn proc~s_nlp_hkmeans_core s_nlp_hkmeans_core proc~s_nlp_hkmeans->proc~s_nlp_hkmeans_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~s_nlp_hclust_core s_nlp_hclust_core proc~s_nlp_hkmeans_core->proc~s_nlp_hclust_core proc~s_nlp_kmeans_core s_nlp_kmeans_core proc~s_nlp_hkmeans_core->proc~s_nlp_kmeans_core proc~f_lin_mahalanobis_core f_lin_mahalanobis_core proc~s_nlp_hclust_core->proc~f_lin_mahalanobis_core proc~f_sts_cov_core f_sts_cov_core proc~s_nlp_hclust_core->proc~f_sts_cov_core proc~f_sts_mean_core f_sts_mean_core proc~s_nlp_hclust_core->proc~f_sts_mean_core proc~f_sts_var_core f_sts_var_core proc~s_nlp_hclust_core->proc~f_sts_var_core proc~s_utl_sort s_utl_sort proc~s_nlp_hclust_core->proc~s_utl_sort proc~s_nlp_kmeans_core->proc~f_lin_mahalanobis_core proc~s_nlp_kmeans_core->proc~f_sts_cov_core proc~s_nlp_kmeans_core->proc~f_sts_mean_core proc~s_nlp_kmeans_core->proc~f_sts_var_core 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_hkmeans(x, nd, nv, nc, gm, cm, cl, cc, cov, sigma)

Impure wrapper procedure for s_nlp_hkmeans_core.

Arguments

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

input data matrix (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 (target)
real(kind=wp), intent(out) :: gm(nv)

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

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

cluster assignments for each data point
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 deviation per variable