Computes cluster membership for a hierarchical cluster tree.

Synopsis                                                                                  

#include <imsls.h>

int *imsls_cluster_number (int npt, int *iclson, int *icrson, int k, …, 0)

Required Arguments

int npt  (Input)
Number of data points to be clustered.

int *iclson  (Input)
Vector of length npt - 1 containing the left son cluster numbers. 
Cluster npt + i is formed by merging clusters iclson[i-1] and icrson[i-1].

int *icrson  (Input)
Vector of length npt - 1 containing the left son cluster numbers. 
Cluster npt + i is formed by merging clusters iclson[i-1] and icrson[i-1].

int k  (Input)
Desired number of clusters.

Return Value

Vector of length npt containing the cluster membership of each observation. 

Synopsis with Optional Arugments

#include <imsls.h>

int *imsls_cluster_number (int npt, int *iclson, int *icrson, int k,
IMSLS_OBS_PER_CLUSTERS, int **nclus,
IMSLS_OBS_PER_CLUSTERS_USER, int nclus[],
IMSLS_RETURN_USER, int iclus[],
0)

Optional Arguments

IMSLS_OBS_PER_CLUSTERS, int **nclus   (Output)
Address of a pointer to an internally allocated array of length k containing the number of observations in each cluster.

IMSLS_OBS_PER_CLUSTERS_USER, int nclus[]   (Output)   
Storage for array nclus is provided by the user.  See IMSLS_OBS_PER_CLUSTERS.

IMSLS_RETURN_USER, float iclus[]  (Output)
User allocated array of length npt containing the cluster membership of each observation.

Description

Given a fixed number of clusters (K) and the cluster tree (vectors icrson and iclson) produced by the hierarchical clustering algorithm (see function imsls_f_cluster_hierarchical, function imsls_cluster_number determines the cluster membership of each observation. The function imsls_cluster_number first determines the root nodes for the K distinct subtrees forming the K clusters and then traverses each subtree to determine the cluster membership of each observation. The function imsls_cluster_number also returns the number of observations found in each cluster.

Example 1

In the following example, cluster membership for K = 2 clusters is found for the displayed cluster tree. The output vector iclus contains the cluster numbers for each observation.

 

#include "imsls.h"

 

void main()

{

  int  k = 2, npt = 5, *iclus;

  int iclson[] = {5, 6, 4, 7};

  int icrson[] = {3, 1, 2, 8};

 

  iclus = imsls_cluster_number(npt, iclson, icrson, k, 0);

  imsls_i_write_matrix("iclus", 1, 5, iclus, 0);

}

Output

       iclus

 1   2   3   4   5

 1   2   1   2   1   

Example 2

This example illustrates the typical usage of imsls_cluster_number. The Fisher iris data (see function imsls_f_data_sets, see Chapter 15,   “Utilities”.p<.STCH19.DOC!GDATA;;) is clustered. First the distance between the irises are computed using function imsls_f_dissimilarities. The resulting distance matrix is then clustered using function imsls_f_cluster_hierarchical. The cluster membership for 5 clusters is then obtained via function imsls_cluster_number using the output from imsls_f_cluster_hierarchical. The need for 5 clusters can be obtained either by theoretical means or by examining a cluster tree. The cluster membership for each of the iris observations is printed.

 

 

#include "imsls.h"

#define MAX(A,B) ((A)>(B)?(A): (B))

 

 

void main()

{

  int ncol = 5, nrow = 150, nvar = 4, npt = 150, k = 5;

  int i, j, *iclson, *icrson, *iclus, *nclus;

  int ind[4] = {1, 2, 3, 4};

  float *clevel, dist[150][150], *x, f_rand;

  int *p_iclus = NULL, *p_nclus = NULL;

 

  x = imsls_f_data_sets (3, 0);

  imsls_f_dissimilarities(nrow, ncol, x,

                       IMSLS_INDEX, nvar, ind,

                       IMSLS_RETURN_USER, dist,

                       0);

 

  imsls_random_seed_set (4);

  for (i = 0; i < npt; i++)

    {

      for (j = i + 1; j < npt; j++)

       {

         imsls_f_random_uniform (1, IMSLS_RETURN_USER, &f_rand, 0);

         dist[i][j] = MAX (0.0, dist[i][j] + .001 * f_rand);

         dist[j][i] = dist[i][j];

       }

      dist[i][i] = 0.;

    }

  imsls_f_cluster_hierarchical (npt, (float*)dist,

               IMSLS_CLUSTERS, &clevel, &iclson, &icrson,

               0); 

 

  iclus = imsls_cluster_number (npt, iclson, icrson, k,

                           IMSLS_OBS_PER_CLUSTER, &nclus,

                           0);

 

  imsls_i_write_matrix ("iclus", 25, 5, iclus, 0);

  imsls_i_write_matrix ("nclus", 1, 5, nclus, 0); }

Output

         iclus

     1   2   3   4   5

 1   5   5   5   5   5

 2   5   5   5   5   5

 3   5   5   5   5   5

 4   5   5   5   5   5

 5   5   5   5   5   5

 6   5   5   5   5   5

 7   5   5   5   5   5

 8   5   5   5   5   5

 9   5   5   5   5   5

10   5   5   5   5   5

11   2   2   2   2   2

12   2   2   1   2   2

13   1   2   2   2   2

14   2   2   2   2   2

15   2   2   2   2   2

16   2   2   2   2   2

17   2   2   2   2   2

18   2   2   2   2   2

19   2   2   2   1   2

20   2   2   2   1   2

21   2   2   2   2   2

22   2   3   2   2   2

23   2   2   2   2   2

24   2   2   4   2   2

25   2   2   2   2   2

 

         nclus

  1    2    3    4    5

  4   93    1    2   50

Visual Numerics, Inc. Visual Numerics - Developers of IMSL and PV-WAVE http://www.vni.com/ PHONE: 713.784.3131 FAX:713.781.9260