clusterNumber

Computes cluster membership for a hierarchical cluster tree.

Synopsis

clusterNumber (npt, iclson, icrson, k)

Required Arguments

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

An array 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)

An array of length npt - 1 containing the right 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

An array of length npt containing the cluster membership of each observation.

Optional Arguments

obsPerCluster (Output)
An array of length k containing the number of observations in each cluster.

Description

Given a fixed number of clusters (K) and the cluster tree (vectors icrson and iclson) produced by the hierarchical clustering algorithm (see function clusterHierarchical, function clusterNumber determines the cluster membership of each observation. The function clusterNumber 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 clusterNumber also returns the number of observations found in each cluster.

Examples

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.

../../_images/csch9-Example1ClusterTree.png 
from numpy import *
from pyimsl.stat.clusterNumber import clusterNumber
from pyimsl.stat.writeMatrix import writeMatrix

k = 2
npt = 5
iclson = [5, 6, 4, 7]
icrson = [3, 1, 2, 8]

iclus = clusterNumber(npt, iclson, icrson, k)
writeMatrix("iclus", iclus, writeFormat="%5i")

Output

 
              iclus
    1      2      3      4      5
    1      2      1      2      1

Example 2

This example illustrates the typical usage of clusterNumber. The Fisher Iris data (see function dataSets, Utilities) is clustered. First the distance between the irises is computed using function dissimilarities. The resulting distance matrix is then clustered using function clusterHierarchical. The cluster membership for 5 clusters is then obtained via function clusterNumber using the output from clusterHierarchical. 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.

from numpy import *
from pyimsl.stat.clusterHierarchical import clusterHierarchical
from pyimsl.stat.clusterNumber import clusterNumber
from pyimsl.stat.dataSets import dataSets
from pyimsl.stat.dissimilarities import dissimilarities
from pyimsl.stat.randomUniform import randomUniform
from pyimsl.stat.randomSeedSet import randomSeedSet
from pyimsl.stat.writeMatrix import writeMatrix

npt = 150
ind = (1, 2, 3, 4)
k = 5
x = dataSets(3)

dist = dissimilarities(x, index=ind)

randomSeedSet(4)
for i in range(0, npt):
    for j in range(i + 1, npt):
        f_rand = randomUniform(1)
        dist[i][j] = max(0.0, dist[i][j] + .001 * f_rand)
        dist[j][i] = dist[i][j]

clusters = {}
clusterHierarchical(dist,
                    clusters=clusters)

iclson = clusters['iclson']
icrson = clusters['icrson']
nclus = []
iclus = clusterNumber(npt, iclson, icrson, k,
                      obsPerCluster=nclus)

writeMatrix('iclus', iclus, writeFormat="%5i")
writeMatrix('nclus', nclus, writeFormat="%5i")

Output

 
                                   iclus
    1      2      3      4      5      6      7      8      9     10     11
    5      5      5      5      5      5      5      5      5      5      5
 
   12     13     14     15     16     17     18     19     20     21     22
    5      5      5      5      5      5      5      5      5      5      5
 
   23     24     25     26     27     28     29     30     31     32     33
    5      5      5      5      5      5      5      5      5      5      5
 
   34     35     36     37     38     39     40     41     42     43     44
    5      5      5      5      5      5      5      5      5      5      5
 
   45     46     47     48     49     50     51     52     53     54     55
    5      5      5      5      5      5      2      2      2      2      2
 
   56     57     58     59     60     61     62     63     64     65     66
    2      2      1      2      2      1      2      2      2      2      2
 
   67     68     69     70     71     72     73     74     75     76     77
    2      2      2      2      2      2      2      2      2      2      2
 
   78     79     80     81     82     83     84     85     86     87     88
    2      2      2      2      2      2      2      2      2      2      2
 
   89     90     91     92     93     94     95     96     97     98     99
    2      2      2      2      2      1      2      2      2      2      1
 
  100    101    102    103    104    105    106    107    108    109    110
    2      2      2      2      2      2      2      3      2      2      2
 
  111    112    113    114    115    116    117    118    119    120    121
    2      2      2      2      2      2      2      4      2      2      2
 
  122    123    124    125    126    127    128    129    130    131    132
    2      2      2      2      2      2      2      2      2      2      4
 
  133    134    135    136    137    138    139    140    141    142    143
    2      2      2      2      2      2      2      2      2      2      2
 
  144    145    146    147    148    149    150
    2      2      2      2      2      2      2
 
              nclus
    1      2      3      4      5
    4     93      1      2     50