# Clustering with stat_tool
## This notebook illustates how to perform clustering of vectors with stat_tool.cluster ##

Load a data set (chene_sessile.vec)

[1]:
from openalea.stat_tool import get_shared_data
from openalea.stat_tool.data_transform import SelectVariable
from openalea.stat_tool.comparison import Compare
from openalea.stat_tool.cluster import Clustering

from openalea.stat_tool.vectors import VectorDistance, Vectors

vec = Vectors(get_shared_data("chene_sessile.vec"))
Running cmake --build & --install in /home/jdurand/devlp/Git/openalea/stat_tool/build
Running cmake --build & --install in /home/jdurand/devlp/Git/openalea/sequence_analysis/build
[2]:
vec.nb_vector
[2]:
138
[3]:
vec.nb_variable
[3]:
6

vec contains 138 vectors in dimension 6

Discard variables 1, 3 and 6 in vec

[4]:
from openalea.stat_tool.data_transform import SelectVariable
vec2 = SelectVariable(vec, [1, 3, 6], Mode="Reject")
Computation of a 138x138 distance matrix using a standardization procedure
Arguments “N” specify that vector components are Numerical
[5]:
matrix = Compare(vec2, VectorDistance("N", "N", "N"))
[6]:
matrix.nb_column, matrix.nb_row
[6]:
(138, 138)

Clustering using a partitioning method#

[7]:
clust1 = Clustering(matrix, "Partition", 2)
print(clust1)
cluster 1 (69 vectors): 69, 48, 41, 44, 32, 47, 81, 95, 11, 36, 75, 108, 56, 83, 38, 98, 113, 134, 110, 101, 77, 35, 74, 80, 50, 24, 89, 128, 5, 45, 8, 116, 119, 132, 61, 78, 53, 29, 131, 65, 90, 96, 104, 20, 86, 66, 42, 68, 125, 14, 23, 54, 33, 26, 71, 129, 102, 51, 70, 111, 138, 19, 127, 62, 117, 137, 2, 28, 17
cluster 2 (69 vectors): 100, 13, 133, 105, 72, 9, 93, 109, 30, 115, 63, 7, 55, 37, 15, 114, 106, 46, 73, 18, 3, 87, 58, 43, 60, 76, 52, 6, 39, 31, 12, 99, 121, 123, 22, 79, 94, 88, 21, 97, 25, 40, 57, 136, 67, 49, 10, 4, 120, 92, 27, 91, 64, 124, 16, 130, 84, 107, 126, 103, 122, 112, 59, 1, 82, 34, 135, 118, 85

cluster distance matrix

          | cluster 1 | cluster 2
cluster 1   0.444986   1.46646
cluster 2    1.46646  0.608382

          | within-cluster distance | between-cluster distance | diameter | separation
cluster 1   0.444986   1.46646    1.26444  0.0656281
cluster 2   0.608382   1.46646    2.02706  0.0656281

cluster 1: non-isolated
cluster 2: non-isolated

Number of clusters

[8]:
nb_clusters = clust1.get_nb_cluster()
print(nb_clusters)
2

Cluster of individual (“pattern”) 2

[9]:
clust1.get_assignment(2)
[9]:
1

To get the partition:

[10]:
part1 = [[i for i in range(1,vec.nb_vector+1) if clust1.get_assignment(i) == c] for c in range(1,nb_clusters+1)]
print(part1)
[[2, 5, 8, 11, 14, 17, 19, 20, 23, 24, 26, 28, 29, 32, 33, 35, 36, 38, 41, 42, 44, 45, 47, 48, 50, 51, 53, 54, 56, 61, 62, 65, 66, 68, 69, 70, 71, 74, 75, 77, 78, 80, 81, 83, 86, 89, 90, 95, 96, 98, 101, 102, 104, 108, 110, 111, 113, 116, 117, 119, 125, 127, 128, 129, 131, 132, 134, 137, 138], [1, 3, 4, 6, 7, 9, 10, 12, 13, 15, 16, 18, 21, 22, 25, 27, 30, 31, 34, 37, 39, 40, 43, 46, 49, 52, 55, 57, 58, 59, 60, 63, 64, 67, 72, 73, 76, 79, 82, 84, 85, 87, 88, 91, 92, 93, 94, 97, 99, 100, 103, 105, 106, 107, 109, 112, 114, 115, 118, 120, 121, 122, 123, 124, 126, 130, 133, 135, 136]]

Recreate clusters from partition

[11]:
print(matrix.partitioning_clusters(part1))
cluster 1 (69 vectors): 69, 48, 41, 44, 32, 47, 81, 95, 11, 36, 75, 108, 56, 83, 38, 98, 113, 134, 110, 101, 77, 35, 74, 80, 50, 24, 89, 128, 5, 45, 8, 116, 119, 132, 61, 78, 53, 29, 131, 65, 90, 96, 104, 20, 86, 66, 42, 68, 125, 14, 23, 54, 33, 26, 71, 129, 102, 51, 70, 111, 138, 19, 127, 62, 117, 137, 2, 28, 17
cluster 2 (69 vectors): 100, 13, 133, 105, 72, 9, 93, 109, 30, 115, 63, 7, 55, 37, 15, 114, 106, 46, 73, 18, 3, 87, 58, 43, 60, 76, 52, 6, 39, 31, 12, 99, 121, 123, 22, 79, 94, 88, 21, 97, 25, 40, 57, 136, 67, 49, 10, 4, 120, 92, 27, 91, 64, 124, 16, 130, 84, 107, 126, 103, 122, 112, 59, 1, 82, 34, 135, 118, 85

cluster distance matrix

          | cluster 1 | cluster 2
cluster 1   0.444986   1.46646
cluster 2    1.46646  0.608382

          | within-cluster distance | between-cluster distance | diameter | separation
cluster 1   0.444986   1.46646    1.26444  0.0656281
cluster 2   0.608382   1.46646    2.02706  0.0656281

cluster 1: non-isolated
cluster 2: non-isolated

Hierarchical clustering and dendrogram using an agglomerative algorithm#

[12]:
clust2 = Clustering(matrix, "Hierarchy", "Agglomerative")
print(clust2)
138 vectors

        | child cluster distance | within-cluster distance | between-cluster distance | diameter | separation | composition
step   1          0          0   0.845491          0  0.0563999   7, 55
step   2          0          0   0.883565          0  0.0345239   24, 89
step   3          0          0   0.911651          0  0.0345239   41, 44
step   4  0.0126479  0.0126479    1.18625  0.0126479  0.0782759   21, 94
step   5  0.0126479  0.0126479   0.760368  0.0126479   0.021876   27, 120
step   6  0.0126479  0.0126479   0.913273  0.0126479  0.0345239   81, 95
step   7  0.0126479  0.0126479   0.762643  0.0126479  0.0345239   103, 122
step   8  0.0126479  0.0126479     1.0078  0.0126479  0.0345239   113, 134
step   9   0.021876   0.021876    1.08646   0.021876  0.0252957   8, 61
step  10   0.021876   0.021876   0.967306   0.021876  0.0345239   11, 38
step  11     0.0282  0.0230159   0.765583  0.0345239  0.0252957   27, 120, 91
step  12   0.021876   0.021876   0.868665   0.021876  0.0563999   51, 70
step  13  0.0362337  0.0314478    1.09889  0.0471717  0.0471717   8, 61, 29
step  14  0.0252957  0.0252957   0.921014  0.0252957  0.0379436   13, 100
step  15  0.0440957  0.0335558    0.77085  0.0598196  0.0345239   16, 27, 120, 91
step  16  0.0252957  0.0252957     1.2527  0.0252957  0.0345239   23, 33
step  17  0.0252957  0.0252957   0.775549  0.0252957  0.0656281   28, 117
step  18  0.0252957  0.0252957    0.79839  0.0252957  0.0656281   62, 138
step  19  0.0252957  0.0252957   0.890767  0.0252957  0.0345239   83, 110
step  20  0.0454619  0.0375999   0.968891  0.0563999  0.0345239   11, 38, 32
step  21  0.0739196  0.0536893    0.78211   0.106991  0.0345239   16, 27, 120, 91, 103, 122
step  22  0.0471717  0.0398797    1.24669  0.0598196  0.0379436   23, 33, 42
step  23  0.0345239  0.0230159   0.887222  0.0345239  0.0379436   24, 89, 116
step  24   0.047968   0.042784   0.968338  0.0656281  0.0345239   11, 38, 32, 48
step  25  0.0704999  0.0538703   0.981483   0.100152  0.0379436   11, 38, 32, 48, 77
step  26  0.0345239  0.0345239    1.23769  0.0345239  0.0379436   40, 57
step  27  0.0408478  0.0293399   0.925471  0.0471717  0.0379436   41, 44, 81, 95
step  28  0.0345239  0.0314478   0.899478  0.0345239  0.0379436   56, 83, 110
step  29  0.0345239  0.0345239   0.938001  0.0345239   0.043752   63, 93
step  30  0.0408478  0.0314478    1.00594  0.0471717  0.0505915   75, 113, 134
step  31  0.0513877  0.0530317   0.787684   0.106991  0.0656281   16, 27, 120, 91, 103, 122, 124
step  32  0.0379436  0.0379436   0.855993  0.0379436  0.0563999   2, 127
step  33  0.0379436  0.0379436   0.831399  0.0379436  0.0563999   3, 18
step  34  0.0505915  0.0421595   0.937767  0.0632393  0.0656281   9, 13, 100
step  35  0.0379436  0.0379436    0.87456  0.0379436  0.0598196   14, 54
step  36  0.0379436  0.0379436   0.779505  0.0379436  0.0632393   22, 97
step  37  0.0410196  0.0320178   0.894159  0.0471717  0.0690478   24, 89, 116, 53
step  38  0.0379436  0.0379436   0.855449  0.0379436  0.0563999   30, 46
step  39  0.0559222  0.0545543   0.984221   0.100152  0.0379436   11, 38, 32, 48, 77, 108
step  40  0.0749736  0.0603884   0.996551   0.106991  0.0379436   11, 38, 32, 48, 77, 108, 98
step  41  0.0678767  0.0622605     1.0035   0.106991   0.043752   11, 38, 32, 48, 77, 108, 98, 101
step  42  0.0583675  0.0462282   0.936685  0.0851153   0.043752   41, 44, 81, 95, 56, 83, 110
step  43  0.0693914  0.0546356      1.239  0.0977632   0.043752   23, 33, 42, 104
step  44  0.0425577  0.0398797    1.25903  0.0471717  0.0563999   40, 57, 49
step  45  0.0379436  0.0379436    1.07673  0.0379436  0.0471717   119, 128
step  46   0.043752   0.043752   0.947424   0.043752  0.0690478   5, 78
step  47   0.130293  0.0953383     1.0233   0.219791   0.043752   11, 38, 32, 48, 77, 108, 98, 101, 41, 44, 81, 95, 56, 83, 110
step  48  0.0768238  0.0635109    1.23707   0.103572  0.0563999   23, 33, 42, 104, 96
step  49  0.0862301  0.0941997    1.03095   0.219791  0.0471717   11, 38, 32, 48, 77, 108, 98, 101, 41, 44, 81, 95, 56, 83, 110, 69
step  50   0.061014  0.0521839   0.933878  0.0782759  0.0505915   63, 93, 133
step  51  0.0471717  0.0471717    0.95163  0.0471717  0.0471717   36, 47
step  52  0.0471717  0.0471717   0.995691  0.0471717  0.0598196   37, 106
step  53  0.0661435  0.0567436    1.07975  0.0851153  0.0471717   45, 119, 128
step  54   0.118571  0.0989895      1.048   0.219791  0.0505915   11, 38, 32, 48, 77, 108, 98, 101, 41, 44, 81, 95, 56, 83, 110, 69, 36, 47
step  55   0.111207  0.0843627    1.11155   0.179459  0.0656281   8, 61, 29, 45, 119, 128
step  56   0.132286   0.106587    1.08131   0.248507  0.0563999   11, 38, 32, 48, 77, 108, 98, 101, 41, 44, 81, 95, 56, 83, 110, 69, 36, 47, 75, 113, 134
step  57  0.0713276  0.0617558   0.949872   0.103572  0.0563999   63, 93, 133, 109
step  58  0.0505915  0.0505915    1.20298  0.0505915  0.0563999   86, 125
step  59  0.0627238  0.0481398   0.850023  0.0690478  0.0782759   3, 18, 7, 55
step  60  0.0636919  0.0517858    1.27837  0.0690478  0.0816956   10, 40, 57, 49
step  61  0.0753717  0.0628957   0.857606  0.0943435  0.0598196   30, 46, 115
step  62  0.0563999  0.0563999    1.06846  0.0563999   0.122028   31, 60
step  63   0.149733   0.110509    1.08732   0.250895  0.0656281   11, 38, 32, 48, 77, 108, 98, 101, 41, 44, 81, 95, 56, 83, 110, 69, 36, 47, 75, 113, 134, 35
step  64  0.0972477  0.0759525   0.962431   0.134676  0.0782759   63, 93, 133, 109, 73
step  65  0.0736618  0.0590778     0.8741  0.0909238  0.0724675   2, 127, 51, 70
step  66  0.0994026   0.079987    1.25177   0.163391  0.0690478   23, 33, 42, 104, 96, 86, 125
step  67  0.0787914  0.0651755   0.884129  0.0977632  0.0909238   14, 54, 66
step  68  0.0615295  0.0567436    1.01765  0.0632393  0.0690478   37, 106, 87
step  69  0.0808994  0.0718975   0.867262   0.110411  0.0782759   30, 46, 115, 105
step  70  0.0822111  0.0674553   0.790057   0.101183   0.088535   22, 97, 39
step  71  0.0656281  0.0656281   0.914738  0.0656281  0.0724675   15, 43
step  72  0.0782759  0.0606159   0.797547  0.0909238  0.0656281   28, 117, 62, 138
step  73   0.167784   0.112279   0.816318   0.263543   0.113831   16, 27, 120, 91, 103, 122, 124, 28, 117, 62, 138
step  74  0.0656281  0.0656281   0.861875  0.0656281  0.0724675   68, 90
step  75  0.0951397  0.0686496   0.932222   0.128867  0.0690478   9, 13, 100, 72
step  76   0.213303   0.145368    1.16847   0.358918  0.0724675   8, 61, 29, 45, 119, 128, 11, 38, 32, 48, 77, 108, 98, 101, 41, 44, 81, 95, 56, 83, 110, 69, 36, 47, 75, 113, 134, 35
step  77  0.0909238  0.0751999   0.940275     0.1128  0.0690478   5, 78, 80
step  78  0.0954834  0.0761135     1.0311   0.132287  0.0690478   6, 37, 106, 87
step  79   0.154421   0.119261    1.00711   0.261154  0.0782759   6, 37, 106, 87, 9, 13, 100, 72
step  80   0.114053  0.0850638   0.934943     0.1692  0.0690478   5, 78, 80, 24, 89, 116, 53
step  81   0.129015  0.0922439    1.27621   0.172619  0.0690478   23, 33, 42, 104, 96, 86, 125, 26
step  82   0.137668   0.102338    1.29949   0.191076  0.0816956   23, 33, 42, 104, 96, 86, 125, 26, 71
step  83    0.11988  0.0937678   0.936256   0.209532  0.0690478   5, 78, 80, 24, 89, 116, 53, 132
step  84   0.170781   0.110882   0.937799    0.27858  0.0724675   5, 78, 80, 24, 89, 116, 53, 132, 131
step  85  0.0834055  0.0774797   0.933912  0.0943435  0.0977632   15, 43, 76
step  86   0.153907   0.145957    1.17948   0.358918  0.0758872   8, 61, 29, 45, 119, 128, 11, 38, 32, 48, 77, 108, 98, 101, 41, 44, 81, 95, 56, 83, 110, 69, 36, 47, 75, 113, 134, 35, 74
step  87   0.113912  0.0810117    0.87747   0.163391  0.0782759   2, 127, 51, 70, 102
step  88   0.170795   0.129667   0.942781   0.322332  0.0758872   5, 78, 80, 24, 89, 116, 53, 132, 131, 68, 90
step  89  0.0724675  0.0724675    1.15619  0.0724675  0.0782759   121, 123
step  90   0.263482   0.192873    1.24421   0.591357  0.0782759   5, 78, 80, 24, 89, 116, 53, 132, 131, 68, 90, 8, 61, 29, 45, 119, 128, 11, 38, 32, 48, 77, 108, 98, 101, 41, 44, 81, 95, 56, 83, 110, 69, 36, 47, 75, 113, 134, 35, 74
step  91   0.130301  0.0974413   0.881249   0.216371  0.0875041   2, 127, 51, 70, 102, 17
step  92    0.09699  0.0676799   0.852929    0.10938   0.088535   3, 18, 7, 55, 12
step  93   0.120834  0.0947416     1.1869   0.163391  0.0816956   21, 94, 121, 123
step  94   0.106136  0.0855931    0.86533   0.144935  0.0782759   30, 46, 115, 105, 58
step  95   0.224119   0.194397    1.25595   0.591357  0.0816956   5, 78, 80, 24, 89, 116, 53, 132, 131, 68, 90, 8, 61, 29, 45, 119, 128, 11, 38, 32, 48, 77, 108, 98, 101, 41, 44, 81, 95, 56, 83, 110, 69, 36, 47, 75, 113, 134, 35, 74, 50
step  96   0.178217   0.132363    1.02524   0.314135  0.0909238   6, 37, 106, 87, 9, 13, 100, 72, 52
step  97   0.196191   0.144894   0.941916   0.326783  0.0851153   30, 46, 115, 105, 58, 63, 93, 133, 109, 73
step  98   0.404658   0.255027    1.41022   0.864128   0.119639   5, 78, 80, 24, 89, 116, 53, 132, 131, 68, 90, 8, 61, 29, 45, 119, 128, 11, 38, 32, 48, 77, 108, 98, 101, 41, 44, 81, 95, 56, 83, 110, 69, 36, 47, 75, 113, 134, 35, 74, 50, 23, 33, 42, 104, 96, 86, 125, 26, 71
step  99   0.132287   0.106991    1.26649   0.176039   0.113831   10, 40, 57, 49, 21, 94, 121, 123
step 100   0.233774   0.161054   0.958578   0.411898  0.0977632   30, 46, 115, 105, 58, 63, 93, 133, 109, 73, 114
step 101   0.199508   0.126603   0.893597   0.303876  0.0943435   2, 127, 51, 70, 102, 17, 19
step 102   0.196735   0.136793   0.847374   0.280642  0.0943435   3, 18, 7, 55, 12, 22, 97, 39
step 103  0.0909238  0.0909238    1.34261  0.0909238   0.113831   4, 84
step 104   0.200689   0.146028     1.0366   0.314135  0.0943435   6, 37, 106, 87, 9, 13, 100, 72, 52, 99
step 105   0.143451   0.104313   0.891958   0.188687   0.101183   14, 54, 66, 65
step 106   0.370684   0.261805   0.994816   0.667244  0.0943435   3, 18, 7, 55, 12, 22, 97, 39, 6, 37, 106, 87, 9, 13, 100, 72, 52, 99
step 107   0.334707   0.269479    1.00892   0.667244  0.0977632   3, 18, 7, 55, 12, 22, 97, 39, 6, 37, 106, 87, 9, 13, 100, 72, 52, 99, 25
step 108   0.146153   0.131491   0.891046   0.303876   0.123059   2, 127, 51, 70, 102, 17, 19, 137
step 109   0.347239   0.277255    1.00693   0.667244  0.0977632   3, 18, 7, 55, 12, 22, 97, 39, 6, 37, 106, 87, 9, 13, 100, 72, 52, 99, 25, 79
step 110   0.220267   0.261371    1.03144   0.667244  0.0977632   3, 18, 7, 55, 12, 22, 97, 39, 6, 37, 106, 87, 9, 13, 100, 72, 52, 99, 25, 79, 15, 43, 76
step 111   0.291649   0.265191    1.10851   0.667244   0.110411   3, 18, 7, 55, 12, 22, 97, 39, 6, 37, 106, 87, 9, 13, 100, 72, 52, 99, 25, 79, 15, 43, 76, 30, 46, 115, 105, 58, 63, 93, 133, 109, 73, 114
step 112   0.182281   0.135501   0.896034    0.28987   0.119639   14, 54, 66, 65, 129
step 113   0.106991   0.106991    1.32714   0.106991    0.11622   64, 130
step 114   0.428133   0.274502    1.10848   0.726032   0.113831   3, 18, 7, 55, 12, 22, 97, 39, 6, 37, 106, 87, 9, 13, 100, 72, 52, 99, 25, 79, 15, 43, 76, 30, 46, 115, 105, 58, 63, 93, 133, 109, 73, 114, 136
step 115   0.159912   0.120218    0.82177   0.263543   0.113831   16, 27, 120, 91, 103, 122, 124, 28, 117, 62, 138, 126
step 116   0.211336   0.143735    1.30904   0.315166   0.132287   4, 84, 10, 40, 57, 49, 21, 94, 121, 123
step 117   0.598735   0.391056    1.10724    1.06888   0.122028   3, 18, 7, 55, 12, 22, 97, 39, 6, 37, 106, 87, 9, 13, 100, 72, 52, 99, 25, 79, 15, 43, 76, 30, 46, 115, 105, 58, 63, 93, 133, 109, 73, 114, 136, 16, 27, 120, 91, 103, 122, 124, 28, 117, 62, 138, 126
step 118   0.119124    0.11508    1.30321   0.122028   0.138096   64, 130, 67
step 119   0.435425   0.284593    1.44209    1.00222   0.134676   5, 78, 80, 24, 89, 116, 53, 132, 131, 68, 90, 8, 61, 29, 45, 119, 128, 11, 38, 32, 48, 77, 108, 98, 101, 41, 44, 81, 95, 56, 83, 110, 69, 36, 47, 75, 113, 134, 35, 74, 50, 23, 33, 42, 104, 96, 86, 125, 26, 71, 14, 54, 66, 65, 129
step 120   0.521526     0.4012    1.13007    1.08289   0.123059   3, 18, 7, 55, 12, 22, 97, 39, 6, 37, 106, 87, 9, 13, 100, 72, 52, 99, 25, 79, 15, 43, 76, 30, 46, 115, 105, 58, 63, 93, 133, 109, 73, 114, 136, 16, 27, 120, 91, 103, 122, 124, 28, 117, 62, 138, 126, 31, 60
step 121   0.728048   0.476747    1.14449    1.29345   0.125448   2, 127, 51, 70, 102, 17, 19, 137, 3, 18, 7, 55, 12, 22, 97, 39, 6, 37, 106, 87, 9, 13, 100, 72, 52, 99, 25, 79, 15, 43, 76, 30, 46, 115, 105, 58, 63, 93, 133, 109, 73, 114, 136, 16, 27, 120, 91, 103, 122, 124, 28, 117, 62, 138, 126, 31, 60
step 122   0.392487   0.473841    1.15256    1.29345   0.125448   2, 127, 51, 70, 102, 17, 19, 137, 3, 18, 7, 55, 12, 22, 97, 39, 6, 37, 106, 87, 9, 13, 100, 72, 52, 99, 25, 79, 15, 43, 76, 30, 46, 115, 105, 58, 63, 93, 133, 109, 73, 114, 136, 16, 27, 120, 91, 103, 122, 124, 28, 117, 62, 138, 126, 31, 60, 88
step 123   0.449042   0.473001    1.15882    1.29345   0.132287   2, 127, 51, 70, 102, 17, 19, 137, 3, 18, 7, 55, 12, 22, 97, 39, 6, 37, 106, 87, 9, 13, 100, 72, 52, 99, 25, 79, 15, 43, 76, 30, 46, 115, 105, 58, 63, 93, 133, 109, 73, 114, 136, 16, 27, 120, 91, 103, 122, 124, 28, 117, 62, 138, 126, 31, 60, 88, 107
step 124   0.781825   0.544352    1.29264    1.65682   0.138096   2, 127, 51, 70, 102, 17, 19, 137, 3, 18, 7, 55, 12, 22, 97, 39, 6, 37, 106, 87, 9, 13, 100, 72, 52, 99, 25, 79, 15, 43, 76, 30, 46, 115, 105, 58, 63, 93, 133, 109, 73, 114, 136, 16, 27, 120, 91, 103, 122, 124, 28, 117, 62, 138, 126, 31, 60, 88, 107, 4, 84, 10, 40, 57, 49, 21, 94, 121, 123
step 125   0.601927   0.295926    1.44608    1.08631   0.147324   5, 78, 80, 24, 89, 116, 53, 132, 131, 68, 90, 8, 61, 29, 45, 119, 128, 11, 38, 32, 48, 77, 108, 98, 101, 41, 44, 81, 95, 56, 83, 110, 69, 36, 47, 75, 113, 134, 35, 74, 50, 23, 33, 42, 104, 96, 86, 125, 26, 71, 14, 54, 66, 65, 129, 111
step 126   0.766519    0.56184    1.33938    1.65682   0.148355   2, 127, 51, 70, 102, 17, 19, 137, 3, 18, 7, 55, 12, 22, 97, 39, 6, 37, 106, 87, 9, 13, 100, 72, 52, 99, 25, 79, 15, 43, 76, 30, 46, 115, 105, 58, 63, 93, 133, 109, 73, 114, 136, 16, 27, 120, 91, 103, 122, 124, 28, 117, 62, 138, 126, 31, 60, 88, 107, 4, 84, 10, 40, 57, 49, 21, 94, 121, 123, 64, 130, 67
step 127   0.144935   0.144935     1.9959   0.144935   0.561283   118, 135
step 128   0.347105   0.297722    1.46352    1.08631   0.568157   5, 78, 80, 24, 89, 116, 53, 132, 131, 68, 90, 8, 61, 29, 45, 119, 128, 11, 38, 32, 48, 77, 108, 98, 101, 41, 44, 81, 95, 56, 83, 110, 69, 36, 47, 75, 113, 134, 35, 74, 50, 23, 33, 42, 104, 96, 86, 125, 26, 71, 14, 54, 66, 65, 129, 111, 20
step 129   0.546575   0.561422    1.34825    1.65682   0.238247   2, 127, 51, 70, 102, 17, 19, 137, 3, 18, 7, 55, 12, 22, 97, 39, 6, 37, 106, 87, 9, 13, 100, 72, 52, 99, 25, 79, 15, 43, 76, 30, 46, 115, 105, 58, 63, 93, 133, 109, 73, 114, 136, 16, 27, 120, 91, 103, 122, 124, 28, 117, 62, 138, 126, 31, 60, 88, 107, 4, 84, 10, 40, 57, 49, 21, 94, 121, 123, 64, 130, 67, 92
step 130   0.209532   0.209532    1.46808   0.209532    0.39138   59, 82
step 131     1.0355   0.574235    1.36504    1.89507   0.274833   2, 127, 51, 70, 102, 17, 19, 137, 3, 18, 7, 55, 12, 22, 97, 39, 6, 37, 106, 87, 9, 13, 100, 72, 52, 99, 25, 79, 15, 43, 76, 30, 46, 115, 105, 58, 63, 93, 133, 109, 73, 114, 136, 16, 27, 120, 91, 103, 122, 124, 28, 117, 62, 138, 126, 31, 60, 88, 107, 4, 84, 10, 40, 57, 49, 21, 94, 121, 123, 64, 130, 67, 92, 112
step 132    1.03976   0.586649    1.38213    1.89507   0.568157   1, 2, 127, 51, 70, 102, 17, 19, 137, 3, 18, 7, 55, 12, 22, 97, 39, 6, 37, 106, 87, 9, 13, 100, 72, 52, 99, 25, 79, 15, 43, 76, 30, 46, 115, 105, 58, 63, 93, 133, 109, 73, 114, 136, 16, 27, 120, 91, 103, 122, 124, 28, 117, 62, 138, 126, 31, 60, 88, 107, 4, 84, 10, 40, 57, 49, 21, 94, 121, 123, 64, 130, 67, 92, 112
step 133   0.483498   0.392176    1.42835   0.575616   0.561283   34, 59, 82
step 134   0.861739    0.64919    1.67072    1.18065   0.611909   34, 59, 82, 118, 135
step 135    1.39162   0.931329    1.75421    2.85325   0.611909   1, 2, 127, 51, 70, 102, 17, 19, 137, 3, 18, 7, 55, 12, 22, 97, 39, 6, 37, 106, 87, 9, 13, 100, 72, 52, 99, 25, 79, 15, 43, 76, 30, 46, 115, 105, 58, 63, 93, 133, 109, 73, 114, 136, 16, 27, 120, 91, 103, 122, 124, 28, 117, 62, 138, 126, 31, 60, 88, 107, 4, 84, 10, 40, 57, 49, 21, 94, 121, 123, 64, 130, 67, 92, 112, 5, 78, 80, 24, 89, 116, 53, 132, 131, 68, 90, 8, 61, 29, 45, 119, 128, 11, 38, 32, 48, 77, 108, 98, 101, 41, 44, 81, 95, 56, 83, 110, 69, 36, 47, 75, 113, 134, 35, 74, 50, 23, 33, 42, 104, 96, 86, 125, 26, 71, 14, 54, 66, 65, 129, 111, 20
step 136    1.67595   0.983779      2.103    3.35236   0.678568   1, 2, 127, 51, 70, 102, 17, 19, 137, 3, 18, 7, 55, 12, 22, 97, 39, 6, 37, 106, 87, 9, 13, 100, 72, 52, 99, 25, 79, 15, 43, 76, 30, 46, 115, 105, 58, 63, 93, 133, 109, 73, 114, 136, 16, 27, 120, 91, 103, 122, 124, 28, 117, 62, 138, 126, 31, 60, 88, 107, 4, 84, 10, 40, 57, 49, 21, 94, 121, 123, 64, 130, 67, 92, 112, 5, 78, 80, 24, 89, 116, 53, 132, 131, 68, 90, 8, 61, 29, 45, 119, 128, 11, 38, 32, 48, 77, 108, 98, 101, 41, 44, 81, 95, 56, 83, 110, 69, 36, 47, 75, 113, 134, 35, 74, 50, 23, 33, 42, 104, 96, 86, 125, 26, 71, 14, 54, 66, 65, 129, 111, 20, 34, 59, 82, 118, 135
step 137      2.103          1               3.35236              1, 2, 127, 51, 70, 102, 17, 19, 137, 3, 18, 7, 55, 12, 22, 97, 39, 6, 37, 106, 87, 9, 13, 100, 72, 52, 99, 25, 79, 15, 43, 76, 30, 46, 115, 105, 58, 63, 93, 133, 109, 73, 114, 136, 16, 27, 120, 91, 103, 122, 124, 28, 117, 62, 138, 126, 31, 60, 88, 107, 4, 84, 10, 40, 57, 49, 21, 94, 121, 123, 64, 130, 67, 92, 112, 5, 78, 80, 24, 89, 116, 53, 132, 131, 68, 90, 8, 61, 29, 45, 119, 128, 11, 38, 32, 48, 77, 108, 98, 101, 41, 44, 81, 95, 56, 83, 110, 69, 36, 47, 75, 113, 134, 35, 74, 50, 23, 33, 42, 104, 96, 86, 125, 26, 71, 14, 54, 66, 65, 129, 111, 20, 34, 59, 82, 118, 135, 85


dendrogram scale: child cluster distance
  1           2         127          51          70         102          17          19         137           3          18           7          55          12          22          97          39           6          37         106          87           9          13         100          72          52          99          25          79          15          43          76          30          46         115         105          58          63          93         133         109          73         114         136          16          27         120          91         103         122         124          28         117          62         138         126          31          60          88         107           4          84          10          40          57          49          21          94         121         123          64         130          67          92         112           5          78          80          24          89         116          53         132         131          68          90           8          61          29          45         119         128          11          38          32          48          77         108          98         101          41          44          81          95          56          83         110          69          36          47          75         113         134          35          74          50          23          33          42         104          96          86         125          26          71          14          54          66          65         129         111          20          34          59          82         118         135          85
     1.03976   0.0379436   0.0736618    0.021876    0.113912    0.130301    0.199508    0.146153    0.728048   0.0379436   0.0627238           0     0.09699    0.196735   0.0379436   0.0822111    0.370684   0.0954834   0.0471717   0.0615295    0.154421   0.0505915   0.0252957   0.0951397    0.178217    0.200689    0.334707    0.347239    0.220267   0.0656281   0.0834055    0.291649   0.0379436   0.0753717   0.0808994    0.106136    0.196191   0.0345239    0.061014   0.0713276   0.0972477    0.233774    0.428133    0.598735   0.0440957   0.0126479      0.0282   0.0739196   0.0126479   0.0513877    0.167784   0.0252957   0.0782759   0.0252957    0.159912    0.521526   0.0563999    0.392487    0.449042    0.781825   0.0909238    0.211336   0.0636919   0.0345239   0.0425577    0.132287   0.0126479    0.120834   0.0724675    0.766519    0.106991    0.119124    0.546575      1.0355     1.39162    0.043752   0.0909238    0.114053           0   0.0345239   0.0410196     0.11988    0.170781    0.170795   0.0656281    0.263482    0.021876   0.0362337    0.111207   0.0661435   0.0379436    0.213303    0.021876   0.0454619    0.047968   0.0704999   0.0559222   0.0749736   0.0678767    0.130293           0   0.0408478   0.0126479   0.0583675   0.0345239   0.0252957   0.0862301    0.118571   0.0471717    0.132286   0.0408478   0.0126479    0.149733    0.153907    0.224119    0.404658   0.0252957   0.0471717   0.0693914   0.0768238   0.0994026   0.0505915    0.129015    0.137668    0.435425   0.0379436   0.0787914    0.143451    0.182281    0.601927    0.347105     1.67595    0.483498    0.209532    0.861739    0.144935       2.103

  1 ___________________________________________________________________________________________________
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  2 _________________________________________________|               |             |                   |
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127 _| | |   |                       |   |           |               |             |                   |
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 51 ___| |   |                       |   |           |               |             |                   |
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 70 _|   |   |                       |   |           |               |             |                   |
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102 _____|   |                       |   |           |               |             |                   |
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 17 _____|   |                       |   |           |               |             |                   |
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 19 _________|                       |   |           |               |             |                   |
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137 _____|                           |   |           |               |             |                   |
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  3 _________________________________|   |           |               |             |                   |
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 18 _| |     |       | |       |         |           |               |             |                   |
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  7 _| |     |       | |       |         |           |               |             |                   |
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 55 |  |     |       | |       |         |           |               |             |                   |
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 12 ___|     |       | |       |         |           |               |             |                   |
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 22 _________|       | |       |         |           |               |             |                   |
     | |             | |       |         |           |               |             |                   |
 97 _| |             | |       |         |           |               |             |                   |
       |             | |       |         |           |               |             |                   |
 39 ___|             | |       |         |           |               |             |                   |
                     | |       |         |           |               |             |                   |
  6 _________________| |       |         |           |               |             |                   |
       |   | |     |   |       |         |           |               |             |                   |
 37 ___|   | |     |   |       |         |           |               |             |                   |
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106 _|     | |     |   |       |         |           |               |             |                   |
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 87 _|     | |     |   |       |         |           |               |             |                   |
           | |     |   |       |         |           |               |             |                   |
  9 _______| |     |   |       |         |           |               |             |                   |
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 13 _| |   | |     |   |       |         |           |               |             |                   |
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100 _| |   | |     |   |       |         |           |               |             |                   |
       |   | |     |   |       |         |           |               |             |                   |
 72 ___|   | |     |   |       |         |           |               |             |                   |
           | |     |   |       |         |           |               |             |                   |
 52 _______| |     |   |       |         |           |               |             |                   |
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 99 _________|     |   |       |         |           |               |             |                   |
                   |   |       |         |           |               |             |                   |
 25 _______________|   |       |         |           |               |             |                   |
                   |   |       |         |           |               |             |                   |
 79 _______________|   |       |         |           |               |             |                   |
             |   |     |       |         |           |               |             |                   |
 15 _________|   |     |       |         |           |               |             |                   |
       |         |     |       |         |           |               |             |                   |
 43 ___|         |     |       |         |           |               |             |                   |
       |         |     |       |         |           |               |             |                   |
 76 ___|         |     |       |         |           |               |             |                   |
                 |     |       |         |           |               |             |                   |
 30 _____________|     |       |         |           |               |             |                   |
     | | |   | |       |       |         |           |               |             |                   |
 46 _| | |   | |       |       |         |           |               |             |                   |
       | |   | |       |       |         |           |               |             |                   |
115 ___| |   | |       |       |         |           |               |             |                   |
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105 ___| |   | |       |       |         |           |               |             |                   |
         |   | |       |       |         |           |               |             |                   |
 58 _____|   | |       |       |         |           |               |             |                   |
             | |       |       |         |           |               |             |                   |
 63 _________| |       |       |         |           |               |             |                   |
     | |       |       |       |         |           |               |             |                   |
 93 _| |       |       |       |         |           |               |             |                   |
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133 _| |       |       |       |         |           |               |             |                   |
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109 ___|       |       |       |         |           |               |             |                   |
       |       |       |       |         |           |               |             |                   |
 73 ___|       |       |       |         |           |               |             |                   |
               |       |       |         |           |               |             |                   |
114 ___________|       |       |         |           |               |             |                   |
                       |       |         |           |               |             |                   |
136 ___________________|       |         |           |               |             |                   |
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 16 ___________________________|         |           |               |             |                   |
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 27 _| |   |               |             |           |               |             |                   |
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120 || |   |               |             |           |               |             |                   |
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 91 _| |   |               |             |           |               |             |                   |
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103 ___|   |               |             |           |               |             |                   |
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122 ||     |               |             |           |               |             |                   |
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124 _|     |               |             |           |               |             |                   |
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 28 _______|               |             |           |               |             |                   |
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117 _| |   |               |             |           |               |             |                   |
       |   |               |             |           |               |             |                   |
 62 ___|   |               |             |           |               |             |                   |
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138 _|     |               |             |           |               |             |                   |
           |               |             |           |               |             |                   |
126 _______|               |             |           |               |             |                   |
                           |             |           |               |             |                   |
 31 _______________________|             |           |               |             |                   |
     |               |   |               |           |               |             |                   |
 60 _|               |   |               |           |               |             |                   |
                     |   |               |           |               |             |                   |
 88 _________________|   |               |           |               |             |                   |
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107 _____________________|               |           |               |             |                   |
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  4 _____________________________________|           |               |             |                   |
       |     |                         |             |               |             |                   |
 84 ___|     |                         |             |               |             |                   |
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 10 _________|                         |             |               |             |                   |
       | |                             |             |               |             |                   |
 40 ___| |                             |             |               |             |                   |
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 57 _|   |                             |             |               |             |                   |
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 49 _|   |                             |             |               |             |                   |
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 21 _____|                             |             |               |             |                   |
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 94 |    |                             |             |               |             |                   |
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121 _____|                             |             |               |             |                   |
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123 ___|                               |             |               |             |                   |
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 64 ___________________________________|             |               |             |                   |
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130 _____|                   |                       |               |             |                   |
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 67 _____|                   |                       |               |             |                   |
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 92 _________________________|                       |               |             |                   |
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112 _________________________________________________|               |             |                   |
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  5 _________________________________________________________________|             |                   |
     | | | |   |       |       |                                                   |                   |
 78 _| | | |   |       |       |                                                   |                   |
       | | |   |       |       |                                                   |                   |
 80 ___| | |   |       |       |                                                   |                   |
         | |   |       |       |                                                   |                   |
 24 _____| |   |       |       |                                                   |                   |
    ||   | |   |       |       |                                                   |                   |
 89 ||   | |   |       |       |                                                   |                   |
     |   | |   |       |       |                                                   |                   |
116 _|   | |   |       |       |                                                   |                   |
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 53 _|   | |   |       |       |                                                   |                   |
         | |   |       |       |                                                   |                   |
132 _____| |   |       |       |                                                   |                   |
           |   |       |       |                                                   |                   |
131 _______|   |       |       |                                                   |                   |
           |   |       |       |                                                   |                   |
 68 _______|   |       |       |                                                   |                   |
       |       |       |       |                                                   |                   |
 90 ___|       |       |       |                                                   |                   |
               |       |       |                                                   |                   |
  8 ___________|       |       |                                                   |                   |
     |   |   |         |       |                                                   |                   |
 61 _|   |   |         |       |                                                   |                   |
     |   |   |         |       |                                                   |                   |
 29 _|   |   |         |       |                                                   |                   |
         |   |         |       |                                                   |                   |
 45 _____|   |         |       |                                                   |                   |
       |     |         |       |                                                   |                   |
119 ___|     |         |       |                                                   |                   |
     |       |         |       |                                                   |                   |
128 _|       |         |       |                                                   |                   |
             |         |       |                                                   |                   |
 11 _________|         |       |                                                   |                   |
     | | | | |         |       |                                                   |                   |
 38 _| | | | |         |       |                                                   |                   |
     | | | | |         |       |                                                   |                   |
 32 _| | | | |         |       |                                                   |                   |
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 48 _| | | | |         |       |                                                   |                   |
       | | | |         |       |                                                   |                   |
 77 ___| | | |         |       |                                                   |                   |
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108 _| | | | |         |       |                                                   |                   |
       | | | |         |       |                                                   |                   |
 98 ___| | | |         |       |                                                   |                   |
       | | | |         |       |                                                   |                   |
101 ___| | | |         |       |                                                   |                   |
         | | |         |       |                                                   |                   |
 41 _____| | |         |       |                                                   |                   |
    || | | | |         |       |                                                   |                   |
 44 || | | | |         |       |                                                   |                   |
     | | | | |         |       |                                                   |                   |
 81 _| | | | |         |       |                                                   |                   |
    | | | | | |         |       |                                                   |                   |
 95 || | | | |         |       |                                                   |                   |
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 56 _| | | | |         |       |                                                   |                   |
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 83 _| | | | |         |       |                                                   |                   |
     | | | | |         |       |                                                   |                   |
110 _| | | | |         |       |                                                   |                   |
       | | | |         |       |                                                   |                   |
 69 ___| | | |         |       |                                                   |                   |
         | | |         |       |                                                   |                   |
 36 _____| | |         |       |                                                   |                   |
     |   | | |         |       |                                                   |                   |
 47 _|   | | |         |       |                                                   |                   |
         | | |         |       |                                                   |                   |
 75 _____| | |         |       |                                                   |                   |
     |     | |         |       |                                                   |                   |
113 _|     | |         |       |                                                   |                   |
    |       | |         |       |                                                   |                   |
134 |      | |         |       |                                                   |                   |
           | |         |       |                                                   |                   |
 35 _______| |         |       |                                                   |                   |
           | |         |       |                                                   |                   |
 74 _______| |         |       |                                                   |                   |
             |         |       |                                                   |                   |
 50 _________|         |       |                                                   |                   |
                       |       |                                                   |                   |
 23 ___________________|       |                                                   |                   |
     | | |             |       |                                                   |                   |
 33 _| | |             |       |                                                   |                   |
     | | |             |       |                                                   |                   |
 42 _| | |             |       |                                                   |                   |
       | |             |       |                                                   |                   |
104 ___| |             |       |                                                   |                   |
       | |             |       |                                                   |                   |
 96 ___| |             |       |                                                   |                   |
       | |             |       |                                                   |                   |
 86 ___| |             |       |                                                   |                   |
     |   |             |       |                                                   |                   |
125 _|   |             |       |                                                   |                   |
         |             |       |                                                   |                   |
 26 _____|             |       |                                                   |                   |
         |             |       |                                                   |                   |
 71 _____|             |       |                                                   |                   |
                       |       |                                                   |                   |
 14 ___________________|       |                                                   |                   |
     | | | |                   |                                                   |                   |
 54 _| | | |                   |                                                   |                   |
       | | |                   |                                                   |                   |
 66 ___| | |                   |                                                   |                   |
         | |                   |                                                   |                   |
 65 _____| |                   |                                                   |                   |
           |                   |                                                   |                   |
129 _______|                   |                                                   |                   |
                               |                                                   |                   |
111 ___________________________|                                                   |                   |
                   |                                                               |                   |
 20 _______________|                                                               |                   |
                                                                                   |                   |
 34 _______________________________________________________________________________|                   |
                         |                 |                                                           |
 59 _____________________|                 |                                                           |
             |                             |                                                           |
 82 _________|                             |                                                           |
                                           |                                                           |
118 _______________________________________|                                                           |
         |                                                                                             |
135 _____|                                                                                             |
                                                                                                       |
 85 ___________________________________________________________________________________________________|

child cluster distance scale coefficient: 0.943282
diameter scale coefficient: 0.940673

Hierarchical clustering and dendrogram using a divise algorithm#

[13]:
clust3 = Clustering(matrix, "Hierarchy", "Divisive")
print(clust3)
138 vectors

        | child cluster distance | within-cluster distance | between-cluster distance | diameter | separation | composition
step   1          0          0   0.845491          0  0.0563999   7, 55
step   2          0          0   0.883565          0  0.0345239   24, 89
step   3          0          0   0.911651          0  0.0345239   41, 44
step   4  0.0126479  0.0126479    1.18625  0.0126479  0.0782759   21, 94
step   5  0.0126479  0.0126479   0.760368  0.0126479   0.021876   27, 120
step   6  0.0126479  0.0126479   0.913273  0.0126479  0.0345239   81, 95
step   7  0.0126479  0.0126479   0.762643  0.0126479  0.0345239   103, 122
step   8  0.0126479  0.0126479     1.0078  0.0126479  0.0345239   113, 134
step   9   0.021876   0.021876    1.08646   0.021876  0.0252957   8, 61
step  10   0.021876   0.021876   0.967306   0.021876  0.0345239   11, 38
step  11     0.0282  0.0230159   0.765583  0.0345239  0.0252957   27, 120, 91
step  12   0.021876   0.021876   0.868665   0.021876  0.0563999   51, 70
step  13  0.0362337  0.0314478    1.09889  0.0471717  0.0471717   8, 61, 29
step  14  0.0252957  0.0252957   0.921014  0.0252957  0.0379436   13, 100
step  15  0.0440957  0.0335558    0.77085  0.0598196  0.0345239   16, 27, 120, 91
step  16  0.0252957  0.0252957     1.2527  0.0252957  0.0345239   23, 33
step  17  0.0252957  0.0252957   0.775549  0.0252957  0.0656281   28, 117
step  18  0.0252957  0.0252957    0.79839  0.0252957  0.0656281   62, 138
step  19  0.0252957  0.0252957   0.890767  0.0252957  0.0345239   83, 110
step  20  0.0454619  0.0375999   0.968891  0.0563999  0.0345239   11, 38, 32
step  21  0.0739196  0.0536893    0.78211   0.106991  0.0345239   16, 27, 120, 91, 103, 122
step  22  0.0471717  0.0398797    1.24669  0.0598196  0.0379436   23, 33, 42
step  23  0.0345239  0.0230159   0.887222  0.0345239  0.0379436   24, 89, 116
step  24   0.047968   0.042784   0.968338  0.0656281  0.0345239   11, 38, 32, 48
step  25  0.0704999  0.0538703   0.981483   0.100152  0.0379436   11, 38, 32, 48, 77
step  26  0.0345239  0.0345239    1.23769  0.0345239  0.0379436   40, 57
step  27  0.0408478  0.0293399   0.925471  0.0471717  0.0379436   41, 44, 81, 95
step  28  0.0345239  0.0314478   0.899478  0.0345239  0.0379436   56, 83, 110
step  29  0.0345239  0.0345239   0.938001  0.0345239   0.043752   63, 93
step  30  0.0408478  0.0314478    1.00594  0.0471717  0.0505915   75, 113, 134
step  31  0.0513877  0.0530317   0.787684   0.106991  0.0656281   16, 27, 120, 91, 103, 122, 124
step  32  0.0379436  0.0379436   0.855993  0.0379436  0.0563999   2, 127
step  33  0.0379436  0.0379436   0.831399  0.0379436  0.0563999   3, 18
step  34  0.0505915  0.0421595   0.937767  0.0632393  0.0656281   9, 13, 100
step  35  0.0379436  0.0379436    0.87456  0.0379436  0.0598196   14, 54
step  36  0.0379436  0.0379436   0.779505  0.0379436  0.0632393   22, 97
step  37  0.0410196  0.0320178   0.894159  0.0471717  0.0690478   24, 89, 116, 53
step  38  0.0379436  0.0379436   0.855449  0.0379436  0.0563999   30, 46
step  39  0.0559222  0.0545543   0.984221   0.100152  0.0379436   11, 38, 32, 48, 77, 108
step  40  0.0749736  0.0603884   0.996551   0.106991  0.0379436   11, 38, 32, 48, 77, 108, 98
step  41  0.0678767  0.0622605     1.0035   0.106991   0.043752   11, 38, 32, 48, 77, 108, 98, 101
step  42  0.0583675  0.0462282   0.936685  0.0851153   0.043752   41, 44, 81, 95, 56, 83, 110
step  43  0.0693914  0.0546356      1.239  0.0977632   0.043752   23, 33, 42, 104
step  44  0.0425577  0.0398797    1.25903  0.0471717  0.0563999   40, 57, 49
step  45  0.0379436  0.0379436    1.07673  0.0379436  0.0471717   119, 128
step  46   0.043752   0.043752   0.947424   0.043752  0.0690478   5, 78
step  47   0.130293  0.0953383     1.0233   0.219791   0.043752   11, 38, 32, 48, 77, 108, 98, 101, 41, 44, 81, 95, 56, 83, 110
step  48  0.0768238  0.0635109    1.23707   0.103572  0.0563999   23, 33, 42, 104, 96
step  49  0.0862301  0.0941997    1.03095   0.219791  0.0471717   11, 38, 32, 48, 77, 108, 98, 101, 41, 44, 81, 95, 56, 83, 110, 69
step  50   0.061014  0.0521839   0.933878  0.0782759  0.0505915   63, 93, 133
step  51  0.0471717  0.0471717    0.95163  0.0471717  0.0471717   36, 47
step  52  0.0471717  0.0471717   0.995691  0.0471717  0.0598196   37, 106
step  53  0.0661435  0.0567436    1.07975  0.0851153  0.0471717   45, 119, 128
step  54   0.118571  0.0989895      1.048   0.219791  0.0505915   11, 38, 32, 48, 77, 108, 98, 101, 41, 44, 81, 95, 56, 83, 110, 69, 36, 47
step  55   0.111207  0.0843627    1.11155   0.179459  0.0656281   8, 61, 29, 45, 119, 128
step  56   0.132286   0.106587    1.08131   0.248507  0.0563999   11, 38, 32, 48, 77, 108, 98, 101, 41, 44, 81, 95, 56, 83, 110, 69, 36, 47, 75, 113, 134
step  57  0.0713276  0.0617558   0.949872   0.103572  0.0563999   63, 93, 133, 109
step  58  0.0505915  0.0505915    1.20298  0.0505915  0.0563999   86, 125
step  59  0.0627238  0.0481398   0.850023  0.0690478  0.0782759   3, 18, 7, 55
step  60  0.0636919  0.0517858    1.27837  0.0690478  0.0816956   10, 40, 57, 49
step  61  0.0753717  0.0628957   0.857606  0.0943435  0.0598196   30, 46, 115
step  62  0.0563999  0.0563999    1.06846  0.0563999   0.122028   31, 60
step  63   0.149733   0.110509    1.08732   0.250895  0.0656281   11, 38, 32, 48, 77, 108, 98, 101, 41, 44, 81, 95, 56, 83, 110, 69, 36, 47, 75, 113, 134, 35
step  64  0.0972477  0.0759525   0.962431   0.134676  0.0782759   63, 93, 133, 109, 73
step  65  0.0736618  0.0590778     0.8741  0.0909238  0.0724675   2, 127, 51, 70
step  66  0.0994026   0.079987    1.25177   0.163391  0.0690478   23, 33, 42, 104, 96, 86, 125
step  67  0.0787914  0.0651755   0.884129  0.0977632  0.0909238   14, 54, 66
step  68  0.0615295  0.0567436    1.01765  0.0632393  0.0690478   37, 106, 87
step  69  0.0808994  0.0718975   0.867262   0.110411  0.0782759   30, 46, 115, 105
step  70  0.0822111  0.0674553   0.790057   0.101183   0.088535   22, 97, 39
step  71  0.0656281  0.0656281   0.914738  0.0656281  0.0724675   15, 43
step  72  0.0782759  0.0606159   0.797547  0.0909238  0.0656281   28, 117, 62, 138
step  73   0.167784   0.112279   0.816318   0.263543   0.113831   16, 27, 120, 91, 103, 122, 124, 28, 117, 62, 138
step  74  0.0656281  0.0656281   0.861875  0.0656281  0.0724675   68, 90
step  75  0.0951397  0.0686496   0.932222   0.128867  0.0690478   9, 13, 100, 72
step  76   0.213303   0.145368    1.16847   0.358918  0.0724675   8, 61, 29, 45, 119, 128, 11, 38, 32, 48, 77, 108, 98, 101, 41, 44, 81, 95, 56, 83, 110, 69, 36, 47, 75, 113, 134, 35
step  77  0.0909238  0.0751999   0.940275     0.1128  0.0690478   5, 78, 80
step  78  0.0954834  0.0761135     1.0311   0.132287  0.0690478   6, 37, 106, 87
step  79   0.154421   0.119261    1.00711   0.261154  0.0782759   6, 37, 106, 87, 9, 13, 100, 72
step  80   0.114053  0.0850638   0.934943     0.1692  0.0690478   5, 78, 80, 24, 89, 116, 53
step  81   0.129015  0.0922439    1.27621   0.172619  0.0690478   23, 33, 42, 104, 96, 86, 125, 26
step  82   0.137668   0.102338    1.29949   0.191076  0.0816956   23, 33, 42, 104, 96, 86, 125, 26, 71
step  83    0.11988  0.0937678   0.936256   0.209532  0.0690478   5, 78, 80, 24, 89, 116, 53, 132
step  84   0.170781   0.110882   0.937799    0.27858  0.0724675   5, 78, 80, 24, 89, 116, 53, 132, 131
step  85  0.0834055  0.0774797   0.933912  0.0943435  0.0977632   15, 43, 76
step  86   0.153907   0.145957    1.17948   0.358918  0.0758872   8, 61, 29, 45, 119, 128, 11, 38, 32, 48, 77, 108, 98, 101, 41, 44, 81, 95, 56, 83, 110, 69, 36, 47, 75, 113, 134, 35, 74
step  87   0.113912  0.0810117    0.87747   0.163391  0.0782759   2, 127, 51, 70, 102
step  88   0.170795   0.129667   0.942781   0.322332  0.0758872   5, 78, 80, 24, 89, 116, 53, 132, 131, 68, 90
step  89  0.0724675  0.0724675    1.15619  0.0724675  0.0782759   121, 123
step  90   0.263482   0.192873    1.24421   0.591357  0.0782759   5, 78, 80, 24, 89, 116, 53, 132, 131, 68, 90, 8, 61, 29, 45, 119, 128, 11, 38, 32, 48, 77, 108, 98, 101, 41, 44, 81, 95, 56, 83, 110, 69, 36, 47, 75, 113, 134, 35, 74
step  91   0.130301  0.0974413   0.881249   0.216371  0.0875041   2, 127, 51, 70, 102, 17
step  92    0.09699  0.0676799   0.852929    0.10938   0.088535   3, 18, 7, 55, 12
step  93   0.120834  0.0947416     1.1869   0.163391  0.0816956   21, 94, 121, 123
step  94   0.106136  0.0855931    0.86533   0.144935  0.0782759   30, 46, 115, 105, 58
step  95   0.224119   0.194397    1.25595   0.591357  0.0816956   5, 78, 80, 24, 89, 116, 53, 132, 131, 68, 90, 8, 61, 29, 45, 119, 128, 11, 38, 32, 48, 77, 108, 98, 101, 41, 44, 81, 95, 56, 83, 110, 69, 36, 47, 75, 113, 134, 35, 74, 50
step  96   0.178217   0.132363    1.02524   0.314135  0.0909238   6, 37, 106, 87, 9, 13, 100, 72, 52
step  97   0.196191   0.144894   0.941916   0.326783  0.0851153   30, 46, 115, 105, 58, 63, 93, 133, 109, 73
step  98   0.404658   0.255027    1.41022   0.864128   0.119639   5, 78, 80, 24, 89, 116, 53, 132, 131, 68, 90, 8, 61, 29, 45, 119, 128, 11, 38, 32, 48, 77, 108, 98, 101, 41, 44, 81, 95, 56, 83, 110, 69, 36, 47, 75, 113, 134, 35, 74, 50, 23, 33, 42, 104, 96, 86, 125, 26, 71
step  99   0.132287   0.106991    1.26649   0.176039   0.113831   10, 40, 57, 49, 21, 94, 121, 123
step 100   0.233774   0.161054   0.958578   0.411898  0.0977632   30, 46, 115, 105, 58, 63, 93, 133, 109, 73, 114
step 101   0.199508   0.126603   0.893597   0.303876  0.0943435   2, 127, 51, 70, 102, 17, 19
step 102   0.196735   0.136793   0.847374   0.280642  0.0943435   3, 18, 7, 55, 12, 22, 97, 39
step 103  0.0909238  0.0909238    1.34261  0.0909238   0.113831   4, 84
step 104   0.200689   0.146028     1.0366   0.314135  0.0943435   6, 37, 106, 87, 9, 13, 100, 72, 52, 99
step 105   0.143451   0.104313   0.891958   0.188687   0.101183   14, 54, 66, 65
step 106   0.370684   0.261805   0.994816   0.667244  0.0943435   3, 18, 7, 55, 12, 22, 97, 39, 6, 37, 106, 87, 9, 13, 100, 72, 52, 99
step 107   0.334707   0.269479    1.00892   0.667244  0.0977632   3, 18, 7, 55, 12, 22, 97, 39, 6, 37, 106, 87, 9, 13, 100, 72, 52, 99, 25
step 108   0.146153   0.131491   0.891046   0.303876   0.123059   2, 127, 51, 70, 102, 17, 19, 137
step 109   0.347239   0.277255    1.00693   0.667244  0.0977632   3, 18, 7, 55, 12, 22, 97, 39, 6, 37, 106, 87, 9, 13, 100, 72, 52, 99, 25, 79
step 110   0.220267   0.261371    1.03144   0.667244  0.0977632   3, 18, 7, 55, 12, 22, 97, 39, 6, 37, 106, 87, 9, 13, 100, 72, 52, 99, 25, 79, 15, 43, 76
step 111   0.291649   0.265191    1.10851   0.667244   0.110411   3, 18, 7, 55, 12, 22, 97, 39, 6, 37, 106, 87, 9, 13, 100, 72, 52, 99, 25, 79, 15, 43, 76, 30, 46, 115, 105, 58, 63, 93, 133, 109, 73, 114
step 112   0.182281   0.135501   0.896034    0.28987   0.119639   14, 54, 66, 65, 129
step 113   0.106991   0.106991    1.32714   0.106991    0.11622   64, 130
step 114   0.428133   0.274502    1.10848   0.726032   0.113831   3, 18, 7, 55, 12, 22, 97, 39, 6, 37, 106, 87, 9, 13, 100, 72, 52, 99, 25, 79, 15, 43, 76, 30, 46, 115, 105, 58, 63, 93, 133, 109, 73, 114, 136
step 115   0.159912   0.120218    0.82177   0.263543   0.113831   16, 27, 120, 91, 103, 122, 124, 28, 117, 62, 138, 126
step 116   0.211336   0.143735    1.30904   0.315166   0.132287   4, 84, 10, 40, 57, 49, 21, 94, 121, 123
step 117   0.598735   0.391056    1.10724    1.06888   0.122028   3, 18, 7, 55, 12, 22, 97, 39, 6, 37, 106, 87, 9, 13, 100, 72, 52, 99, 25, 79, 15, 43, 76, 30, 46, 115, 105, 58, 63, 93, 133, 109, 73, 114, 136, 16, 27, 120, 91, 103, 122, 124, 28, 117, 62, 138, 126
step 118   0.119124    0.11508    1.30321   0.122028   0.138096   64, 130, 67
step 119   0.435425   0.284593    1.44209    1.00222   0.134676   5, 78, 80, 24, 89, 116, 53, 132, 131, 68, 90, 8, 61, 29, 45, 119, 128, 11, 38, 32, 48, 77, 108, 98, 101, 41, 44, 81, 95, 56, 83, 110, 69, 36, 47, 75, 113, 134, 35, 74, 50, 23, 33, 42, 104, 96, 86, 125, 26, 71, 14, 54, 66, 65, 129
step 120   0.521526     0.4012    1.13007    1.08289   0.123059   3, 18, 7, 55, 12, 22, 97, 39, 6, 37, 106, 87, 9, 13, 100, 72, 52, 99, 25, 79, 15, 43, 76, 30, 46, 115, 105, 58, 63, 93, 133, 109, 73, 114, 136, 16, 27, 120, 91, 103, 122, 124, 28, 117, 62, 138, 126, 31, 60
step 121   0.728048   0.476747    1.14449    1.29345   0.125448   2, 127, 51, 70, 102, 17, 19, 137, 3, 18, 7, 55, 12, 22, 97, 39, 6, 37, 106, 87, 9, 13, 100, 72, 52, 99, 25, 79, 15, 43, 76, 30, 46, 115, 105, 58, 63, 93, 133, 109, 73, 114, 136, 16, 27, 120, 91, 103, 122, 124, 28, 117, 62, 138, 126, 31, 60
step 122   0.392487   0.473841    1.15256    1.29345   0.125448   2, 127, 51, 70, 102, 17, 19, 137, 3, 18, 7, 55, 12, 22, 97, 39, 6, 37, 106, 87, 9, 13, 100, 72, 52, 99, 25, 79, 15, 43, 76, 30, 46, 115, 105, 58, 63, 93, 133, 109, 73, 114, 136, 16, 27, 120, 91, 103, 122, 124, 28, 117, 62, 138, 126, 31, 60, 88
step 123   0.449042   0.473001    1.15882    1.29345   0.132287   2, 127, 51, 70, 102, 17, 19, 137, 3, 18, 7, 55, 12, 22, 97, 39, 6, 37, 106, 87, 9, 13, 100, 72, 52, 99, 25, 79, 15, 43, 76, 30, 46, 115, 105, 58, 63, 93, 133, 109, 73, 114, 136, 16, 27, 120, 91, 103, 122, 124, 28, 117, 62, 138, 126, 31, 60, 88, 107
step 124   0.781825   0.544352    1.29264    1.65682   0.138096   2, 127, 51, 70, 102, 17, 19, 137, 3, 18, 7, 55, 12, 22, 97, 39, 6, 37, 106, 87, 9, 13, 100, 72, 52, 99, 25, 79, 15, 43, 76, 30, 46, 115, 105, 58, 63, 93, 133, 109, 73, 114, 136, 16, 27, 120, 91, 103, 122, 124, 28, 117, 62, 138, 126, 31, 60, 88, 107, 4, 84, 10, 40, 57, 49, 21, 94, 121, 123
step 125   0.601927   0.295926    1.44608    1.08631   0.147324   5, 78, 80, 24, 89, 116, 53, 132, 131, 68, 90, 8, 61, 29, 45, 119, 128, 11, 38, 32, 48, 77, 108, 98, 101, 41, 44, 81, 95, 56, 83, 110, 69, 36, 47, 75, 113, 134, 35, 74, 50, 23, 33, 42, 104, 96, 86, 125, 26, 71, 14, 54, 66, 65, 129, 111
step 126   0.766519    0.56184    1.33938    1.65682   0.148355   2, 127, 51, 70, 102, 17, 19, 137, 3, 18, 7, 55, 12, 22, 97, 39, 6, 37, 106, 87, 9, 13, 100, 72, 52, 99, 25, 79, 15, 43, 76, 30, 46, 115, 105, 58, 63, 93, 133, 109, 73, 114, 136, 16, 27, 120, 91, 103, 122, 124, 28, 117, 62, 138, 126, 31, 60, 88, 107, 4, 84, 10, 40, 57, 49, 21, 94, 121, 123, 64, 130, 67
step 127   0.144935   0.144935     1.9959   0.144935   0.561283   118, 135
step 128   0.347105   0.297722    1.46352    1.08631   0.568157   5, 78, 80, 24, 89, 116, 53, 132, 131, 68, 90, 8, 61, 29, 45, 119, 128, 11, 38, 32, 48, 77, 108, 98, 101, 41, 44, 81, 95, 56, 83, 110, 69, 36, 47, 75, 113, 134, 35, 74, 50, 23, 33, 42, 104, 96, 86, 125, 26, 71, 14, 54, 66, 65, 129, 111, 20
step 129   0.546575   0.561422    1.34825    1.65682   0.238247   2, 127, 51, 70, 102, 17, 19, 137, 3, 18, 7, 55, 12, 22, 97, 39, 6, 37, 106, 87, 9, 13, 100, 72, 52, 99, 25, 79, 15, 43, 76, 30, 46, 115, 105, 58, 63, 93, 133, 109, 73, 114, 136, 16, 27, 120, 91, 103, 122, 124, 28, 117, 62, 138, 126, 31, 60, 88, 107, 4, 84, 10, 40, 57, 49, 21, 94, 121, 123, 64, 130, 67, 92
step 130   0.209532   0.209532    1.46808   0.209532    0.39138   59, 82
step 131     1.0355   0.574235    1.36504    1.89507   0.274833   2, 127, 51, 70, 102, 17, 19, 137, 3, 18, 7, 55, 12, 22, 97, 39, 6, 37, 106, 87, 9, 13, 100, 72, 52, 99, 25, 79, 15, 43, 76, 30, 46, 115, 105, 58, 63, 93, 133, 109, 73, 114, 136, 16, 27, 120, 91, 103, 122, 124, 28, 117, 62, 138, 126, 31, 60, 88, 107, 4, 84, 10, 40, 57, 49, 21, 94, 121, 123, 64, 130, 67, 92, 112
step 132    1.03976   0.586649    1.38213    1.89507   0.568157   1, 2, 127, 51, 70, 102, 17, 19, 137, 3, 18, 7, 55, 12, 22, 97, 39, 6, 37, 106, 87, 9, 13, 100, 72, 52, 99, 25, 79, 15, 43, 76, 30, 46, 115, 105, 58, 63, 93, 133, 109, 73, 114, 136, 16, 27, 120, 91, 103, 122, 124, 28, 117, 62, 138, 126, 31, 60, 88, 107, 4, 84, 10, 40, 57, 49, 21, 94, 121, 123, 64, 130, 67, 92, 112
step 133   0.483498   0.392176    1.42835   0.575616   0.561283   34, 59, 82
step 134   0.861739    0.64919    1.67072    1.18065   0.611909   34, 59, 82, 118, 135
step 135    1.39162   0.931329    1.75421    2.85325   0.611909   1, 2, 127, 51, 70, 102, 17, 19, 137, 3, 18, 7, 55, 12, 22, 97, 39, 6, 37, 106, 87, 9, 13, 100, 72, 52, 99, 25, 79, 15, 43, 76, 30, 46, 115, 105, 58, 63, 93, 133, 109, 73, 114, 136, 16, 27, 120, 91, 103, 122, 124, 28, 117, 62, 138, 126, 31, 60, 88, 107, 4, 84, 10, 40, 57, 49, 21, 94, 121, 123, 64, 130, 67, 92, 112, 5, 78, 80, 24, 89, 116, 53, 132, 131, 68, 90, 8, 61, 29, 45, 119, 128, 11, 38, 32, 48, 77, 108, 98, 101, 41, 44, 81, 95, 56, 83, 110, 69, 36, 47, 75, 113, 134, 35, 74, 50, 23, 33, 42, 104, 96, 86, 125, 26, 71, 14, 54, 66, 65, 129, 111, 20
step 136    1.67595   0.983779      2.103    3.35236   0.678568   1, 2, 127, 51, 70, 102, 17, 19, 137, 3, 18, 7, 55, 12, 22, 97, 39, 6, 37, 106, 87, 9, 13, 100, 72, 52, 99, 25, 79, 15, 43, 76, 30, 46, 115, 105, 58, 63, 93, 133, 109, 73, 114, 136, 16, 27, 120, 91, 103, 122, 124, 28, 117, 62, 138, 126, 31, 60, 88, 107, 4, 84, 10, 40, 57, 49, 21, 94, 121, 123, 64, 130, 67, 92, 112, 5, 78, 80, 24, 89, 116, 53, 132, 131, 68, 90, 8, 61, 29, 45, 119, 128, 11, 38, 32, 48, 77, 108, 98, 101, 41, 44, 81, 95, 56, 83, 110, 69, 36, 47, 75, 113, 134, 35, 74, 50, 23, 33, 42, 104, 96, 86, 125, 26, 71, 14, 54, 66, 65, 129, 111, 20, 34, 59, 82, 118, 135
step 137      2.103          1               3.35236              1, 2, 127, 51, 70, 102, 17, 19, 137, 3, 18, 7, 55, 12, 22, 97, 39, 6, 37, 106, 87, 9, 13, 100, 72, 52, 99, 25, 79, 15, 43, 76, 30, 46, 115, 105, 58, 63, 93, 133, 109, 73, 114, 136, 16, 27, 120, 91, 103, 122, 124, 28, 117, 62, 138, 126, 31, 60, 88, 107, 4, 84, 10, 40, 57, 49, 21, 94, 121, 123, 64, 130, 67, 92, 112, 5, 78, 80, 24, 89, 116, 53, 132, 131, 68, 90, 8, 61, 29, 45, 119, 128, 11, 38, 32, 48, 77, 108, 98, 101, 41, 44, 81, 95, 56, 83, 110, 69, 36, 47, 75, 113, 134, 35, 74, 50, 23, 33, 42, 104, 96, 86, 125, 26, 71, 14, 54, 66, 65, 129, 111, 20, 34, 59, 82, 118, 135, 85


dendrogram scale: child cluster distance
  1           2         127          51          70         102          17          19         137           3          18           7          55          12          22          97          39           6          37         106          87           9          13         100          72          52          99          25          79          15          43          76          30          46         115         105          58          63          93         133         109          73         114         136          16          27         120          91         103         122         124          28         117          62         138         126          31          60          88         107           4          84          10          40          57          49          21          94         121         123          64         130          67          92         112           5          78          80          24          89         116          53         132         131          68          90           8          61          29          45         119         128          11          38          32          48          77         108          98         101          41          44          81          95          56          83         110          69          36          47          75         113         134          35          74          50          23          33          42         104          96          86         125          26          71          14          54          66          65         129         111          20          34          59          82         118         135          85
     1.03976   0.0379436   0.0736618    0.021876    0.113912    0.130301    0.199508    0.146153    0.728048   0.0379436   0.0627238           0     0.09699    0.196735   0.0379436   0.0822111    0.370684   0.0954834   0.0471717   0.0615295    0.154421   0.0505915   0.0252957   0.0951397    0.178217    0.200689    0.334707    0.347239    0.220267   0.0656281   0.0834055    0.291649   0.0379436   0.0753717   0.0808994    0.106136    0.196191   0.0345239    0.061014   0.0713276   0.0972477    0.233774    0.428133    0.598735   0.0440957   0.0126479      0.0282   0.0739196   0.0126479   0.0513877    0.167784   0.0252957   0.0782759   0.0252957    0.159912    0.521526   0.0563999    0.392487    0.449042    0.781825   0.0909238    0.211336   0.0636919   0.0345239   0.0425577    0.132287   0.0126479    0.120834   0.0724675    0.766519    0.106991    0.119124    0.546575      1.0355     1.39162    0.043752   0.0909238    0.114053           0   0.0345239   0.0410196     0.11988    0.170781    0.170795   0.0656281    0.263482    0.021876   0.0362337    0.111207   0.0661435   0.0379436    0.213303    0.021876   0.0454619    0.047968   0.0704999   0.0559222   0.0749736   0.0678767    0.130293           0   0.0408478   0.0126479   0.0583675   0.0345239   0.0252957   0.0862301    0.118571   0.0471717    0.132286   0.0408478   0.0126479    0.149733    0.153907    0.224119    0.404658   0.0252957   0.0471717   0.0693914   0.0768238   0.0994026   0.0505915    0.129015    0.137668    0.435425   0.0379436   0.0787914    0.143451    0.182281    0.601927    0.347105     1.67595    0.483498    0.209532    0.861739    0.144935       2.103

  1 ___________________________________________________________________________________________________
                                                     |               |             |                   |
  2 _________________________________________________|               |             |                   |
     | | |   |                       |   |           |               |             |                   |
127 _| | |   |                       |   |           |               |             |                   |
       | |   |                       |   |           |               |             |                   |
 51 ___| |   |                       |   |           |               |             |                   |
     |   |   |                       |   |           |               |             |                   |
 70 _|   |   |                       |   |           |               |             |                   |
         |   |                       |   |           |               |             |                   |
102 _____|   |                       |   |           |               |             |                   |
         |   |                       |   |           |               |             |                   |
 17 _____|   |                       |   |           |               |             |                   |
             |                       |   |           |               |             |                   |
 19 _________|                       |   |           |               |             |                   |
         |                           |   |           |               |             |                   |
137 _____|                           |   |           |               |             |                   |
                                     |   |           |               |             |                   |
  3 _________________________________|   |           |               |             |                   |
     | |     |       | |       |         |           |               |             |                   |
 18 _| |     |       | |       |         |           |               |             |                   |
     | |     |       | |       |         |           |               |             |                   |
  7 _| |     |       | |       |         |           |               |             |                   |
    |  |     |       | |       |         |           |               |             |                   |
 55 |  |     |       | |       |         |           |               |             |                   |
       |     |       | |       |         |           |               |             |                   |
 12 ___|     |       | |       |         |           |               |             |                   |
             |       | |       |         |           |               |             |                   |
 22 _________|       | |       |         |           |               |             |                   |
     | |             | |       |         |           |               |             |                   |
 97 _| |             | |       |         |           |               |             |                   |
       |             | |       |         |           |               |             |                   |
 39 ___|             | |       |         |           |               |             |                   |
                     | |       |         |           |               |             |                   |
  6 _________________| |       |         |           |               |             |                   |
       |   | |     |   |       |         |           |               |             |                   |
 37 ___|   | |     |   |       |         |           |               |             |                   |
     |     | |     |   |       |         |           |               |             |                   |
106 _|     | |     |   |       |         |           |               |             |                   |
     |     | |     |   |       |         |           |               |             |                   |
 87 _|     | |     |   |       |         |           |               |             |                   |
           | |     |   |       |         |           |               |             |                   |
  9 _______| |     |   |       |         |           |               |             |                   |
     | |   | |     |   |       |         |           |               |             |                   |
 13 _| |   | |     |   |       |         |           |               |             |                   |
     | |   | |     |   |       |         |           |               |             |                   |
100 _| |   | |     |   |       |         |           |               |             |                   |
       |   | |     |   |       |         |           |               |             |                   |
 72 ___|   | |     |   |       |         |           |               |             |                   |
           | |     |   |       |         |           |               |             |                   |
 52 _______| |     |   |       |         |           |               |             |                   |
             |     |   |       |         |           |               |             |                   |
 99 _________|     |   |       |         |           |               |             |                   |
                   |   |       |         |           |               |             |                   |
 25 _______________|   |       |         |           |               |             |                   |
                   |   |       |         |           |               |             |                   |
 79 _______________|   |       |         |           |               |             |                   |
             |   |     |       |         |           |               |             |                   |
 15 _________|   |     |       |         |           |               |             |                   |
       |         |     |       |         |           |               |             |                   |
 43 ___|         |     |       |         |           |               |             |                   |
       |         |     |       |         |           |               |             |                   |
 76 ___|         |     |       |         |           |               |             |                   |
                 |     |       |         |           |               |             |                   |
 30 _____________|     |       |         |           |               |             |                   |
     | | |   | |       |       |         |           |               |             |                   |
 46 _| | |   | |       |       |         |           |               |             |                   |
       | |   | |       |       |         |           |               |             |                   |
115 ___| |   | |       |       |         |           |               |             |                   |
       | |   | |       |       |         |           |               |             |                   |
105 ___| |   | |       |       |         |           |               |             |                   |
         |   | |       |       |         |           |               |             |                   |
 58 _____|   | |       |       |         |           |               |             |                   |
             | |       |       |         |           |               |             |                   |
 63 _________| |       |       |         |           |               |             |                   |
     | |       |       |       |         |           |               |             |                   |
 93 _| |       |       |       |         |           |               |             |                   |
     | |       |       |       |         |           |               |             |                   |
133 _| |       |       |       |         |           |               |             |                   |
       |       |       |       |         |           |               |             |                   |
109 ___|       |       |       |         |           |               |             |                   |
       |       |       |       |         |           |               |             |                   |
 73 ___|       |       |       |         |           |               |             |                   |
               |       |       |         |           |               |             |                   |
114 ___________|       |       |         |           |               |             |                   |
                       |       |         |           |               |             |                   |
136 ___________________|       |         |           |               |             |                   |
                               |         |           |               |             |                   |
 16 ___________________________|         |           |               |             |                   |
     | |   |               |             |           |               |             |                   |
 27 _| |   |               |             |           |               |             |                   |
    | | |   |               |             |           |               |             |                   |
120 || |   |               |             |           |               |             |                   |
     | |   |               |             |           |               |             |                   |
 91 _| |   |               |             |           |               |             |                   |
       |   |               |             |           |               |             |                   |
103 ___|   |               |             |           |               |             |                   |
    | |     |               |             |           |               |             |                   |
122 ||     |               |             |           |               |             |                   |
     |     |               |             |           |               |             |                   |
124 _|     |               |             |           |               |             |                   |
           |               |             |           |               |             |                   |
 28 _______|               |             |           |               |             |                   |
     | |   |               |             |           |               |             |                   |
117 _| |   |               |             |           |               |             |                   |
       |   |               |             |           |               |             |                   |
 62 ___|   |               |             |           |               |             |                   |
     |     |               |             |           |               |             |                   |
138 _|     |               |             |           |               |             |                   |
           |               |             |           |               |             |                   |
126 _______|               |             |           |               |             |                   |
                           |             |           |               |             |                   |
 31 _______________________|             |           |               |             |                   |
     |               |   |               |           |               |             |                   |
 60 _|               |   |               |           |               |             |                   |
                     |   |               |           |               |             |                   |
 88 _________________|   |               |           |               |             |                   |
                         |               |           |               |             |                   |
107 _____________________|               |           |               |             |                   |
                                         |           |               |             |                   |
  4 _____________________________________|           |               |             |                   |
       |     |                         |             |               |             |                   |
 84 ___|     |                         |             |               |             |                   |
             |                         |             |               |             |                   |
 10 _________|                         |             |               |             |                   |
       | |                             |             |               |             |                   |
 40 ___| |                             |             |               |             |                   |
     |   |                             |             |               |             |                   |
 57 _|   |                             |             |               |             |                   |
     |   |                             |             |               |             |                   |
 49 _|   |                             |             |               |             |                   |
         |                             |             |               |             |                   |
 21 _____|                             |             |               |             |                   |
    |     |                             |             |               |             |                   |
 94 |    |                             |             |               |             |                   |
         |                             |             |               |             |                   |
121 _____|                             |             |               |             |                   |
       |                               |             |               |             |                   |
123 ___|                               |             |               |             |                   |
                                       |             |               |             |                   |
 64 ___________________________________|             |               |             |                   |
         |                   |                       |               |             |                   |
130 _____|                   |                       |               |             |                   |
         |                   |                       |               |             |                   |
 67 _____|                   |                       |               |             |                   |
                             |                       |               |             |                   |
 92 _________________________|                       |               |             |                   |
                                                     |               |             |                   |
112 _________________________________________________|               |             |                   |
                                                                     |             |                   |
  5 _________________________________________________________________|             |                   |
     | | | |   |       |       |                                                   |                   |
 78 _| | | |   |       |       |                                                   |                   |
       | | |   |       |       |                                                   |                   |
 80 ___| | |   |       |       |                                                   |                   |
         | |   |       |       |                                                   |                   |
 24 _____| |   |       |       |                                                   |                   |
    ||   | |   |       |       |                                                   |                   |
 89 ||   | |   |       |       |                                                   |                   |
     |   | |   |       |       |                                                   |                   |
116 _|   | |   |       |       |                                                   |                   |
     |   | |   |       |       |                                                   |                   |
 53 _|   | |   |       |       |                                                   |                   |
         | |   |       |       |                                                   |                   |
132 _____| |   |       |       |                                                   |                   |
           |   |       |       |                                                   |                   |
131 _______|   |       |       |                                                   |                   |
           |   |       |       |                                                   |                   |
 68 _______|   |       |       |                                                   |                   |
       |       |       |       |                                                   |                   |
 90 ___|       |       |       |                                                   |                   |
               |       |       |                                                   |                   |
  8 ___________|       |       |                                                   |                   |
     |   |   |         |       |                                                   |                   |
 61 _|   |   |         |       |                                                   |                   |
     |   |   |         |       |                                                   |                   |
 29 _|   |   |         |       |                                                   |                   |
         |   |         |       |                                                   |                   |
 45 _____|   |         |       |                                                   |                   |
       |     |         |       |                                                   |                   |
119 ___|     |         |       |                                                   |                   |
     |       |         |       |                                                   |                   |
128 _|       |         |       |                                                   |                   |
             |         |       |                                                   |                   |
 11 _________|         |       |                                                   |                   |
     | | | | |         |       |                                                   |                   |
 38 _| | | | |         |       |                                                   |                   |
     | | | | |         |       |                                                   |                   |
 32 _| | | | |         |       |                                                   |                   |
     | | | | |         |       |                                                   |                   |
 48 _| | | | |         |       |                                                   |                   |
       | | | |         |       |                                                   |                   |
 77 ___| | | |         |       |                                                   |                   |
     | | | | |         |       |                                                   |                   |
108 _| | | | |         |       |                                                   |                   |
       | | | |         |       |                                                   |                   |
 98 ___| | | |         |       |                                                   |                   |
       | | | |         |       |                                                   |                   |
101 ___| | | |         |       |                                                   |                   |
         | | |         |       |                                                   |                   |
 41 _____| | |         |       |                                                   |                   |
    || | | | |         |       |                                                   |                   |
 44 || | | | |         |       |                                                   |                   |
     | | | | |         |       |                                                   |                   |
 81 _| | | | |         |       |                                                   |                   |
    | | | | | |         |       |                                                   |                   |
 95 || | | | |         |       |                                                   |                   |
     | | | | |         |       |                                                   |                   |
 56 _| | | | |         |       |                                                   |                   |
     | | | | |         |       |                                                   |                   |
 83 _| | | | |         |       |                                                   |                   |
     | | | | |         |       |                                                   |                   |
110 _| | | | |         |       |                                                   |                   |
       | | | |         |       |                                                   |                   |
 69 ___| | | |         |       |                                                   |                   |
         | | |         |       |                                                   |                   |
 36 _____| | |         |       |                                                   |                   |
     |   | | |         |       |                                                   |                   |
 47 _|   | | |         |       |                                                   |                   |
         | | |         |       |                                                   |                   |
 75 _____| | |         |       |                                                   |                   |
     |     | |         |       |                                                   |                   |
113 _|     | |         |       |                                                   |                   |
    |       | |         |       |                                                   |                   |
134 |      | |         |       |                                                   |                   |
           | |         |       |                                                   |                   |
 35 _______| |         |       |                                                   |                   |
           | |         |       |                                                   |                   |
 74 _______| |         |       |                                                   |                   |
             |         |       |                                                   |                   |
 50 _________|         |       |                                                   |                   |
                       |       |                                                   |                   |
 23 ___________________|       |                                                   |                   |
     | | |             |       |                                                   |                   |
 33 _| | |             |       |                                                   |                   |
     | | |             |       |                                                   |                   |
 42 _| | |             |       |                                                   |                   |
       | |             |       |                                                   |                   |
104 ___| |             |       |                                                   |                   |
       | |             |       |                                                   |                   |
 96 ___| |             |       |                                                   |                   |
       | |             |       |                                                   |                   |
 86 ___| |             |       |                                                   |                   |
     |   |             |       |                                                   |                   |
125 _|   |             |       |                                                   |                   |
         |             |       |                                                   |                   |
 26 _____|             |       |                                                   |                   |
         |             |       |                                                   |                   |
 71 _____|             |       |                                                   |                   |
                       |       |                                                   |                   |
 14 ___________________|       |                                                   |                   |
     | | | |                   |                                                   |                   |
 54 _| | | |                   |                                                   |                   |
       | | |                   |                                                   |                   |
 66 ___| | |                   |                                                   |                   |
         | |                   |                                                   |                   |
 65 _____| |                   |                                                   |                   |
           |                   |                                                   |                   |
129 _______|                   |                                                   |                   |
                               |                                                   |                   |
111 ___________________________|                                                   |                   |
                   |                                                               |                   |
 20 _______________|                                                               |                   |
                                                                                   |                   |
 34 _______________________________________________________________________________|                   |
                         |                 |                                                           |
 59 _____________________|                 |                                                           |
             |                             |                                                           |
 82 _________|                             |                                                           |
                                           |                                                           |
118 _______________________________________|                                                           |
         |                                                                                             |
135 _____|                                                                                             |
                                                                                                       |
 85 ___________________________________________________________________________________________________|

child cluster distance scale coefficient: 0.943282
diameter scale coefficient: 0.940673

[14]:
matrix.nb_row
[14]:
138
[49]:
import matplotlib.pyplot as plt
[50]:
%matplotlib inline
[51]:
plt.rcParams['figure.figsize'] = [100, 100]

fig, ax = plt.subplots()
ax.plot(range(1000), 'w')

fig.patch.set_visible(False)
ax.axis('off')
fig.text(0.1, 0.9, clust3, fontsize=12)

plt.show()
../_images/examples_clustering_28_0.png
[ ]: