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Table 1 The cophenetic correlation coefficient values for μ=0 , σ 2 =1 (without outliers)

From: Comparison of hierarchical cluster analysis methods by cophenetic correlation

Distance measure Clustering method Cophenetic correlation coefficient
x = 3 x = 5 x = 10
n = 10 n = 50 n = 100 n = 10 n = 50 n = 100 n = 10 n = 50 n = 100
Euclidean Average 0.7552 0.6358 0.6009 0.7255 0.6017 0.5753 0.6922 0.5728 0.5339
Centroid 0.6927 0.6393 0.6038 0.6463 0.6028 0.5557 0.5829 0.5759 0.5605
Complete 0.6858 0.4940 0.4313 0.6397 0.4135 0.3386 0.5920 0.3439 0.2640
Median 0.7309 0.5600 0.4797 0.6897 0.5412 0.4605 0.6220 0.5338 0.4989
Single 0.7034 0.6033 0.5947 0.6633 0.5663 0.5577 0.6157 0.5332 0.5295
Ward 0.6832 0.4956 0.4422 0.6384 0.4124 0.3496 0.5895 0.3367 0.2664
Weighted 0.7367 0.5428 0.4692 0.7064 0.5024 0.4105 0.6749 0.4791 0.3941
Squared Euclidean Average 0.7381 0.6352 0.5978 0.7090 0.5974 0.5546 0.6792 0.5700 0.5315
Centroid 0.7285 0.6402 0.6056 0.6874 0.6085 0.5765 0.6254 0.5831 0.5632
Complete 0.6565 0.4826 0.4271 0.6128 0.4014 0.3325 0.5659 0.3318 0.2586
Median 0.7102 0.5538 0.4745 0.6679 0.5386 0.4553 0.6013 0.5344 0.5039
Single 0.6874 0.6038 0.5950 0.6453 0.5656 0.5578 0.6009 0.5324 0.5301
Ward 0.6533 0.4830 0.4350 0.6093 0.3995 0.3421 0.5661 0.3264 0.2589
Weighted 0.7191 0.5351 0.4615 0.6904 0.4978 0.4054 0.6623 0.4768 0.3969
Mahalanobis Average 0.6957 0.6276 0.5950 0.6176 0.5865 0.5469 NaN 0.5591 0.5284
Centroid 0.6749 0.6325 0.6010 0.5864 0.5993 0.5723 NaN 0.5789 0.5630
Complete 0.5627 0.4578 0.4121 0.3958 0.3625 0.3097 NaN 0.2711 0.2270
Median 0.6587 0.5426 0.4719 0.5762 0.5320 0.4538 NaN 0.5385 0.5106
Single 0.6565 0.6032 0.5956 0.5642 0.5655 0.5589 NaN 0.5293 0.5317
Ward 0.5541 0.4621 0.4235 0.3876 0.3539 0.3147 NaN 0.2495 0.2155
Weighted 0.6760 0.5202 0.4549 0.6078 0.4843 0.3963 NaN 0.4869 0.4013
Cityblock Average 0.7427 0.6228 0.5844 0.7120 0.5810 0.5349 0.6787 0.5484 0.5076
Centroid 0.7372 0.6280 0.5944 0.6983 0.5902 0.5557 0.6343 0.5579 0.5368
Complete 0.6716 0.4780 0.4229 0.6247 0.3976 0.3272 0.5771 0.3285 0.2502
Median 0.7194 0.5460 0.4710 0.6799 0.5233 0.4455 0.6129 0.5117 0.4774
Single 0.6876 0.5839 0.5756 0.6443 0.5410 0.5324 0.5975 0.5037 0.5009
Ward 0.6728 0.4869 0.4348 0.6281 0.4052 0.3427 0.5823 0.3322 0.2596
Weighted 0.7244 0.5290 0.4546 0.6936 0.4878 0.3969 0.6615 0.4601 0.3824
Minkowski Average 0.7552 0.6393 0.6009 0.7255 0.6017 0.5557 0.6922 0.5728 0.5339
Centroid 0.7497 0.6447 0.6087 0.7099 0.6124 0.5791 0.6450 0.5833 0.5629
Complete 0.6858 0.4940 0.4313 0.6397 0.4135 0.3386 0.5920 0.3439 0.2640
Median 0.7309 0.5600 0.4797 0.6897 0.5412 0.4605 0.6220 0.5338 0.4989
Single 0.7034 0.6033 0.5947 0.6633 0.5663 0.5577 0.6157 0.5332 0.5295
Ward 0.6832 0.4956 0.4422 0.6384 0.4124 0.3496 0.5895 0.3367 0.2664
Weighted 0.7367 0.5428 0.4692 0.7064 0.5024 0.4105 0.6749 0.4791 0.3941
Cosine Average 0.7590 0.6277 0.5839 0.6994 0.5143 0.4524 0.6441 0.4152 0.3413
Centroid 0.7518 0.6045 0.5478 0.6866 0.4711 0.3894 0.6097 0.3242 0.2312
Complete 0.7230 0.5782 0.5320 0.6501 0.4518 0.3929 0.5808 0.3428 0.2700
Median 0.7340 0.5530 0.5040 0.6681 0.4273 0.3546 0.5911 0.3004 0.2146
Single 0.6931 0.4695 0.3898 0.6034 0.3070 0.2202 0.5211 0.2017 0.1275
Ward 0.7381 0.6142 0.5730 0.6716 0.4979 0.4418 0.6083 0.3974 0.3280
Weighted 0.7433 0.5786 0.5336 0.6854 0.4711 0.4093 0.6311 0.3834 0.3069
Correlation Average 0.8217 0.7470 0.7226 0.7229 0.5581 0.5065 0.6507 0.4268 0.3542
Centroid 0.8169 0.7358 0.7037 0.7124 0.5245 0.4594 0.6212 0.3441 0.2518
Complete 0.7979 0.7083 0.6775 0.6791 0.4987 0.4514 0.5893 0.3545 0.2855
Median 0.7982 0.6886 0.6621 0.6952 0.4754 0.4128 0.6028 0.3177 0.2324
Single 0.7939 0.6715 0.6285 0.6389 0.3624 0.2781 0.5307 0.2124 0.1355
Ward 0.8069 0.7388 0.7155 0.6974 0.5429 0.4938 0.6170 0.4099 0.3426
Weighted 0.8052 0.7061 0.6816 0.7075 0.5105 0.4534 0.6379 0.3916 0.3185
Spearman Average 0.8207 0.7600 0.7441 0.7240 0.5636 0.5163 0.6487 0.4274 0.3567
Centroid 0.8116 0.7413 0.7199 0.7132 0.5336 0.4715 0.6184 0.3452 0.2511
Complete 0.8094 0.7788 0.7780 0.6815 0.5337 0.4966 0.5884 0.3572 0.2896
Median 0.7903 0.7162 0.7114 0.6958 0.4818 0.4235 0.5990 0.3175 0.2329
Single 0.6854 0.6737 0.6738 0.6397 0.4010 0.1830 0.5287 0.2198 0.1427
Ward 0.7892 0.7358 0.7275 0.6973 0.5488 0.5030 0.6145 0.4093 0.3434
Weighted 0.8118 0.7788 0.7780 0.7086 0.5154 0.4672 0.6357 0.3916 0.3194
Chebychev Average 0.7375 0.6183 0.5804 0.6933 0.5595 0.5141 0.6448 0.4958 0.4523
Centroid 0.7317 0.6241 0.5870 0.6811 0.5693 0.5334 0.6100 0.5067 0.4805
Complete 0.6647 0.4780 0.4235 0.6035 0.3824 0.3164 0.5423 0.2962 0.2281
Median 0.7140 0.5431 0.4630 0.6625 0.5036 0.4287 0.5928 0.4628 0.4249
Single 0.6833 0.5792 0.5695 0.6223 0.5199 0.5084 0.5536 0.4468 0.4405
Ward 0.6680 0.4852 0.4317 0.6128 0.3949 0.3341 0.5595 0.3140 0.2423
Weighted 0.7189 0.5255 0.4494 0.6759 0.4734 0.3878 0.6294 0.4249 0.3525