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Table 2 The cophenetic correlation coefficient values for μ=0 , σ 2 =1 (with 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 0.8478 0.8065 0.7848 0.8280 0.7818 0.7629 0.8102 0.7647 0.7488
Centroid 0.8188 0.8061 0.7875 0.7872 0.7816 0.7704 0.7484 0.7638 0.7606
Complete 0.8095 0.7273 0.7006 0.7808 0.6865 0.6551 0.7535 0.6494 0.6136
Median 0.8342 0.7644 0.7262 0.8073 0.7509 0.7182 0.7661 0.7432 0.7311
Single 0.8168 0.7836 0.7774 0.7903 0.7582 0.7578 0.7653 0.7400 0.7426
Ward 0.8064 0.7278 0.7050 0.7801 0.6869 0.6606 0.7531 0.6464 0.6161
Weighted 0.8382 0.7551 0.7185 0.8182 0.7352 0.6918 0.8006 0.7197 0.6835
Squared Euclidean Average 0.8434 0.8088 0.7859 0.8239 0.7837 0.7636 0.8087 0.7663 0.7490
Centroid 0.8386 0.8107 0.7900 0.8123 0.7880 0.7730 0.7768 0.7695 0.7629
Complete 0.8022 0.7331 0.7027 0.7724 0.6937 0.6580 0.7505 0.6550 0.6166
Median 0.8289 0.7652 0.7275 0.8017 0.7525 0.7177 0.7637 0.7417 0.7313
Single 0.8142 0.7838 0.7774 0.7865 0.7584 0.7575 0.7633 0.7397 0.7424
Ward 0.7996 0.7337 0.7070 0.7725 0.6929 0.6645 0.7506 0.6532 0.6191
Weighted 0.8333 0.7592 0.7197 0.8141 0.7358 0.6956 0.7997 0.7192 0.6824
Mahalanobis Average 0.8103 0.8565 0.8315 0.6965 0.8239 0.8053 NaN 0.7705 0.7782
Centroid 0.7976 0.8570 0.8333 0.6701 0.8276 0.8113 NaN 0.7770 0.7882
Complete 0.6966 0.8051 0.7787 0.4529 0.7575 0.7380 NaN 0.6480 0.6848
Median 0.7895 0.8219 0.7843 0.6695 0.7875 0.7600 NaN 0.7453 0.7309
Single 0.7908 0.8220 0.8030 0.6633 0.7841 0.7680 NaN 0.7510 0.7515
Ward 0.7313 0.8018 0.7755 0.5497 0.7523 0.7350 NaN 0.6442 0.6839
Weighted 0.7980 0.8181 0.7848 0.6899 0.7824 0.7531 NaN 0.7230 0.7173
Cityblock Average 0.8404 0.7982 0.7767 0.8206 0.7707 0.7518 0.8027 0.7522 0.7352
Centroid 0.8367 0.7997 0.7805 0.8113 0.7741 0.7611 0.7739 0.7552 0.7482
Complete 0.7995 0.7226 0.6935 0.7727 0.6761 0.6484 0.7464 0.6418 0.6059
Median 0.8267 0.7566 0.7196 0.8018 0.7412 0.7074 0.7623 0.7306 0.7174
Single 0.8077 0.7737 0.7676 0.7804 0.7448 0.7447 0.7533 0.7248 0.7269
Ward 0.8004 0.7243 0.7003 0.7744 0.6817 0.6568 0.7493 0.6446 0.6131
Weighted 0.8305 0.7507 0.7114 0.8111 0.7241 0.6867 0.7936 0.7102 0.6718
Minkowski Average 0.8478 0.8065 0.7848 0.8280 0.7818 0.7629 0.8102 0.7647 0.7488
Centroid 0.8441 0.8088 0.7883 0.8179 0.7860 0.7721 0.7797 0.7695 0.7628
Complete 0.8095 0.7273 0.7006 0.7808 0.6865 0.6551 0.7535 0.6494 0.6136
Median 0.8342 0.7644 0.7262 0.8073 0.7509 0.7182 0.7661 0.7432 0.7311
Single 0.8168 0.7836 0.7774 0.7903 0.7582 0.7578 0.7653 0.7400 0.7426
Ward 0.8064 0.7278 0.7050 0.7801 0.6869 0.6606 0.7531 0.6464 0.6161
Weighted 0.8382 0.7551 0.7185 0.8182 0.7352 0.6918 0.8006 0.7197 0.6835
Cosine Average 0.7689 0.6484 0.6138 0.7107 0.5463 0.4946 0.6596 0.4549 0.3908
Centroid 0.7618 0.6285 0.5866 0.6982 0.5106 0.4462 0.6270 0.3717 0.2936
Complete 0.7320 0.5960 0.5568 0.6604 0.4773 0.4226 0.5977 0.3743 0.3064
Median 0.7438 0.5702 0.5265 0.6802 0.4521 0.3862 0.6058 0.3286 0.2517
Single 0.7082 0.4942 0.4287 0.6182 0.3484 0.2651 0.5429 0.2451 0.1693
Ward 0.7467 0.6325 0.5991 0.6808 0.5240 0.4733 0.6213 0.4232 0.3521
Weighted 0.7534 0.5961 0.5531 0.6961 0.4958 0.4296 0.6454 0.4104 0.3378
Correlation Average 0.8214 0.7466 0.7239 0.7213 0.5584 0.5060 0.6508 0.4269 0.3550
Centroid 0.8171 0.7330 0.7064 0.7117 0.5248 0.4587 0.6210 0.3434 0.2560
Complete 0.7978 0.7102 0.6794 0.6770 0.4992 0.4457 0.5887 0.3561 0.2874
Median 0.7984 0.6852 0.6596 0.6935 0.4756 0.4128 0.6027 0.3150 0.2328
Single 0.7931 0.6647 0.6319 0.6374 0.3624 0.2748 0.5293 0.2157 0.1354
Ward 0.8069 0.7378 0.7162 0.6955 0.5431 0.4940 0.6161 0.4096 0.3428
Weighted 0.8052 0.7017 0.6843 0.7059 0.5106 0.4557 0.6373 0.3914 0.3191
Spearman Average 0.8198 0.7583 0.7455 0.7233 0.5638 0.5159 0.6505 0.4267 0.3567
Centroid 0.8113 0.7396 0.7212 0.7133 0.5336 0.4729 0.6199 0.3429 0.2537
Complete 0.8090 0.7788 0.7762 0.6802 0.5341 0.4983 0.5909 0.3558 0.2887
Median 0.7887 0.7136 0.7140 0.6960 0.4819 0.4238 0.6021 0.3126 0.2304
Single 0.6861 0.6736 0.6742 0.6404 0.4008 0.1821 0.5302 0.2190 0.1404
Ward 0.7881 0.7364 0.7273 0.6963 0.5488 0.5037 0.6170 0.4081 0.3425
Weighted 0.8112 0.7788 0.7762 0.7076 0.5157 0.4687 0.6366 0.3926 0.3197
Chebychev Average 0.8373 0.7945 0.7740 0.8094 0.7588 0.7398 0.7824 0.7246 0.7059
Centroid 0.8338 0.7966 0.7774 0.8008 0.7627 0.7483 0.7601 0.7280 0.7181
Complete 0.7965 0.7182 0.6953 0.7581 0.6707 0.6424 0.7262 0.6226 0.5951
Median 0.8244 0.7546 0.7195 0.7913 0.7315 0.6996 0.7510 0.7061 0.6907
Single 0.8044 0.7700 0.7640 0.7663 0.7329 0.7324 0.7289 0.6940 0.6951
Ward 0.7978 0.7216 0.6996 0.7647 0.6761 0.6495 0.7351 0.6345 0.6038
Weighted 0.8279 0.7470 0.7135 0.8007 0.7171 0.6783 0.7745 0.6895 0.6557
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