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. Author manuscript; available in PMC: 2017 Feb 1.
Published in final edited form as: Pattern Recognit. 2016 Feb;50:155–177. doi: 10.1016/j.patcog.2015.08.009

Table 8.

Clustering performance (NMI, RI, and DBI) of all involved algorithms on real-life datasets.

Dataset Validity index Algorithm
FCM (m=2) FCM MEC FC-QR QWGSD-FC PCM ECM LSSMTC CombKM STC TSC TI-KT-CM TII-KT-CM
TIS-1 NMI-mean 0.4959 0.4965 0.5116 0.5306 0.5473 0.5044 0.4925 0.5757 0.5200 0.5148 0.6385 ➂ 0.6419 ➁ 0.6589 ➀
NMI-std 0 0.0030 7.85E-17 0.0259 0 0.0004 0.0006 0 0 0 0 0 0
RI-mean 0.7685 0.7760 0.8409 0.7838 0.7834 0.7834 0.7970 0.7965 0.7807 0.7680 0.8468 ➂ 0.8713 ➀ 0.8626 ➁
RI-std 0 0.0039 1.36E-16 0.0223 0 0.0001 0.0002 0 0 0 0 0 0
DBI-mean 1.8865 ➂ 2.5104 2.6407 2.1269 2.2703 2.8019 2.3504 2.0075 1.8885 3.5779 2.8991 1.8782 ➀ 1.8852 ➁
DBI-std 0 0.9534 1.57E-16 0.2079 0 0.0035 0.0034 0 0 0 0 0 0
TIS-2 NMI-mean 0.4595 0.4641 0.4897 0.4767 0.5134 0.4501 0.4183 0.4630 0.4480 0.3237 0.5462 ➂ 0.5885 ➁ 0.6034 ➀
NMI-std 0 3.37E-04 0 0.0387 0 0.0017 0.0234 0.1301 0 0 0 0 0
RI-mean 0.7502 0/7497 0.7800 0.7766 0.7695 0.7420 0.7332 0.7587 0.7569 0.6577 0.7960 ➂ 0.8231 ➁ 0.8344 ➀
RI-std 0 0.0013 0 0.0072 0 0.0025 0.0119 0.0594 1.36E-16 0 0 0 0
DBI-mean 4.4014 3.8952 3.0241 ➁ 4.5383 2.5411 ➀ 3.9065 3.7990 3.4821 3.7441 3.2161 3.3464 3.1236 ➂ 3.2931
DBI-std 0 0.2034 0 0.6003 0 0.7946 0.2185 0.2656 0 0 0 0 0
rec VS talk NMI-mean 0.2021 0.2021 0.2691 0.1021 0.2925 0.2047 0.2697 0.0818 0.0572 0.1865 0.4224 ➁ 0.3767 ➂ 0.4282 ➀
NMI-std 5.85E-17 5.85E-17 0 1.70E-17 0.0377 0 0.0089 1.46E-17 0.0201 0.0055 0 1.17E-16 5.85E-17
RI-mean 0.5925 0.5925 0.5960 0.5048 0.6124 0.5942 0.5856 0.5021 0.5002 0.5747 0.7359 ➀ 0.6199 ➂ 0.6842 ➁
RI-std 0 0 0 0 0.0161 0 0.0142 0 0.0004 0.0078 0 1.17E-16 0
DBI-mean 4.5510 4.5510 4.2649 2.7448 4.3947 4.5578 5.9097 2.2505 ➂ 2.5320 3.9824 1.7190 ➁ 2.8726 1.6871 ➀
DBI-std 9.36E-16 9.36E-16 9.36E-16 5.44E-16 0.2925 0 0.1332 0 4.68E-16 0 0 0 9.36E-16
comp VS sci NMI-mean 0.0509 0.0509 0.1049 0.1108 0.1216 0.0408 0.1015 0.0196 0.0021 0.1240 0.3073 ➀ 0.1565 ➂ 0.2065 ➁
NMI-std 7.31E-18 0 0.0717 0.0942 0.0212 0 0.0149 1.83E-18 0 0.0027 0 7.31E-18 7.31E-18
RI-mean 0.5160 0.5160 0.5321 0.5241 0.5272 0.5813 0.5534 0.4990 0.4990 0.5372 0.6781 ➀ 0.6138 ➂ 0.6238 ➁
RI-std 1.17E-16 0 0.0262 0.0218 0.0056 0 0.0704 5.85E-17 5.85E-17 0.0140 0 0 0
DBI-mean 6.1346 6.1346 6.1826 4.3646 5.6124 5.1346 5.3052 1.2699 ➀ 2.0238 ➂ 5.6792 1.8979 ➁ 3.6788 2.8678
DBI-std 9.36E-16 0 0.6981 2.6814 0.1901 0 0.0256 0 0.3801 0 0.01673 9.36E-16 9.36E-16
ORL NMI-mean 0.3365 0.3563 0.3157 0.3663 0.3637 0.3812 ➂ 0.3594 0.3582 0.2124 0.3310 0.2950 0.4979 ➁ 0.7970 ➀
NMI-std 0.0363 0 0.0593 0.0058 0.0388 0 0.0514 0 0.0954 0.0183 0.0054 5.85E-17 0
RI-mean 0.8031 0.8129 0.8057 0.8168 0.8062 0.8200 ➁ 0.7991 0.7748 0.5870 0.8116 0.8124 ➂ 0.7730 0.9253 ➀
RI-std 0.0108 0 0.0093 5.12E-4 0.0119 0 0.0100 0 0.1806 0.0034 0.0004 1.17E-16 0
DBI-mean 3.3226 3.2060 ➁ 3.3761 3.2942 3.3282 3.2974 3.3717 5.7024 6.1604 3.5186 3.2240 ➂ 3.1844 ➀ 3.4174
DBI-std 0.0363 0 0.0551 0.0570 0.0774 5.44E-16 0.0229 0 9.36E-16 0.0361 0 4.68E-16 4.68E-16
cleveland NMI-mean 0.2632 0.2832 0.3211 0.3250 0.3360 ➂ 0.2527 0.3016 0.2598 0.2356 0.2252 0.1946 0.3432 ➁ 0.3701 ➀
NMI-std 0.0157 0 0.0063 0 5.85E-17 0 0.0276 0 0.0449 0 0.0006 0 5.85E-17
RI-mean 0.6676 ➀ 0.6023 0.6589 ➁ 0.6207 0.6580 ➂ 0.5862 0.6299 0.6138 0.5795 0.6137 0.6195 0.6506 0.6016
RI-std 0.0047 0 0.0029 0 0 0 0.0033 0 0.0188 0 0.0008 0 0
DBI-mean 2.5283 1.5314 1.6296 1.8426 1.8564 1.4324 ➁ 1.9479 1.6003 1.6257 2.5723 0.9642 ➀ 2.1132 1.5101 ➂
DBI-std 0.2801 0 0.0069 0 0 2.72E-16 0.5797 0 0.0028 0 0.0081 4.68E-16 2.34E-16
mammographic NMI-mean 0.5429 0.5429 0.5233 0.5512 0.5512 0.5544 ➂ 0.5336 0.4723 0.5233 0.5233 0.3926 0.5920 ➁ 0.6559 ➀
NMI-std 1.17E-16 0 1.17E-16 0 1.17E-16 0 0 5.85E-17 1.17E-16 0 0 1.17E-16 1.17E-16
RI-mean 0.8213 0.8213 0.7855 0.8043 0.8043 0.8234 ➂ 0.8125 0.7496 0.7855 0.7881 0.7205 0.8424 ➁ 0.8668 ➀
RI-std 1.17E-16 1.17E-16 1.17E-16 0 1.17E-16 0 0 1.17E-16 1.17E-16 0 0 1.17E-16 1.17E-16
DBI-mean 0.8706 0.8706 0.7051 ➂ 0.7114 0.7114 0.7274 0.7601 0.7051 ➂ 0.6883 ➁ 0.7051 ➂ 0.7658 0.6601 ➀ 0.7051 ➂
DBI-std 1.17E-16 1.17E-16 1.17E-16 0 0 0 0 1.17E-16 0 0 0 0 1.17E-16
HMTS NMI-mean 0.5660 0.5771 0.5655 0.6203 ➂ 0.6162 0.4287 0.6020 0.4491 0.5120 0.5914 0.5986 0.6549 ➁ 0.6765 ➀
NMI-std 0.0089 1/12E-16 0.0154 0.0225 0.0203 6.80E-16 0.0224 0 0 0.0101 0.0040 1.17E-16 0
RI-mean 0.8671 0.8820 0.7929 0.8814 0.8829 0.6773 0.8847 ➂ 0.7515 0.7745 0.8686 0.8862 ➁ 0.8726 0.9020 ➀
RI-std 0.0028 0 0.0065 0.0105 0.0106 1.36E-16 0.0109 0 1.17E-16 0.0003 0.0002 1.17E-16 0
DBI-mean 1.6870 1.7065 1.4513 1.5514 1.4000 3.3071 2.1048 1.0867 ➁ 1.0951 ➂ 1.4873 0.7434 ➀ 1.4931 1.3209
DBI-std 0.1424 0 0.1386 0.1176 0.1515 5.44E-16 0.0861 2.34E-16 2.34E-16 0 0.0046 0 0
ESF-1 NMI-mean 0.2357 0.2811 0.3219 0.3607 0.3808 ➂ 0.2473 0.2086 0.2654 0.2373 0.3072 0.2748 0.4624 ➁ 0.5159 ➀
NMI-std 0 0.0171 0.0092 6.80E-16 0 0 0.0034 0 0.0522 0 0 0 0
RI-mean 0.5907 0.6073 0.6958 ➂ 0.6359 0.6500 0.5785 0.5408 0.6704 0.6125 0.6556 0.5964 0.7518 ➁ 0.8030 ➀
RI-std 0 0.0152 0.0039 0 0 0 0.0016 0 0.0271 0 0 0 0
DBI-mean 5.5604 5.0228 4.9623 4.1555 ➂ 4.2210 6.3618 4.2102 5.2584 5.5093 4.2970 4.6440 3.8630 ➁ 3.1765 ➀
DBI-std 0 0.2583 0.0149 0 0 0 0.0220 0 0.3404 0 0 0 0
ESF-2 NMI-mean 0.3929 0.3946 0.4128 0.4595 0.4780 ➂ 0.3445 0.3389 0.4121 0.3997 0.3895 0.3492 0.5218 ➁ 0.5926 ➀
NMI-std 0.0024 0 0 0 0 0 0.0719 6.20E-16 0.1747 0 0 0 0
RI-mean 0.7427 0.7438 0.7067 0.7410 0.7791 ➂ 07485 0.6901 0.7062 0.6840 0.6043 0.6498 0.8410 ➁ 0.8467 ➀
RI-std 0.0016 0 0 0 0 0 0.0220 0 0.0769 0 0 0 0
DBI-mean 5.5225 5.5217 5.4036 5.4342 5.4882 5.7682 5.3934 5.4030 5.4648 4.7678 4.3788 ➂ 3.9202 ➁ 3.8236 ➀
DBI-std 0.0011 0 0 0 0 0 0.6351 0 0.5785 0 0 0 0