Table 4.
Performance comparisons of ten involved algorithms on TI_T 1_1 to TI_T 1_8.
| Data sets | Validity Metrics | FCM | LSSMTC | CombKM | DRCC | CKM | SFCM | STC | TSC | KL-TFCM-c | KL-TFCM-f |
|---|---|---|---|---|---|---|---|---|---|---|---|
| TI_T1_1 | NMI-mean | 0.4151 | 0.2508 | 0.2500 | 0.2480 | 0.3762 | 0.4468 | 0.4986 | 0.5133 | 0.6287 | 0.6336 |
| NMI-std | 0.0052 | 0.0191 | 0.0308 | 0.0213 | 0.0068 | 0.0295 | 0 | 0.0066 | 0.0084 | 0.0049 | |
| RI-mean | 0.8268 | 0.7893 | 0.7532 | 0.7905 | 0.8342 | 0.7882 | 0.8690 | 0.8772 | 0.9055 | 0.9063 | |
| RI-std | 0.0087 | 0.0043 | 0.0154 | 0.0037 | 0.0021 | 0.0126 | 0 | 0.0022 | 0.0020 | 0.0011 | |
| TI_T1_2 | NMI-mean | 0.3027 | 0.2331 | 0.2311 | 0.2264 | 0.2999 | 0.2836 | 0.3696 | 0.3470 | 0.5362 | 0.5350 |
| NMI-std | 0.0048 | 0.0237 | 0.0481 | 0.0188 | 0.0169 | 0.0444 | 0 | 0 | 0.0140 | 0.0091 | |
| RI-mean | 0.7777 | 0.7695 | 0.7063 | 0.7783 | 0.8156 | 0.6630 | 0.7839 | 0.7708 | 0.8600 | 0.8569 | |
| RI-std | 0.0052 | 0.0050 | 0.0287 | 0.0015 | 0.0021 | 0.0764 | 0 | 0 | 0.0170 | 0.0124 | |
| TI_T1_3 | NMI-mean | 0.6039 | 0.6087 | 0.6092 | 0.3422 | 0.5738 | 0.5713 | 0.6511 | 0.6104 | 0.6200 | 0.6198 |
| NMI-std | 0.0359 | 0.0326 | 0.0240 | 0.0241 | 0.0513 | 0.0312 | 0 | 5.77e–004 | 0.0037 | 0.0032 | |
| RI-mean | 0.8553 | 0.8710 | 0.8611 | 0.7849 | 0.8463 | 0.8534 | 0.8877 | 0.8726 | 0.8643 | 0.8644 | |
| RI-std | 0.0185 | 0.0112 | 0.0268 | 0.0204 | 0.0270 | 0.0195 | 0 | 2.31e–004 | 0.0010 | 0.0008 | |
| TI_T1_4 | NMI-mean | 0.4557 | 0.4789 | 0.4261 | 0.2413 | 0.4109 | 0.2836 | 0.5497 | 0.5511 | 0.6136 | 0.6147 |
| NMI-std | 0.0197 | 0.0013 | 0.0193 | 0.0143 | 0.0015 | 0.0240 | 0 | 0 | 0.0006 | 0.0011 | |
| RI-mean | 0.8178 | 0.8185 | 0.8082 | 0.7848 | 0.7956 | 0.6598 | 0.8472 | 0.8496 | 0.8754 | 0.8757 | |
| RI-std | 0.0044 | 0.0028 | 0.0073 | 0.0013 | 2.96e–04 | 0.0363 | 0 | 0 | 0.0005 | 0.0008 | |
| TI_T1_5 | NMI-mean | 0.4644 | – | 0.5557 | – | 0.4103 | – | – | – | 0.6006 | 0.6501 |
| NMI-std | 0.0002 | – | 0.0201 | – | 0.0021 | – | – | – | 0 | 7.06e–05 | |
| RI-mean | 0.7817 | – | 0.7310 | – | 0.6895 | – | – | – | 0.8021 | 0.8360 | |
| RI-std | 0.0001 | – | 0.0220 | – | 0.0012 | – | – | – | 0 | 5.90e–05 | |
| TI_T1_6 | NMI-mean | 0.2680 | – | 0.5087 | – | 0.5082 | – | – | – | 0.7398 | 0.7628 |
| NMI-std | 0.0050 | – | 0.0690 | – | 0.0055 | – | – | – | 1.35e-16 | 1.11e–16 | |
| RI-mean | 0.6872 | – | 0.6578 | – | 0.7943 | – | – | – | 0.9103 | 0.9168 | |
| RI-std | 0.0020 | – | 0.0888 | – | 0.0028 | – | – | – | 1.35e-16 | 1.35e–16 | |
| TI_T1_7 | NMI-mean | 0.2910 | – | 0.5769 | – | 0.4239 | – | – | – | 0.7227 | 0.7278 |
| NMI-std | 0.0080 | – | 0.0189 | – | 0.0014 | – | – | – | 7.85e-17 | 0 | |
| RI-mean | 0.7325 | – | 0.7347 | – | 0.7911 | – | – | – | 0.9085 | 0.9054 | |
| RI-std | 0.0033 | – | 0.0476 | – | 7.03e–04 | – | – | – | 0 | 0 | |
| TI_T1_8 | NMI-mean | 0.2038 | – | 0.5728 | – | 0.5190 | – | – | – | 0.6827 | 0.6914 |
| NMI-std | 0.0225 | – | 0.0329 | – | 0.0019 | – | – | – | 0.0005 | 1.11e–16 | |
| RI-mean | 0.7399 | – | 0.7941 | – | 0.8615 | – | – | – | 0.9010 | 0.9032 | |
| RI-std | 0.0059 | – | 0.0160 | – | 6.58e–04 | – | – | – | 0.0002 | 0 |