Figure 1.
Figure 2.
Comparison of criterion function values for the UNGA networks_
| UNGA Military resolutions network | UNGA Ideological resolutions network | ||||||||
| K | L | TMKLMedK | RH | TS | VNS | TMKLMedH | RH | TS | VNS |
| 4 | 4 | 1743 | 1743 | 1743 | 1743 | 4220 | 4220 | 4220 | 4220 |
| 4 | 5 | 1730 | 1730 | 1730 | 1730 | 4144 | 4144 | 4144 | 4144 |
| 4 | 6 | 1730 | 1730 | 1730 | 1730 | 4136 | 4136 | 4144 | 4136 |
| 4 | 7 | 1730 | 1730 | 1730 | 1730 | 4131 | 4136 | 4136 | 4136 |
| 5 | 4 | 1713 | 1713 | 1713 | 1713 | 4200 | 4200 | 4200 | 4200 |
| 5 | 5 | 1663 | 1663 | 1663 | 1663 | 4020 | 4020 | 4020 | 4020 |
| 5 | 6 | 1649 | 1657 | 1649 | 1649 | 3947 | 3950 | 3947 | 3947 |
| 5 | 7 | 1646 | 1650 | 1646 | 1649 | 3890 | 3896 | 3947 | 3890 |
| 6 | 4 | 1707 | 1707 | 1709 | 1709 | 4194 | 4198 | 4194 | 4196 |
| 6 | 5 | 1633 | 1633 | 1633 | 1633 | 4001 | 4001 | 4001 | 4001 |
| 6 | 6 | 1614 | 1619 | 1612 | 1612 | 3841 | 3841 | 3841 | 3841 |
| 6 | 7 | 1599 | 1613 | 1608 | 1599 | 3763 | 3772 | 3763 | 3763 |
| 7 | 4 | 1702 | 1707 | 1707 | 1707 | 4194 | 4194 | 4194 | 4196 |
| 7 | 5 | 1627 | 1634 | 1627 | 1630 | 3997 | 4001 | 3999 | 3998 |
| 7 | 6 | 1577 | 1588 | 1577 | 1577 | 3822 | 3822 | 3825 | 3822 |
| 7 | 7 | 1565 | 1566 | 1565 | 1565 | 3691 | 3695 | 3691 | 3691 |
Comparison of criterion function values and number of restarts for the MovieLens network_
| Criterion function values | Number of restarts | ||||||
| K | L | TMKLMedH | RH | PICF | TMKLMedH | RH | RatioTMKLMedH / RH |
| 2 | 2 | 90971 | 90971 | 0.000 | 2000 | 342 | 5.848 |
| 2 | 3 | 90889 | 90901 | 0.013 | 1980 | 201 | 9.851 |
| 2 | 4 | 90875 | 90900 | 0.028 | 1863 | 171 | 10.895 |
| 2 | 5 | 90875 | 90899 | 0.026 | 1799 | 129 | 13.946 |
| 2 | 6 | 90875 | 90892 | 0.019 | 1749 | 113 | 15.478 |
| 2 | 7 | 90875 | 90889 | 0.015 | 1687 | 103 | 16.379 |
| 3 | 2 | 90971 | 90971 | 0.000 | 1494 | 129 | 11.581 |
| 3 | 3 | 88846 | 88859 | 0.015 | 1345 | 86 | 15.640 |
| 3 | 4 | 88799 | 88858 | 0.066 | 1176 | 80 | 14.700 |
| 3 | 5 | 88783 | 88864 | 0.091 | 1130 | 59 | 19.153 |
| 3 | 6 | 88781 | 88852 | 0.080 | 1109 | 56 | 19.804 |
| 3 | 7 | 88773 | 88823 | 0.056 | 1111 | 52 | 21.365 |
| 4 | 2 | 90971 | 90971 | 0.000 | 1218 | 86 | 14.163 |
| 4 | 3 | 88846 | 88864 | 0.020 | 1079 | 57 | 18.930 |
| 4 | 4 | 87603 | 87907 | 0.347 | 936 | 42 | 22.286 |
| 4 | 5 | 87205 | 87237 | 0.037 | 893 | 42 | 21.262 |
| 4 | 6 | 87142 | 87550 | 0.468 | 806 | 36 | 22.389 |
| 4 | 7 | 87124 | 87748 | 0.716 | 782 | 36 | 21.722 |
| 5 | 2 | 90971 | 90971 | 0.000 | 1041 | 68 | 15.309 |
| 5 | 3 | 88850 | 88863 | 0.015 | 897 | 42 | 21.357 |
| 5 | 4 | 87165 | 87662 | 0.570 | 779 | 34 | 22.912 |
| 5 | 5 | 86498 | 87146 | 0.749 | 747 | 33 | 22.636 |
| 5 | 6 | 86043 | 86514 | 0.547 | 680 | 28 | 24.286 |
| 5 | 7 | 86010 | 86082 | 0.084 | 647 | 24 | 26.958 |
| 6 | 2 | 90971 | 90971 | 0.000 | 897 | 56 | 16.018 |
| 6 | 3 | 88846 | 88876 | 0.034 | 784 | 32 | 24.500 |
| 6 | 4 | 87172 | 87720 | 0.629 | 673 | 29 | 23.207 |
| 6 | 5 | 86105 | 87338 | 1.432 | 651 | 24 | 27.125 |
| 6 | 6 | 85790 | 86678 | 1.035 | 597 | 21 | 28.429 |
| 6 | 7 | 85529 | 86197 | 0.781 | 567 | 18 | 31.500 |
| 7 | 2 | 90971 | 90971 | 0.000 | 792 | 46 | 17.217 |
| 7 | 3 | 88846 | 88883 | 0.042 | 690 | 30 | 23.000 |
| 7 | 4 | 87169 | 87456 | 0.329 | 603 | 22 | 27.409 |
| 7 | 5 | 85999 | 86330 | 0.385 | 572 | 20 | 28.600 |
| 7 | 6 | 85573 | 85982 | 0.478 | 511 | 15 | 34.067 |
| 7 | 7 | 85188 | 85617 | 0.504 | 498 | 14 | 35.571 |
Simulation results: (i) MPICF: mean percentage improvement in the criterion function realized from using TMKLMedH instead of RH; (ii) MPbetter: Mean percentage of test problems for which TMKLMedH provided a better criterion function value than RH; (iii) MRR: mean ratio of the number of restarts for TMKLMedH to the number for RH within the three-minute time limit; and (iv) ARI recovery measures for row and column clusters for RH and TMLKMedH_
| Design feature levels | MPICF | MPbetter | MRR | RH (Row-ARI) | TMKLMedH (Row-ARI) | RH (Col-ARI) | TMKLMedH (Col-ARI) |
|---|---|---|---|---|---|---|---|
| Overall average | .344 | 47.786 | 24.824 | .745 | .831 | .741 | .829 |
| n = 180 row objects | .264 | 48.698 | 20.543 | .748 | .810 | .715 | .778 |
| n = 540 row objects | .425 | 46.875 | 29.105 | .741 | .852 | .767 | .880 |
| m = 180 column objects | .300 | 50.521 | 18.512 | .710 | .779 | .736 | .807 |
| m = 540 column objects | .388 | 45.052 | 31.136 | .780 | .853 | .746 | .850 |
| K = 3 row clusters | .039 | 29.167 | 23.709 | .967 | .966 | .695 | .791 |
| K = 6 row clusters | .649 | 66.406 | 25.938 | .523 | .696 | .787 | .866 |
| L = 3 column clusters | .038 | 29.948 | 21.900 | .698 | .790 | .968 | .968 |
| L = 6 column clusters | .651 | 65.625 | 27.747 | .792 | .872 | .514 | .690 |
| Even row cluster density | .280 | 41.146 | 27.886 | .785 | .817 | .765 | .849 |
| 60% row cluster density | .409 | 54.427 | 21.762 | .705 | .845 | .717 | .808 |
| Even column cluster density | .240 | 41.667 | 28.412 | .771 | .853 | .788 | .820 |
| 60% column cluster density | .449 | 53.906 | 21.236 | .719 | .809 | .694 | .837 |
| 33% Image matrix density | .367 | 48.438 | 26.753 | .745 | .829 | .740 | .830 |
| 66% Image matrix density | .321 | 47.135 | 22.895 | .744 | .833 | .742 | .827 |
| 70% block strength | .364 | 26.042 | 24.647 | .808 | .911 | .804 | .911 |
| 60% block strength | .325 | 69.531 | 25.001 | .682 | .751 | .678 | .747 |