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Deterministic Blockmodeling of Two-Mode Binary Networks Using a Two-Mode KL-Median Heuristic

Michael Brusco
Michael Brusco
, 
Hannah J. Stolze
Hannah J. Stolze
, 
Michaela Hoffman
Michaela Hoffman
, 
Douglas Steinley
Douglas Steinley
 and 
Patrick Doreian
Patrick Doreian
   | Sep 27, 2018
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Published Online: Sep 27, 2018
Page range: 1 - 22
DOI: https://doi.org/10.21307/joss-2018-007
Keywords
© 2018 Michael Brusco et al., published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Figure 1.

Heatmaps for RH (top panel) and TMKLMedH (bottom panel) criterion values for the MovieLens network.
Heatmaps for RH (top panel) and TMKLMedH (bottom panel) criterion values for the MovieLens network.

Figure 2.

RH (top panel) and TMKLMedH (bottom panel) image matrices for blockmodels obtained using K = L = 5. The sizes of each cluster of individuals (n 1,…, n 5) and movies (m 1,…, m 5) are also provided.
RH (top panel) and TMKLMedH (bottom panel) image matrices for blockmodels obtained using K = L = 5. The sizes of each cluster of individuals (n 1,…, n 5) and movies (m 1,…, m 5) are also provided.

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
eISSN:
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Language:
English
Publication timeframe:
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Journal Subjects:
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