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

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

Journal of Social Structure
Volume 19 (2018): Issue 1 (January 2018)
By: ,  ,  ,   and    
Open Access
|Sep 2018
Figures & tables

Figures & Tables

Table 1.

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 levelsMPICFMPbetterMRRRH (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.26448.698 20.543.748.810.715.778
n = 540 row objects.42546.875 29.105.741.852.767.880
m = 180 column objects.30050.521 18.512.710.779.736.807
m = 540 column objects.38845.052 31.136.780.853.746.850
K = 3 row clusters .039 29.16723.709 .967 .966.695.791
K = 6 row clusters .649 66.40625.938 .523 .696.787.866
L = 3 column clusters .038 29.94821.900.698.790 .968 .968
L = 6 column clusters .651 65.62527.747.792.872 .514 .690
Even row cluster density.28041.14627.886 .785 .817.765.849
60% row cluster density.40954.42721.762 .705 .845.717.808
Even column cluster density.24041.66728.412.771.853 .788 .820
60% column cluster density.44953.90621.236.719.809 .694 .837
33% Image matrix density.36748.43826.753.745.829.740.830
66% Image matrix density.32147.13522.895.744.833.742.827
70% block strength.36426.04224.647.808.911.804.911
60% block strength.32569.53125.001.682.751.678.747

1 Note – the overall averages and the results for the design features with the two biggest effects in each column are highlighted for emphasis.

Table 2.

Comparison of criterion function values for the UNGA networks.

  UNGA Military resolutions networkUNGA Ideological resolutions network
K L TMKLMedKRHTSVNSTMKLMedHRHTSVNS
4417431743174317434220422042204220
4517301730173017304144414441444144
46173017301730173041364136 41444136
4717301730173017304131 4136 4136 4136
5417131713171317134200420042004200
5516631663166316634020402040204020
561649 1657164916493947 395039473947
571646 16501646 16493890 3896 39473890
6417071707 1709 17094194 41984194 4196
6516331633163316334001400140014001
66 1614 1619161216123841384138413841
671599 1613 160815993763 377237633763
741702 1707 1707 1707419441944194 4196
751627 16341627 16303997 4001 3999 3998
761577 15881577157738223822 38253822
771565 1566156515653691 369536913691

1 Note: The criterion function values for the RH, TS, and VNS methods were taken from the article by Brusco et al. (2013a, Tables 2 and 3, pp. 204-205). The cell values shown in bold font reflect instances where the heuristic method failed to match the best criterion function value found across all four methods

Table 3.

Comparison of criterion function values and number of restarts for the MovieLens network.

  Criterion function valuesNumber of restarts
K L TMKLMedHRHPICFTMKLMedHRHRatioTMKLMedH / RH
2290971909710.00020003425.848
2390889909010.01319802019.851
2490875909000.028186317110.895
2590875908990.026179912913.946
2690875908920.019174911315.478
2790875908890.015168710316.379
3290971909710.000149412911.581
3388846888590.01513458615.640
3488799888580.06611768014.700
3588783888640.09111305919.153
3688781888520.08011095619.804
3788773888230.05611115221.365
4290971909710.00012188614.163
4388846888640.02010795718.930
4487603879070.3479364222.286
4587205872370.0378934221.262
4687142875500.4688063622.389
4787124877480.7167823621.722
5290971909710.00010416815.309
5388850888630.0158974221.357
5487165876620.5707793422.912
5586498871460.7497473322.636
5686043865140.5476802824.286
5786010860820.0846472426.958
6290971909710.0008975616.018
6388846888760.0347843224.500
6487172877200.6296732923.207
6586105873381.4326512427.125
6685790866781.0355972128.429
6785529861970.7815671831.500
7290971909710.0007924617.217
7388846888830.0426903023.000
7487169874560.3296032227.409
7585999863300.3855722028.600
7685573859820.4785111534.067
7785188856170.5044981435.571

1 Note: PICF is the percentage improvement in the criterion function from using TMKLMedH instead of RH.

Figure 1.

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.

DOI: https://doi.org/10.21307/joss-2018-007 | Journal eISSN: 1529-1227
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Language: English
Page range: 1 - 22
Published on: Sep 27, 2018
Published by: International Network for Social Network Analysis (INSNA)
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year
Keywords:
Deterministic blockmodeling,
Heuristics,
Two-mode networks
Related subjects:
Social sciences,
Social sciences, other

© 2018 Michael Brusco, Hannah J. Stolze, Michaela Hoffman, Douglas Steinley, Patrick Doreian, published by International Network for Social Network Analysis (INSNA)
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 19 (2018): Issue 1 (January 2018)
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