Table 1.
Simulation 1 –Cell Means for Proportion of Suboptimal Walktrap SSE’s, ARIs, Proportion of Test Problems for Which Each Method Yielded a Better ARI, and ARI.
| Proportion |
Proportion with better ARI
|
Mean ARI |
||||||
|---|---|---|---|---|---|---|---|---|
| Dist | K | Cohesion | Overlap | Ward’s SSE > K-means SSEs | Ward’s | K-means | Ward’s | K-means |
|
| ||||||||
| Equal | 2 | 0.9 | 0.1 | 0.00 | 0.00 | 0.00 | 0.9900 | 0.9900 |
| Equal | 2 | 0.9 | 0.2 | 0.00 | 0.00 | 0.00 | 0.9900 | 0.9900 |
| Equal | 2 | 0.9 | 0.3 | 0.00 | 0.00 | 0.00 | 0.9900 | 0.9900 |
| Equal | 2 | 0.8 | 0.1 | 0.00 | 0.00 | 0.00 | 1.0000 | 1.0000 |
| Equal | 2 | 0.8 | 0.2 | 0.00 | 0.00 | 0.00 | 1.0000 | 1.0000 |
| Equal | 2 | 0.8 | 0.3 | 0.00 | 0.00 | 0.00 | 1.0000 | 1.0000 |
| Equal | 2 | 0.7 | 0.1 | 0.00 | 0.00 | 0.00 | 0.9983 | 0.9983 |
| Equal | 2 | 0.7 | 0.2 | 0.00 | 0.00 | 0.00 | 1.0000 | 1.0000 |
| Equal | 2 | 0.7 | 0.3 | 0.00 | 0.00 | 0.00 | 1.0000 | 1.0000 |
| Equal | 3 | 0.9 | 0.1 | 0.00 | 0.00 | 0.00 | 1.0000 | 1.0000 |
| Equal | 3 | 0.9 | 0.2 | 0.00 | 0.00 | 0.00 | 1.0000 | 1.0000 |
| Equal | 3 | 0.9 | 0.3 | 0.00 | 0.00 | 0.00 | 1.0000 | 1.0000 |
| Equal | 3 | 0.8 | 0.1 | 0.00 | 0.00 | 0.00 | 1.0000 | 1.0000 |
| Equal | 3 | 0.8 | 0.2 | 0.01 | 0.00 | 0.01 | 1.0000 | 0.9987 |
| Equal | 3 | 0.8 | 0.3 | 0.05 | 0.04 | 0.01 | 0.9863 | 0.9910 |
| Equal | 3 | 0.7 | 0.1 | 0.03 | 0.01 | 0.02 | 0.9974 | 0.9962 |
| Equal | 3 | 0.7 | 0.2 | 0.07 | 0.06 | 0.01 | 0.9768 | 0.9852 |
| Equal | 3 | 0.7 | 0.3 | 0.18 | 0.12 | 0.04 | 0.9493 | 0.9590 |
| Equal | 4 | 0.9 | 0.1 | 0.00 | 0.00 | 0.00 | 0.9988 | 0.9988 |
| Equal | 4 | 0.9 | 0.2 | 0.01 | 0.01 | 0.00 | 0.9977 | 0.9988 |
| Equal | 4 | 0.9 | 0.3 | 0.04 | 0.03 | 0.01 | 0.9865 | 0.9896 |
| Equal | 4 | 0.8 | 0.1 | 0.01 | 0.01 | 0.00 | 0.9956 | 0.9968 |
| Equal | 4 | 0.8 | 0.2 | 0.10 | 0.08 | 0.02 | 0.9663 | 0.9748 |
| Equal | 4 | 0.8 | 0.3 | 0.22 | 0.13 | 0.06 | 0.9346 | 0.9481 |
| Equal | 4 | 0.7 | 0.1 | 0.11 | 0.06 | 0.05 | 0.9730 | 0.9730 |
| Equal | 4 | 0.7 | 0.2 | 0.33 | 0.19 | 0.13 | 0.8830 | 0.8912 |
| Equal | 4 | 0.7 | 0.3 | 0.58 | 0.36 | 0.19 | 0.7864 | 0.8166 |
| Equal | 5 | 0.9 | 0.1 | 0.03 | 0.02 | 0.01 | 0.9905 | 0.9916 |
| Equal | 5 | 0.9 | 0.2 | 0.11 | 0.08 | 0.03 | 0.9756 | 0.9808 |
| Equal | 5 | 0.9 | 0.3 | 0.19 | 0.12 | 0.07 | 0.9445 | 0.9530 |
| Equal | 5 | 0.8 | 0.1 | 0.11 | 0.06 | 0.05 | 0.9653 | 0.9714 |
| Equal | 5 | 0.8 | 0.2 | 0.18 | 0.09 | 0.09 | 0.9194 | 0.9173 |
| Equal | 5 | 0.8 | 0.3 | 0.37 | 0.19 | 0.14 | 0.8227 | 0.8354 |
| Equal | 5 | 0.7 | 0.1 | 0.26 | 0.12 | 0.14 | 0.8982 | 0.8947 |
| Equal | 5 | 0.7 | 0.2 | 0.42 | 0.18 | 0.20 | 0.8037 | 0.8004 |
| Equal | 5 | 0.7 | 0.3 | 0.55 | 0.33 | 0.19 | 0.6738 | 0.6878 |
| Equal | 6 | 0.9 | 0.1 | 0.08 | 0.03 | 0.03 | 0.9777 | 0.9794 |
| Equal | 6 | 0.9 | 0.2 | 0.17 | 0.05 | 0.10 | 0.9454 | 0.9392 |
| Equal | 6 | 0.9 | 0.3 | 0.31 | 0.22 | 0.09 | 0.8585 | 0.8800 |
| Equal | 6 | 0.8 | 0.1 | 0.09 | 0.05 | 0.03 | 0.9226 | 0.9217 |
| Equal | 6 | 0.8 | 0.2 | 0.43 | 0.19 | 0.23 | 0.8168 | 0.8150 |
| Equal | 6 | 0.8 | 0.3 | 0.51 | 0.28 | 0.20 | 0.7242 | 0.7306 |
| Equal | 6 | 0.7 | 0.1 | 0.37 | 0.18 | 0.17 | 0.8280 | 0.8285 |
| Equal | 6 | 0.7 | 0.2 | 0.68 | 0.37 | 0.29 | 0.6769 | 0.6942 |
| Equal | 6 | 0.7 | 0.3 | 0.69 | 0.43 | 0.25 | 0.5830 | 0.6032 |
| Unequal | 2 | 0.9 | 0.1 | 0.01 | 0.00 | 0.01 | 0.9900 | 0.9865 |
| Unequal | 2 | 0.9 | 0.2 | 0.01 | 0.00 | 0.01 | 0.9900 | 0.9882 |
| Unequal | 2 | 0.9 | 0.3 | 0.02 | 0.00 | 0.02 | 0.9846 | 0.9811 |
| Unequal | 2 | 0.8 | 0.1 | 0.00 | 0.00 | 0.00 | 0.9982 | 0.9982 |
| Unequal | 2 | 0.8 | 0.2 | 0.00 | 0.00 | 0.00 | 0.9930 | 0.9930 |
| Unequal | 2 | 0.8 | 0.3 | 0.02 | 0.01 | 0.01 | 0.9822 | 0.9821 |
| Unequal | 2 | 0.7 | 0.1 | 0.01 | 0.00 | 0.01 | 0.9928 | 0.9911 |
| Unequal | 2 | 0.7 | 0.2 | 0.08 | 0.01 | 0.07 | 0.9876 | 0.9734 |
| Unequal | 2 | 0.7 | 0.3 | 0.12 | 0.03 | 0.09 | 0.9529 | 0.9454 |
| Unequal | 3 | 0.9 | 0.1 | 0.00 | 0.00 | 0.00 | 0.9967 | 0.9967 |
| Unequal | 3 | 0.9 | 0.2 | 0.02 | 0.00 | 0.02 | 0.9947 | 0.9927 |
| Unequal | 3 | 0.9 | 0.3 | 0.04 | 0.02 | 0.02 | 0.9891 | 0.9896 |
| Unequal | 3 | 0.8 | 0.1 | 0.01 | 0.01 | 0.00 | 0.9926 | 0.9936 |
| Unequal | 3 | 0.8 | 0.2 | 0.05 | 0.00 | 0.05 | 0.9950 | 0.9897 |
| Unequal | 3 | 0.8 | 0.3 | 0.10 | 0.03 | 0.07 | 0.9687 | 0.9649 |
| Unequal | 3 | 0.7 | 0.1 | 0.05 | 0.03 | 0.02 | 0.9804 | 0.9804 |
| Unequal | 3 | 0.7 | 0.2 | 0.12 | 0.07 | 0.05 | 0.9609 | 0.9613 |
| Unequal | 3 | 0.7 | 0.3 | 0.28 | 0.15 | 0.13 | 0.9359 | 0.9355 |
| Unequal | 4 | 0.9 | 0.1 | 0.03 | 0.01 | 0.02 | 0.9962 | 0.9954 |
| Unequal | 4 | 0.9 | 0.2 | 0.02 | 0.02 | 0.00 | 0.9889 | 0.9905 |
| Unequal | 4 | 0.9 | 0.3 | 0.08 | 0.04 | 0.04 | 0.9739 | 0.9762 |
| Unequal | 4 | 0.8 | 0.1 | 0.05 | 0.03 | 0.02 | 0.9824 | 0.9839 |
| Unequal | 4 | 0.8 | 0.2 | 0.06 | 0.02 | 0.04 | 0.9658 | 0.9632 |
| Unequal | 4 | 0.8 | 0.3 | 0.17 | 0.12 | 0.05 | 0.9436 | 0.9508 |
| Unequal | 4 | 0.7 | 0.1 | 0.08 | 0.03 | 0.04 | 0.9789 | 0.9775 |
| Unequal | 4 | 0.7 | 0.2 | 0.31 | 0.17 | 0.13 | 0.9256 | 0.9287 |
| Unequal | 4 | 0.7 | 0.3 | 0.41 | 0.18 | 0.23 | 0.8468 | 0.8485 |
| Unequal | 5 | 0.9 | 0.1 | 0.02 | 0.01 | 0.01 | 0.9917 | 0.9916 |
| Unequal | 5 | 0.9 | 0.2 | 0.15 | 0.06 | 0.09 | 0.9569 | 0.9540 |
| Unequal | 5 | 0.9 | 0.3 | 0.19 | 0.11 | 0.07 | 0.9307 | 0.9336 |
| Unequal | 5 | 0.8 | 0.1 | 0.11 | 0.05 | 0.06 | 0.9657 | 0.9645 |
| Unequal | 5 | 0.8 | 0.2 | 0.20 | 0.14 | 0.06 | 0.9173 | 0.9245 |
| Unequal | 5 | 0.8 | 0.3 | 0.36 | 0.22 | 0.13 | 0.8527 | 0.8609 |
| Unequal | 5 | 0.7 | 0.1 | 0.27 | 0.12 | 0.15 | 0.9217 | 0.9202 |
| Unequal | 5 | 0.7 | 0.2 | 0.45 | 0.21 | 0.23 | 0.8582 | 0.8597 |
| Unequal | 5 | 0.7 | 0.3 | 0.50 | 0.26 | 0.23 | 0.7510 | 0.7578 |
| Unequal | 6 | 0.9 | 0.1 | 0.09 | 0.04 | 0.04 | 0.9732 | 0.9717 |
| Unequal | 6 | 0.9 | 0.2 | 0.24 | 0.15 | 0.07 | 0.9267 | 0.9331 |
| Unequal | 6 | 0.9 | 0.3 | 0.22 | 0.15 | 0.05 | 0.8832 | 0.8916 |
| Unequal | 6 | 0.8 | 0.1 | 0.12 | 0.02 | 0.09 | 0.9460 | 0.9387 |
| Unequal | 6 | 0.8 | 0.2 | 0.32 | 0.13 | 0.17 | 0.8808 | 0.8780 |
| Unequal | 6 | 0.8 | 0.3 | 0.46 | 0.23 | 0.23 | 0.8090 | 0.8122 |
| Unequal | 6 | 0.7 | 0.1 | 0.21 | 0.11 | 0.10 | 0.9280 | 0.9291 |
| Unequal | 6 | 0.7 | 0.2 | 0.40 | 0.24 | 0.15 | 0.8376 | 0.8450 |
| Unequal | 6 | 0.7 | 0.3 | 0.49 | 0.22 | 0.27 | 0.7300 | 0.7317 |
Note. The first four columns correspond to the cells of the experimental design: the distribution of vertices across communities, the number of communities, cohesion, and overlap, respectively. The fifth column is the proportion of cell replicates for which the Ward’s method SSE exceeded the K-means SSE. The sixth and seventh columns for which Ward’s method and K-means partitions, respectively, yielded better agreement with the true partition. The eighth and ninth columns correspond to the cell average ARI values for the Ward’s and K-means implementations, respectively.