Table 2.
Simulation 2 –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 | n | Ward’s SEE > K-means SSEs | Ward’s | K-means | Ward’s | K-means |
|
| |||||||
| Equal | 2 | 1000 | 0.12 | 0.09 | 0.03 | 0.9668 | 0.9768 |
| Equal | 2 | 2000 | 0.00 | 0.00 | 0.00 | 1.0000 | 1.0000 |
| Equal | 2 | 4000 | 0.00 | 0.00 | 0.00 | 1.0000 | 1.0000 |
| Equal | 3 | 1000 | 0.68 | 0.38 | 0.28 | 0.7104 | 0.7500 |
| Equal | 3 | 2000 | 0.03 | 0.03 | 0.00 | 0.9910 | 0.9949 |
| Equal | 3 | 4000 | 0.00 | 0.00 | 0.00 | 1.0000 | 1.0000 |
| Equal | 4 | 1000 | 0.76 | 0.52 | 0.24 | 0.4580 | 0.5055 |
| Equal | 4 | 2000 | 0.22 | 0.17 | 0.05 | 0.9348 | 0.9418 |
| Equal | 4 | 4000 | 0.00 | 0.00 | 0.00 | 1.0000 | 1.0000 |
| Equal | 5 | 1000 | 0.77 | 0.43 | 0.32 | 0.3446 | 0.3595 |
| Equal | 5 | 2000 | 0.52 | 0.36 | 0.15 | 0.7517 | 0.7852 |
| Equal | 5 | 4000 | 0.05 | 0.04 | 0.01 | 0.9883 | 0.9947 |
| Equal | 6 | 1000 | 0.87 | 0.50 | 0.37 | 0.2534 | 0.2678 |
| Equal | 6 | 2000 | 0.66 | 0.37 | 0.27 | 0.6150 | 0.6272 |
| Equal | 6 | 4000 | 0.09 | 0.05 | 0.02 | 0.9585 | 0.9652 |
| Unequal | 2 | 1000 | 0.18 | 0.13 | 0.05 | 0.9110 | 0.9282 |
| Unequal | 2 | 2000 | 0.02 | 0.00 | 0.02 | 0.9982 | 0.9946 |
| Unequal | 2 | 4000 | 0.00 | 0.00 | 0.00 | 1.0000 | 1.0000 |
| Unequal | 3 | 1000 | 0.67 | 0.36 | 0.31 | 0.7269 | 0.7227 |
| Unequal | 3 | 2000 | 0.15 | 0.10 | 0.05 | 0.9635 | 0.9699 |
| Unequal | 3 | 4000 | 0.01 | 0.01 | 0.00 | 0.9980 | 0.9991 |
| Unequal | 4 | 1000 | 0.68 | 0.39 | 0.29 | 0.5183 | 0.5294 |
| Unequal | 4 | 2000 | 0.38 | 0.21 | 0.17 | 0.8902 | 0.8877 |
| Unequal | 4 | 4000 | 0.04 | 0.00 | 0.04 | 0.9915 | 0.9888 |
| Unequal | 5 | 1000 | 0.76 | 0.38 | 0.38 | 0.3794 | 0.3856 |
| Unequal | 5 | 2000 | 0.45 | 0.19 | 0.26 | 0.7933 | 0.7816 |
| Unequal | 5 | 4000 | 0.11 | 0.07 | 0.04 | 0.9616 | 0.9619 |
| Unequal | 6 | 1000 | 0.80 | 0.43 | 0.35 | 0.3083 | 0.3097 |
| Unequal | 6 | 2000 | 0.64 | 0.26 | 0.33 | 0.6501 | 0.6413 |
| Unequal | 6 | 4000 | 0.30 | 0.18 | 0.10 | 0.8950 | 0.9019 |
Note. The first three columns correspond to the cells of the experimental design: the distribution of vertices across communities, the number of communities, and the sample size, respectively. The fourth column is the proportion of cell replicates for which the Ward’s method SSE exceeded the K-means SSE. The fifth and sixth columns for which Ward’s method and K-means partitions, respectively, yielded better agreement with the true partition. The seventh and eight columns correspond to the cell average ARI values for the Ward’s and K-means implementations, respectively.