Introduction
Related works
The proposed model
Parameter inference
Uncollapsed Gibbs sampler
Collapsed Gibbs sampler
Inference tricks
Per-iteration running times
Experiments
Experiment on synthetic data
4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | ||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
U | chain1 | 0 | 5 | 439 | 2660 | 2672 | 959 | 187 | 16 | 2 | 0 | 0 | 0 |
chain2 | 0 | 0 | 184 | 1393 | 2396 | 1952 | 836 | 199 | 35 | 4 | 1 | 0 | |
chain3 | 2 | 66 | 406 | 1311 | 1951 | 1784 | 954 | 393 | 104 | 27 | 2 | 0 | |
C | chain4 | 9 | 181 | 742 | 1628 | 1754 | 1106 | 427 | 127 | 21 | 4 | 1 | 0 |
chain5 | 8 | 100 | 581 | 1418 | 2004 | 1707 | 827 | 268 | 77 | 9 | 1 | 0 | |
chain6 | 3 | 62 | 338 | 1137 | 1842 | 1825 | 1127 | 490 | 125 | 42 | 8 | 1 |
Communities | Size | |
---|---|---|
Ground truth | C1 = \(\{2,3,4,5,7,8,9, 10, 11, 14, 16, 17,18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29\}\) | 23 |
C2 = \(\{1, 3, 4,6, 7,9, 10, 11, 12, 13, 14, 15, 16, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30\}\) | 23 | |
C3 = \(\{1,2,5,6,13,17,26,30\}\) | 8 | |
C4 = \(\{1,8,15,16,28\}\) | 5 | |
C5 = \(\{5,12,17,24,28\}\) | 5 | |
C6 = \(\{3,7,10,13,18,30\}\) | 6 | |
C7 = \(\{4,12,20,25\}\) | 4 | |
C8 = \(\{13,14,23\}\) | 3 | |
Inferred result, the 6997th sample | C1 = \(\{2,3,4,5,7,8,9, 10, 11, 14, 16, 17,18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29\}\) | 23 |
C2 = \(\{1, 3, 4,6, 7,9, 10, 11, 12, 13, 14, 15, 16, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30\}\) | 23 | |
C3 = \(\{5,12,13,17,24,25,28\}\) | 7 | |
C4 = \(\{1,2,5,6,17,26,30\}\) | 7 | |
C5 = \(\{1,2,8,15,16,28\}\) | 6 | |
C6 = \(\{6,13,18,23,30\}\) | 5 | |
C7 = \(\{3,10,21\}\) | 3 | |
C8 = \(\{10,13,21\}\) | 3 | |
The 1000th sample | C1 = \(V_t\) | 30 |
C2 = \(\{3,4,7,10,11,14,16,20,21,22,23,25,29\}\) | 13 | |
C3 = \(\{5,20,23,24,25,27\}\) | 6 | |
C4 = \(\{2,5,8,17,26\}\) | 5 | |
C5 = \(\{1,2,6,30\}\) | 4 | |
C6 = \(\{6,21,26,27,28\}\) | 5 | |
C7 = \(\{9,12,14,20,27\}\) | 5 | |
C8 = \(\{9,10,30\}\) | 3 |
chain1 | chain2 | chain3 | chain1 | chain2 | chain3 | ||
---|---|---|---|---|---|---|---|
Mode of \(\alpha \) | 2.46 | 2.75 | 2.97 | \(95\%\) HPD of \(\alpha \) | 1.11, 4.47 | 1.33, 4.78 | 1.37, 4.94 |
Mode of \(\lambda \) | 1.24 | 1.25 | 1.25 | \(95\%\) HPD of \(\lambda \) | 1.2, 1.27 | 1.21, 1.28 | 1.22, 1.29 |
Experiment on the LESMIS network
\(K_s=13\) | \(K_s=14\) | \(K_s=15\) | \(K_s=16\) | \(K_s=17\) | \(K_s=18\) | \(K_s=19\) | |
---|---|---|---|---|---|---|---|
chain1 | 183 | 2284 | 2878 | 626 | 25 | 4 | 0 |
chain2 | 377 | 1776 | 2020 | 1246 | 507 | 70 | 4 |