Table 5 A comparative summary of ChoiceRank and ReversePR (abbreviated as CR and RPR, respectively)
From: Efficient algorithm to compute Markov transitional probabilities for a desired PageRank
(a) Network properties and the running times of the algorithms | |||||
|V| | |E| | Density \((\frac{\lvert E\rvert }{\lvert V \rvert ^{2}} )\) | CR running time | RPR running time | |
Wikipedia | ≈1∗107 | ≈4∗108 | 3∗10−6 | 5500 seconds | 2400 seconds |
Clickstream | ≈2∗106 | ≈1∗107 | 3∗10−6 | 240 seconds | 30 seconds |
Kosarak | ≈4∗104 | ≈1∗106 | 6∗10−4 | 4 seconds | 2.5 seconds |
Citibike | ≈5∗102 | ≈5∗103 | 2∗10−2 | 0.3 seconds | 0.05 seconds |
(b) The mean values of the different evaluation criteria for the different networks. Bold means better result and significant differences (p≪0.01) are marked with † | ||||||||
Displacement | KL divergence | RMSE | MRR | |||||
CR | RPR | CR | RPR | CR | RPR | CR | RPR | |
Wikipedia | 0.325 | \(\textbf{0.307}^{\dagger }\) | 3.005 | \(\textbf{2.866}^{\dagger }\) | 0.101 | \(\textbf{0.099}^{\dagger }\) | 0.094 | \(\textbf{0.257}^{\dagger }\) |
Clickstream | 0.299 | \(\textbf{0.276}^{\dagger }\) | 0.242 | \(\textbf{0.241}^{\dagger }\) | 0.0979 | \(\textbf{0.0978}^{\dagger }\) | 0.447 | \(\textbf{0.517}^{\dagger }\) |
Kosarak | \(\textbf{0.332}^{\dagger }\) | 0.359 | 0.885 | \(\textbf{0.480}^{\dagger }\) | 0.150 | \(\textbf{0.074}^{\dagger }\) | \(\textbf{0.554}^{\dagger }\) | 0.431 |
Citibike | 0.267 | 0.264 | 0.073 | 0.070 | 0.047 | 0.045 | 0.439 | 0.447 |
(c) The median values of the different evaluation criteria for the different networks. Bold means better result and significant differences (p≪0.01) are marked with † | ||||||||
Displacement | KL divergence | RMSE | MRR | |||||
CR | RPR | CR | RPR | CR | RPR | CR | RPR | |
Wikipedia | 0.324 | \(\textbf{0.309}^{\dagger }\) | 2.946 | \(\textbf{2.776}^{\dagger }\) | 0.074 | \(\textbf{0.073}^{\dagger }\) | 0.045 | \(\textbf{0.111}^{\dagger }\) |
Clickstream | 0.326 | \(\textbf{0.281}^{\dagger }\) | 0.1433 | 0.1431 | 0.076 | 0.076 | 0.333 | \(\textbf{0.5}^{\dagger }\) |
Kosarak | \(\textbf{0.344}^{\dagger }\) | 0.378 | 0.703 | \(\textbf{0.210}^{\dagger }\) | 0.116 | \(\textbf{0.046}^{\dagger }\) | \(\textbf{0.5}^{\dagger }\) | 0.333 |
Citibike | 0.283 | 0.267 | 0.059 | 0.058 | 0.030 | 0.028 | 0.333 | 0.333 |