Correction to: Scientific Reports, 10.1038/s41598-023-34077-z, published online 27 April 2023
The original Article contained errors in the References and the Data availability sections. The following references were omitted:
[2] Cini, A., Marisca, I. & Alippi, C. Filling the G_ap_s: Multivariate time series imputation by Graph Neural Networks. International Conference on Learning Representations, ICLR (2022)
[37] Marisca, I., Cini, A. & Alippi, C. Learning to Reconstruct Missing Data from Spatiotemporal Graphs with Sparse Observations. Advances in Neural Information Processing Systems, NeurIPS (2022)
As a result, all subsequent references were renumbered.
In addition, Reference [20] contained an error in the author list. The original reference [20] is shown below.
[20] Dao, M. et al. Scalable Spatiotemporal Graph Neural Networks. (2022).
It now reads:
[20] Cini, A., Marisca, I., Bianchi, F.M., & Alippi, C. Scalable Spatiotemporal Graph Neural Networks, NeurIPS (2022)
In the Introduction section, the following sentence was missing a reference to [2]:
Andrea Cini et al. proposed GRIN, which uses a bivariate graph RNN to rebuild missing data in different channels of a multivariate time series by learning the spatiotemporal representation through message passing.
Now reads:
Andrea Cini et al. proposed GRIN [2], which uses a bivariate graph RNN to rebuild missing data in different channels of a multivariate time series by learning the spatiotemporal representation through message passing.
The original Table 1 was missing references to [2] and [33]. The original Table 1 and its accompanying legend are shown below.
Table 1.
Details relating to the datasets.
| Dataset | Node | Time step | Missing% | Constructive missing% |
|---|---|---|---|---|
| AQI-36 | 36 | 36 | 13.24 | 10.67 |
| AQI | 437 | 24 | 25.67 | 11.33 |
| METR-LA (P) | 207 | 24 | 8.10 | 23.0 |
| (B) | – | – | – | 8.4 |
| PEMS-BAY(P) | 325 | 24 | 0.02 | 25.0 |
| (B) | – | – | – | 9.07 |
The original Table 2 was missing references to [2] and [37]. The original Table 2 and its accompanying legend are shown below.
Table 2.
Comparison of model performance for an average of 5 experiments filled on the air quality domain dataset.
| Model | AQI-36 | AQI | ||||
|---|---|---|---|---|---|---|
| mae | mse | mape(%) | mae | mse | mape(%) | |
| MEAN | 53.48 | 4578.08 | 76.77 | 39.60 | 3231.04 | 59.25 |
| KNN | 30.21 | 2892.31 | 43.36 | 34.10 | 3471.14 | 51.02 |
| MF | 30.54 | 2763.06 | 43.84 | 26.74 | 2021.44 | 40.01 |
| MICE | 30.37 | 2594.06 | 43.59 | 26.98 | 1930.92 | 40.37 |
| VAR | 15.64 | 833.46 | 22.02 | 22.95 | 1402.84 | 33.99 |
| E2GAN | 15.78 | 741.81 | 22.66 | 21.52 | 1240.81 | 32.21 |
| rGAIN | 15.37 | 641.92 | 21.63 | 21.78 | 1274.93 | 32.26 |
| BRITS | 14.50 | 662.36 | 20.41 | 20.21 | 1157.89 | 29.94 |
| SAITS | 18.16 | 843.53 | 37.16 | 21.33 | 1253.23 | 31.74 |
| CSDI | 9.74 | 383.63 | 11.32 | 19.71 | 1196.59 | 27.96 |
| MPGRU | 16.79 | 1103.04 | 23.63 | 18.76 | 1194.35 | 27.79 |
| GRIN | 12.08 | 523.14 | 17.00 | 14.73 | 775.91 | 21.82 |
| ADGCN | 11.93 | 502.31 | 17.13 | 13.49 | 642.00 | 20.19 |
The best results are in bold.
The original Table 3 was missing references to [2] and [37]. The original Table 3 and its accompanying legend are shown below.
Table 3.
Comparison of model performance for an average of 5 experimental fills on the traffic flow domain dataset.
| Model | METR-LA | PEMS-BAY | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Blocking missing | Point missing | Blocking missing | Point missing | |||||||||
| mae | mse | mape (%) | mae | mse | Mape (%) | mae | mse | Mape (%) | mae | mse | Mape (%) | |
| MEAN | 7.48 | 139.54 | 12.96 | 7.56 | 142.22 | 13.10 | 5.46 | 87.56 | 8.75 | 5.42 | 86.59 | 8.67 |
| KNN | 7.79 | 124.61 | 13.49 | 7.88 | 129.29 | 13.65 | 4.30 | 49.90 | 6.90 | 4.30 | 49.80 | 6.88 |
| MF | 5.46 | 109.61 | 9.46 | 5.56 | 113.46 | 9.62 | 3.28 | 50.14 | 5.26 | 3.29 | 51.39 | 5.27 |
| MICE | 4.22 | 51.07 | 7.31 | 4.42 | 55.07 | 7.65 | 2.94 | 28.28 | 4.71 | 3.09 | 31.43 | 4.95 |
| VAR | 3.11 | 28.00 | 5.38 | 2.69 | 21.10 | 4.66 | 2.09 | 16.06 | 3.35 | 1.30 | 6.52 | 2.07 |
| E2GAN | 3.00 | 23.49 | 5.21 | 2.98 | 22.80 | 7.99 | 1.97 | 12.20 | 3.16 | 1.77 | 9.73 | 2.83 |
| rGAIN | 2.90 | 21.67 | 5.02 | 2.83 | 20.03 | 4.91 | 2.18 | 13.96 | 3.50 | 1.88 | 10.37 | 3.01 |
| BRITS | 2.34 | 17.00 | 4.05 | 2.34 | 16.46 | 4.05 | 1.70 | 10.50 | 2.72 | 1.47 | 7.94 | 2.36 |
| SAITS | 2.30 | 16.88 | 4.00 | 2.26 | 16.32 | 3.94 | 1.56 | 14.02 | 2.50 | 1.40 | 7.88 | 2.30 |
| CSDI | 2.23 | 15.92 | 3.64 | 2.20 | 14.32 | 3.42 | 1.50 | 13.77 | 2.50 | 1.22 | 7.75 | 1.82 |
| MPGRU | 2.57 | 25.15 | 4.44 | 2.44 | 22.17 | 4.22 | 1.59 | 14.19 | 2.56 | 1.11 | 7.59 | 1.77 |
| GRIN | 2.03 | 13.26 | 3.52 | 1.91 | 10.41 | 3.30 | 1.14 | 6.60 | 1.83 | 0.67 | 1.55 | 1.08 |
| ADGCN | 2.02 | 13.22 | 3.51 | 1.89 | 10.31 | 3.27 | 1.07 | 5.23 | 1.73 | 0.66 | 1.52 | 1.07 |
The best results are in bold.
The original Table 4 was missing references to [37]. The original Table 4 and its accompanying legend are shown below.
Table 4.
Comparison of model MAE results when data absence rate increases.
| Model | METR-LA | PEMS-BAY | ||||
|---|---|---|---|---|---|---|
| 25% | 50% | 75% | 25% | 50% | 75% | |
| BRITS | 2.34 | 2.52 | 3.02 | 1.47 | 1.55 | 2.17 |
| SAITS | 2.26 | 2.48 | 3.74 | 1.40 | 1.50 | 2.96 |
| GRIN | 1.91 | 2.05 | 2.39 | 0.67 | 0.79 | 1.09 |
| ADGCN | 1.89 | 2.01 | 2.35 | 0.66 | 0.75 | 0.99 |
The best results are in bold.
The Data availability section was:
Data is contained within the Supplementary Material. The data presented in this study are available in Supplementary Material here.
It now reads:
Data contained within the Supplementary Material is reproduced from https://github.com/Graph-Machine-Learning-Group/grin. The data presented in this study are available in Supplementary Material here.
The original Article has been corrected.