Table 6: Performance gain of product space UrbanKG embedding on five spatiotemporal prediction tasks. All experimental results are the mean of 5 independent experiments repeated and the standard deviation (Std) are reported.
Model	NYC	311 service	CHI
Taxi MAE/RMSE	Bike MAE/RMSE	Mobility MAE/RMSE	Crime Micro/Macro-F1	MAE/RMSE	Taxi MAE/RMSE	Bike MAE/RMSE	Mobility MAE/RMSE	Crime Micro/Macro-F1	MAE/RMSE	311 service Micro/Macro-F1
GRU	1.802/3.587	0.920/1.115	1.003/1.318	-/-	-/-	3.372/8.895	1.431/2.619	1.157/1.800	-/-	-/-
LSTM	1.425/2.769	0.832/0.994	0.984/1.227	-/-	-/-	3.075/0.976	1.359/2.259	1.107/1.682	-/-	-/-
AE	1.399/2.484	0.701/0.898	0.956/1.233	56.42/52.12	65.68/59.64	3.313/11.64	1.416/2.706	1.148/1.721	57.49/57.27	54.67/55.34
STGCN w/P	0.835/2.069	0.221/0.558	0.553/0.976	76.80/63.10	81.15/78.50	1.967/6.014	0.632/1.537	0.458/1.138	71.86/68.71	79.67/79.47
0.781/1.942	0.201/0.543	0.542/0.947	77.56/64.26	81.98/79.15	1.844/5.826	0.625/1.501	0.414/1.064	72.18/68.93	79.92/79.83
Std	0.001/0.000	0.006/0.002	0.000/0.001	0.001/0.000	0.001/0.001	0.003/0.002	0.006/0.012	0.004/0.001	0.008/0.003	0.002/0.003
Improv %	6.47%/6.14%	9.05%/2.69%	1.99%/2.97%	0.99%/1.84%	1.02%/0.83%	6.25%/3.13%	1.11%/2.34%	9.61%/6.50%	0.45%/0.32%	0.31%/0.45%
MTGNN	1.289/2.275	0.967/1.041	0.963/1.163	72.88/58.61	79.32/75.75	2.167/5.965	1.153/1.723	1.081/1.504	68.48/66.46	76.72/76.32
MTGNN w/P	1.183/2.118	0.920/1.021	0.891/1.083	73.47/60.02	80.28/77.85	1.975/5.882	1.083/1.641	0.983/1.399	71.73/68.65	78.29/77.99
Std	0.007/0.005	0.016/0.009	0.021/0.011	0.008/0.004	0.011/0.009	0.023/0.017	0.005/0.009	0.003/0.002	0.016/0.007	0.000/0.001
Improv %	8.22%/6.90%	4.86%/1.92%	7.48%/6.8%	0.81%/2.41%	1.21%/2.77%	8.86%/1.39%	6.07%/4.76%	9.07%/6.98%	4.75%/3.30%	2.05%/2.19%
AGCRN	1.315/2.391	0.958/1.038	0.945/1.148	65.98/60.62	75.68/69.64	2.403/2.777	1.187/1.768	0.213/1.281	64.14/63.35	71.18/67.07
AGCRN w/P	1.208/2.221	0.875/0.983	0.901/1.067	67.75/61.88	76.35/72.57	2.255/6.945	1.093/1.621	0.205/1.258	66.51/65.27	72.87/70.54
Std	0.016/0.021	0.035/0.011	0.006/0.005	0.000/0.000	0.001/0.003	0.019/0.026	0.007/0.011	0.004/0.015	0.001/0.000	0.000/0.000
Improv %	8.14%/7.11%	8.66%/5.30%	4.66%/7.06%	2.68%/2.08%	0.89%/4.21%	6.16%/4.56%	7.92%/8.31%	3.76%/1.80%	3.71%/3.03%	2.37%/5.17%
ASTGCN	0.832/2.141	0.231/0.579	0.566/0.973	76.69/61.62	80.82/77.45	1.849/5.323	0.745/1.822	0.505/1.259	71.77/68.45	79.18/78.93
ASTGCN w/P	0.805/2.012	0.220/0.564	0.558/0.944	76.94/62.34	81.28/78.85	1.822/5.198	0.690/1.754	0.463/1.191	72.22/68.90	80.09/79.98
Std	0.004/0.005	0.003/0.003	0.000/0.006	0.009/0.008	0.007/0.009	0.001/0.006	0.017/0.003	0.015/0.009	0.012/0.009	0.008/0.007
Improv %	3.25%/6.03%	4.76%/2.59%	1.41%/2.98%	0.33%/1.17%	0.57%/1.81%	1.46%/2.35%	7.38%/3.73%	8.32%/5.40%	0.63%/0.66%	1.15%/1.33%
TGCN	1.701/3.198	0.337/0.685	0.654/1.118	75.22/63.19	77.56/72.96	2.112/6.645	1.127/2.583	0.702/1.665	70.62/66.41	77.89/77.57
TGCN w/P	1.578/2.887	0.319/0.664	0.635/1.054	76.01/63.65	79.29/73.47	1.997/6.502	1.052/2.341	0.677/1.586	71.26/68.38	78.49/78.25
Std	0.012/0.024	0.009/0.007	0.007/0.014	0.000/0.000	0.001/0.000	0.013/0.035	0.015/0.013	0.009/0.011	0.000/0.000	0.000/0.000
Improv %	7.23%/9.72%	5.34%/3.07%	2.91%/5.72%	1.05%/0.73%	2.23%/0.70%	5.45%/2.15%	6.65%/9.37%	3.56%/4.74%	0.91%/2.97%	0.77%/0.88%
HGCN	1.337/2.285	0.951/1.138	0.971/1.200	76.64/62.26	75.68/69.64	2.765/7.849	1.159/1.794	0.661/1.277	67.57/62.31	74.67/73.53
HGCN w/P	1.282/2.124	0.879/1.036	0.921/1.104	76.70/63.25	77.41/72.76	2.609/7.781	1.092/1.682	0.637/1.146	69.17/65.7	75.87/75.32
Std	0.027/0.019	0.016/0.009	0.017/0.028	0.003/0.002	0.009/0.005	0.013/0.035	0.028/0.031	0.006/0.024	0.007/0.005	0.003/0.004
Improv %	4.11%/7.05%	7.57%/8.96%	5.15%/8.00%	0.87%/1.59%	2.29%/4.48%	5.64%/0.87%	5.78%/6.24%	3.63%/10.2%	2.37%/5.44%	1.61%/2.43%