Graph Construction on Complex Spatio-Temporal Data for Enhancing Graph Neural Network-Based Approaches

Authors: Stefan Bloemheuvel, Jurgen van den Hoogen and Martin Atzmueller

Streamlit Demo Page

Link to Streamlit demo page

Data

data can be found at = https://zenodo.org/record/7900964

Requirements

• tensorflow
• torch==1.12.1
• tsl==0.9.0
• numpy==1.23.5
• pandas==1.4.4
• cuda toolkit==11.6
• networkx==2.8.8

Usage

the inputs_la, input_bay, inputs_ci and inputs_cw files should be put in the sensor locations folder. in a 'data' folder the whole data.zip file should be placed. run either the earthquake.py file or traffic.py file for the results. models for the forecasting traffic analysis can be found in all_models.py

Results

The resulting graphs and their characteristics:

Type	Method	CI (741)	CW (741)	METR-LA (21,321)	PEMS-BAY (52,650)
Signal	Correlation	195 (26.3%)	42 (5.7%)	13,478 (63.2%)	35,644 (67.7%)
	DTW	536 (72.3%)	723 (97.6%)	21,365 (100.2%)	26,287 (49.9%)
	MIC	739 (99.7%)	697 (94.1%)	21,315 (100.0%)	52,950 (100.6%)
Location	Gaussian	89 (12.0%)	275 (37.1%)	12,557 (58.9%)	14,527 (27.6%)
	MinMax	618 (83.4%)	533 (71.9%)	18,371 (86.2%)	38,098 (72.4%)
	KNN	212 (28.6%)	439 (59.2%)	3,800 (17.8%)	6,816 (12.9%)
	KNN-W	672 (90.7%)	640 (86.4%)	3,118 (14.6%)	7,030 (13.4%)
	K-means	48 (6.5%)	42 (5.7%)	3,097 (14.5%)	8,025 (15.2%)
	Optics	780 (105.3%)	91 (12.3%)	2,110 (9.9%)	3,144 (6.0%)
	Gabriel	69 (9.3%)	66 (8.9%)	252 (1.2%)	410 (0.8%)
	RNG	105 (14.2%)	101 (13.6%)	591 (2.8%)	938 (1.8%)

The resulting MAE and MSE scores on 4 datasets, where CI and CW are time series regression, and Metr-LA and Pems-Bay are forecasting:

Type	Method	CI (MAE)	CI (MSE)	CW (MAE)	CW (MSE)	METR-LA (MAE)	METR-LA (MSE)	PEMS-BAY (MAE)	PEMS-BAY (MSE)
Signal	Correlation	0.31	0.20	0.37	0.23	3.65	54.43	1.84	18.49
	DTW	0.32	0.21	0.39	0.25	3.65	54.20	1.85	18.46
	MIC	0.30	0.19	0.39	0.25	3.64	53.99	1.85	18.53
Location	Gaussian	0.34	0.24	0.42	0.28	3.66	54.16	1.86	18.80
	MinMax	0.31	0.21	0.41	0.26	3.64	53.74	1.85	18.48
	KNN	0.31	0.20	0.39	0.24	3.68	54.94	1.87	18.74
	KNN-W	0.32	0.22	0.38	0.23	3.69	54.95	1.88	18.93
	Kmeans	0.34	0.23	0.43	0.30	3.69	55.65	1.88	19.44
	Optics	0.32	0.21	0.39	0.25	3.73	57.24	1.93	20.65
	Gabriel	0.36	0.28	0.46	0.34	3.78	59.06	1.94	20.96
	RNG	0.37	0.28	0.46	0.33	3.75	58.05	1.91	20.38
cv ($\mu / \sigma$)		6.6%	13.4%	7.1%	14.4%	1.3%	3.3%	1.9%	4.9%