OD forecasting benchmark

Problem Definition. Given a historical dataset of OD flows $\lbrace f^t_{ij} | t= 1,2,...,k-1 \rbrace$ over a certain period of time, the objective is to forecast the OD flows for future time periods $\lbrace f^t_{ij} | t=k,k+1,... \rbrace$.

Requirements

dgl==1.1.0
matplotlib==3.1.1
numpy==1.21.6
pandas==1.1.5
Pillow==9.5.0
scikit_learn==0.24.2
scipy==1.3.1
tensorflow==2.12.0
tf_slim==1.1.0
torch==1.13.1
torch_geometric==2.3.1
tqdm==4.62.3

Data Description

Grids Spliting

Firstly, divide the area to be studied into several grids on the map.

OD Matrix

The first data description method is to divide time into discrete time intervals, count the OD flow at each time interval, and record it as an OD matrix. In every slot, $X \in R(N,N)$ , $N$ is the number of grids. $x_{ij}$ represents the volume of $i \rightarrow j$.

OD Flow

The second data description method is to record the starting point, ending point, and departure time (arrival time) of each OD flow.

Systematic Comparison of Methods

model	Spatial Topology Construction	Spatial Feature Modeling	Temporal Modeling	Learning
GEML	grids as nodes geo-adjacency graph POI-similarity graph	GCN	LSTM	multi-task learning
MPGCN	regions as nodes distance-based graph POI-similarity graph OD flow-based graph	2DGCN	LSTM	MSELoss
Gallet	regions as nodes OD flow-based graph distance-based graph	spatial attention	temporal attention	MSELoss
gMHC-STA	region-pairs as nodes fully-connected graph	GCN + spatial attention	self-attention	MSELoss
ST-VGCN	region-pairs as nodes OD flow-based graph	GCN + gated mechanism	GRU	MSELoss
MVPF	stations as nodes distance-based graph	GAT	GRU	MSELoss
Hex D-GCN	hexagonal grids as nodes taxi path-based dynamic graph	GCN	GRU	MSELoss
CWGAN-GP	OD matrix as an image	CNN	CNN	GAN-based training
SEHNN	stations as nodes geo-adjacency graph	GCN	LSTM	VAE-based training
HC-LSTM	grids as nodes OD flow-based graph in/out flow as an image OD matrix as an image	CNN + GCN	LSTM	MSELoss
ST-GDL	regions as nodes distance-based graph	CNN + GCN	CNN	MSELoss
PGCN	region pairs as nodes OD flow-based graph	GCN + gated mechanism	none	probabilistic inference with Monte Carlo
MF-ResNet	OD matrix as an image	CNN	none	MSELoss
TS-STN	stations as nodes OD flow-based graph	temporally shifted graph convolution	LSTM + attention	Partially MSELoss
DMGC-GAN	regions as nodes geo-adjacency graph OD flow-based graph in/out flow-based graph	GCN	GRU	GAN-based training
DNEAT	regions as nodes geo-adjacency graph OD flow-based graph	attention	attention	MSELoss
CAS-CNN	OD matrix as image	CNN	channel-wise attention	masked MSELoss
ST-ED-RMGC	region pairs as nodes fully-connected graph geo-adjacency graph POI-based graph disntance-based graph OD flow-based graph	GCN	LSTM	MSELoss
HSTN	regions as nodes geo-adjacency graph in/out flow-based graph	GCN	GRU+Seq2Seq	MSELoss
BGARN	grid clusters as nodes distance-based graph OD flow-based graph	GCN + attention	LSTM	MSELoss
HMOD	regions as nodes OD flow-based graph	random walk for embedding	GRU	MSELoss
STHAN	regions as nodes geo-adjacency graph POI-based graph OD flow-based graph	convolution by meta-paths + attention	GRU	MSELoss
ODformer	regions as nodes	2D-GCN within Transformer	none	MSELoss
CMOD	stations as nodes passengers as edges	multi-level information aggregation	multi-level information aggregation	continous time forecasting
MIAM	stations as nodes railway-based graph	GCGRU	Transformer	online forecasting
DAGNN	regions as nodes fully-connected graph	subgraph + GCN	TCN	MSELoss

Performance Comparison

model	RMSE	NRMSE	MAE	MAPE	sMAPE
LSTNet			24.5363	0.5161
GCRN	120.2321		24.5363	0.5161
GEML	113.8526		39.5888	3.1885
MPGCN	1.1421
PGCN
ST-GDL
Gallet	1081.1332		355.7162	0.6623
Hex D-GCN
BGARN	52.2182		10.3148	0.5017
CMOD
AEST

The performance comparison will be completed soon.