Explainable Spatio-Temporal Inference Network for Car-Sharing Demand Prediction
Abstract
:1. Introduction
2. Literature Review
2.1. Benefits of Accurate Demand Prediction
2.2. Feature Extraction and Selection in Demand Prediction Models
2.3. The eX–STIN Model: Origin and Development
2.4. Explainability in Predictive Models
3. Methodology
3.1. Feature Extraction
3.1.1. Temporal Feature Extraction
- : IMFs from temporal data, with as the IMF index and as the trial index.
- : residual pattern after decomposing .
3.1.2. Spatial Feature Extraction
- : IMFs from the spatial data.
- : residual pattern left after decomposing .
3.1.3. Spatio-Temporal Feature Extraction
- : IMFs from spatio-temporal data.
- : residual pattern after decomposing .
3.2. Mutual Information
- : the probability mass function of .
- : the joint probability mass function of and .
- : the conditional probability mass function of given .
3.3. Feature Selection
3.3.1. Temporal Feature Selection
- : the subset of selected features from .
- : the features within the subset .
- : the mutual information entropy between features and .
- : mutual information between feature and target variable .
3.3.2. Spatial Feature Selection
- : the subset of selected features from .
- : the features within the subset .
- : the mutual information entropy between features and .
- : mutual information between feature and target variable .
3.3.3. Spatio-Temporal Feature Selection
- : the subset of selected features from .
- : the features within the subset .
- : the mutual information entropy between features and .
- : mutual information between feature and target variable .
3.4. Predictive Model
3.4.1. Temporal Feature Unit
- Encoder: temporal convolutional network (TCN)
- : the output of the TCN.
- : the weight matrix of the convolutional filter.
- : the bias term.
- : the convolution operation.
- : batch-normalized output at a specific time step .
- : mean and variance computed over the batch.
- : learnable parameters specific to each feature dimension.
- : small constant added for numerical stability.
- 2.
- Attention mechanism layer
- : the number of attentional correlations from moment to moment .
- : the attentional weight.
- : the current time step in the decoder.
- : the time steps in the encoder’s output.
- : the total number of time steps in the encoder output.
- : an iterator in the normalization sum.
- 3.
- Decoder: long short-term memory layer (LSTM)
- : weight matrices for input gate, forget gate, output gate, and candidate cell state, respectively.
- bias terms for input gate, forget gate, output gate, and candidate cell state, respectively.
- : the current cell state.
- : the cell state from the previous time step.
- : the current hidden state.
- : sigmoid activation function.
- element-wise multiplication.
- : represents the concatenated outputs from the LSTM decoders at four different time scales (daily, weekly, monthly, and yearly).
- : the weight matrix of the fully connected layer.
- : the bias of the dense fully connected layer.
3.4.2. Spatial Feature Unit
- Spatial density calculation
- 2.
- Regression model
- 3.
- Spatio-temporal embedding layer
- 4.
- Graph convolutional network layer (GCN)
- 5.
- Fully connected layer
- : weight of the fully connected layer.
- : bias of the fully connected layer.
3.4.3. Spatio-Temporal Feature Unit
- : weight of the fully connected layer.
- : bias of the fully connected layer.
3.4.4. Shapley Additive Explanation Analysis and Model Training
- : the normalized SHAP output from the temporal feature unit.
- : the normalized SHAP output from the spatial feature unit.
- : the normalized SHAP output from the spatio-temporal feature unit.
- , , and : the weight matrices.
- : the bias.
- : the weight matrix that maps the final integrated feature representation to the predicted car demand.
4. Experimental Section
4.1. Data Description
4.2. Experimental Setting
4.3. Baseline Models’ Configuration
4.4. Model Configuration
4.5. Evaluation Metrics
4.5.1. Mean Absolute Error (MAE)
4.5.2. Mean Square Error (MSE)
4.5.3. Root Mean Square Error (RMSE)
4.5.4. Mean Absolute Percentage Error (MAPE)
- : the actual value.
- : the forecast value.
- : the number of fitted points.
5. Discussion
5.1. Evaluation of eX-STIN for Car-Sharing Demand Prediction
5.2. Prediction Results and Interpretability Analysis
5.3. Features Impact on the Unit’s Output
5.3.1. Temporal Unit
5.3.2. Spatial Unit
5.3.3. Spatio-Temporal Unit
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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First-Level Indicator | Second-Level Indicator |
---|---|
Usage feature | rented cars |
Temporal features | workday (1 for yes and 0 for no); rush hour (1 for yes and 0 for no) |
Weather conditions | temperature (°C), precipitation (1 for yes and 0 for no), and AQI (Air Quality Index) |
Building land attribute | hotel, shopping, domestic services, beauty, tourist attractions, leisure and entertainment, work out, education and training, culture media, medical, car services, transportation facilities, finance, real estate, corporate, government agency, entrance and exit, natural features, administrative landmark, and door address |
Model | Hyperparameters |
---|---|
MLP | 2 fully connected layers, 20 and 15 hidden units |
XGBoost | N_estimators: 25 Max_depth: 5 |
KNN | N_neighbours: 5 Weights: “uniform” |
RF | N_estimators: 100 Max_depth: 5 Min_samples_split: 15 |
LSTM | Hidden layers: 2 Hidden units: 25, 15 neurons Learning rate: 0.01 Drop out: 0.5 Optimizer: Adam Epochs: 80 |
CNN-LSTM | CNN layers: 2 LSTM layers: 2 Filters: 64 Kernel size: 3 LSTM units: 50 Dropout: 0.3 Optimizer: Adam |
Att-LSTM | Layers: 5 Units: 50 Attention type: Bahdanau Dropout: 0.4 Optimizer: Adam |
ConvLSTM | Layers: 2 Filters: 64 Kernel size: 3 × 3 Dropout: 0.3 Optimizer: Adam |
GATs | Number of attention heads: 4 Hidden units: 20 Learning rate: 0.01 Dropout: 0.6 Optimizer: Adam |
Transformer | Heads: 4 Layers: 3 Size: 128 Feedforward size: 512 Dropout: 0.1 Optimizer: Adam |
ST-GCN | Spatial graph convolutional layers: 3 Hidden units: 64 Kernel size: 5 Dropout: 0.2 Optimizer: Adam |
DCN | Cross layers: 3 Deep layers: 2 Hidden units deep layer: 32 Dropout: 0.2 Optimizer: Adam |
Model | Hyperparameters |
---|---|
TCN | Hidden layers: 3 Kernel size: 3 Dilations: [1, 2, 4, 8, 16, 32, 64] Number filters: 64 Learning rate: 0.01 Drop out: 0.2 Optimizer: Adam Epochs: 80 |
LSTM | Hidden layers: 2 Hidden units: 25, 15 neurons Learning rate: 0.01 Drop out: 0.3 Optimizer: Adam Epochs: 100 |
GCN | Hidden layers: 2 (32, 64 neurons) Hidden units: 32, 64 neurons Learning rate: 0.01 Epochs: 80 |
MAE | MSE | RMSE | MAPE | |
---|---|---|---|---|
MLP | 0.626 | 0.554 | 0.744 | 0.887 |
TCN | 0.145 | 0.168 | 0.410 | 0.109 |
KNN | 0.601 | 0.515 | 0.718 | 0.571 |
GCN | 0.048 | 0.182 | 0.427 | 0.195 |
RF | 0.177 | 0.356 | 0.597 | 0.469 |
XGBoost | 0.076 | 0.167 | 0.409 | 0.164 |
LSTM | 0.135 | 0.333 | 0.577 | 0.139 |
CNN-LSTM | 0.033 | 0.175 | 0.418 | 0.115 |
Att-LSTM | 0.181 | 0.354 | 0.595 | 0.108 |
ConvLSTM | 0.428 | 0.139 | 0.373 | 0.484 |
GATs | 0.259 | 0.230 | 0.480 | 0.195 |
Transformer | 0.824 | 0. 575 | 0.758 | 0.488 |
ST-GCN | 0.426 | 0.229 | 0.479 | 0.192 |
DCN | 0.255 | 0.165 | 0.406 | 0.191 |
USTIN | 0.031 | 0.154 | 0.392 | 0.108 |
Our(eX-STIN) | 0.022 | 0.104 | 0.322 | 0.094 |
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Brahimi, N.; Zhang, H.; Razzaq, Z. Explainable Spatio-Temporal Inference Network for Car-Sharing Demand Prediction. ISPRS Int. J. Geo-Inf. 2025, 14, 163. https://doi.org/10.3390/ijgi14040163
Brahimi N, Zhang H, Razzaq Z. Explainable Spatio-Temporal Inference Network for Car-Sharing Demand Prediction. ISPRS International Journal of Geo-Information. 2025; 14(4):163. https://doi.org/10.3390/ijgi14040163
Chicago/Turabian StyleBrahimi, Nihad, Huaping Zhang, and Zahid Razzaq. 2025. "Explainable Spatio-Temporal Inference Network for Car-Sharing Demand Prediction" ISPRS International Journal of Geo-Information 14, no. 4: 163. https://doi.org/10.3390/ijgi14040163
APA StyleBrahimi, N., Zhang, H., & Razzaq, Z. (2025). Explainable Spatio-Temporal Inference Network for Car-Sharing Demand Prediction. ISPRS International Journal of Geo-Information, 14(4), 163. https://doi.org/10.3390/ijgi14040163