💻 computer science

Spatial Fairness in Taxi Demand Prediction: A Hybrid Approach Leveraging District Profiles

This paper proposes a hybrid taxi demand prediction framework that integrates Non-negative Matrix Factorization with White Shark Optimization for data imputation, LSTM for temporal modeling, and a fairness-aware regularization mechanism based on Relative Hardship Proximity to minimize prediction disparities across urban districts while maintaining high accuracy.

Original authors: Ghazalak Eslami, Foad Ghaderi

Published 2026-08-04

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Ghazalak Eslami, Foad Ghaderi

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the city as a giant, living organism where millions of tiny pulses—people needing rides—beat through its veins every second. For a city to run smoothly, the "heart" of its transportation system needs to know exactly where these pulses are strongest and where they are faint. This is the world of taxi demand prediction, a branch of data science that tries to guess how many people will need a ride in a specific neighborhood at a specific time. But here's the tricky part: cities are messy. Data often goes missing (like a ride request that forgot to say where it started), and not all neighborhoods are the same. Some are bustling hubs, while others are quiet or struggling with poverty. If a computer model only learns from the busy, wealthy areas, it might forget the quiet ones, leaving people in those neighborhoods waiting forever for a cab that never comes. This paper asks a crucial question: Can we build a prediction system that is not just smart, but also fair, making sure no neighborhood gets left behind?

The researchers behind this study, Ghazalak Eslami and Foad Ghaderi, decided to build a "super-smart" taxi predictor that doesn't just look at numbers but also understands the story of the city. They treated the city like a giant puzzle with missing pieces. First, they had to fix the broken parts of their data. Imagine trying to solve a jigsaw puzzle where half the pieces are missing; you can't just guess randomly. The authors used a clever trick called Non-negative Matrix Factorization (NMF), which is like finding the hidden patterns in the puzzle to guess what the missing pieces should look like. To make this guessing even sharper, they added a "White Shark Optimization" (WSO) algorithm. Think of this as a hungry, super-smart shark that swims through the data, hunting down the best possible way to fill in the gaps, ensuring the puzzle is complete before they even start solving it.

But a complete puzzle isn't enough; the picture needs to be fair. The team realized that neighborhoods aren't just different in how many people want rides; they are different in their struggles. Some areas have high unemployment, others have crowded housing, and some have lower incomes. The authors invented a new way to measure this called Relative Hardship Proximity (RHP). Instead of just saying "this neighborhood is poor," RHP looks at the pattern of struggles. It's like realizing that two different families might have very different incomes, but if they both struggle with the same mix of high rent, long commutes, and lack of jobs, they are "relatively similar" in their hardship. The model uses this to group neighborhoods together. If the model makes a mistake in one neighborhood, it checks its "friends" (the similar neighborhoods) to see if it made the same mistake there. If it did, the model gets a gentle "scolding" (a mathematical penalty) to try harder to be fair to everyone, not just the easy-to-predict areas.

The results of this experiment, tested on a massive dataset from Chicago, are quite promising. The team found that their hybrid approach, which mixes the shark-like data fixing with the fairness-checking, achieved a very accurate prediction score. Specifically, they reached a Root Mean Square Error (RMSE) of 5.1 and a Mean Absolute Error (MAE) of 3.8. To put that in perspective, when they compared their method to other popular models like ARIMA or standard neural networks, their "shark-and-fairness" model was the clear winner, beating them all.

Perhaps the most exciting finding is the cost of being fair. Usually, when you force a computer to be fair, it gets a little less accurate overall. The authors measured this "Price of Fairness" and found it was incredibly low—only about 2%. This means they got a much more equitable system, where people in struggling neighborhoods got better service predictions, without sacrificing much accuracy for the city as a whole. In fact, the model actually improved predictions for the most disadvantaged areas the most, reducing their errors significantly while only slightly increasing errors in the already well-served areas. It's a bit like a teacher who decides to spend a little extra time helping the students who are struggling the most; the class average might drop a tiny fraction, but no student gets left behind.

In the end, this paper suggests that we don't have to choose between a smart city and a fair city. By using district profiles to understand local needs and a special "fairness penalty" to keep the model honest, we can create transportation systems that work for everyone. The study shows that with the right tools, we can fill in the missing data, connect the dots between similar neighborhoods, and ensure that when you hail a taxi, the system is ready for you, no matter where you live.

Technical Summary: Spatial Fairness in Taxi Demand Prediction

Problem Statement
Accurate taxi demand forecasting is critical for efficient urban transportation management, yet existing models often overlook the equitable distribution of service quality across different socioeconomic regions. In cities like Chicago, disparities in transportation availability can exacerbate existing inequalities, leading to marginalized communities facing longer wait times and limited access to essential services. Furthermore, real-world datasets often suffer from significant missing data (e.g., missing pickup community areas), which hinders the training of robust predictive models. This research addresses the dual challenge of improving prediction accuracy in the presence of missing data while explicitly mitigating algorithmic bias to ensure fair service allocation across demographically diverse urban districts.

Methodology
The proposed framework is a hybrid approach comprising three primary stages: data imputation, spatial dependency modeling with fairness awareness, and multi-resolution prediction refinement.

Data Imputation via Hybrid NMF-WSO:
To address missing demand data, the authors reconstruct the demand matrix using a combination of Non-negative Matrix Factorization (NMF) and White Shark Optimization (WSO).
- District Profiles: Instead of relying on arbitrary initialization, the model utilizes district-specific profiles (average trip distance, duration, and price). These features are normalized and weighted based on their Pearson correlation with observed demand to generate informed initial values for the NMF matrices.
- Optimization: The WSO algorithm, a nature-inspired metaheuristic, is employed to refine the factorization of matrices $W$ and $H$ , optimizing the reconstruction of latent spatial-temporal structures obscured by missing data.
Spatial Dependency Modeling and Fairness Simulation:
The framework models spatial dependencies by identifying similar districts to inform predictions for a target district.
- Relative Hardship Proximity (RHP): A novel metric is introduced to assess similarity between community areas based on their relative socioeconomic challenges rather than absolute hardship levels. RHP is calculated as the cosine similarity between the deviation vectors of demographic features (e.g., poverty rate, unemployment, education level) from the city-wide centroid. This allows the grouping of districts facing structurally similar challenges.
- Combined Similarity: A similarity score is computed by weighting both demand bin proximity and demographic similarity (via RHP). The top $k$ most similar districts are selected to supplement the target district's historical time series.
- LSTM Architecture: A Long Short-Term Memory (LSTM) network processes the combined time series of the target district and its top similar neighbors to forecast future demand.
Fairness-Aware Regularization:
To enforce equity, a spatially-aware regularization term is integrated into the loss function ( $L_{total} = L_{base} + \lambda \cdot L_{fairness}$ ).
- Local Fairness: This term penalizes disparities in prediction errors between demographically similar districts (as defined by RHP). It minimizes the difference between the local fairness metric $F(d)$ of two districts, where $F(d)$ is defined as the difference between the normalized hardship index and the normalized Root Mean Square Error (RMSE) for that specific district.
- Global Fairness: A secondary term ensures that the mean error across predefined demographic groups remains consistent.
- Objective: The regularization guides the model to reduce prediction inconsistencies in high-hardship areas, even if it results in a marginal increase in overall error.
Multi-Resolution Prediction Refinement:
To enhance accuracy, the system employs a two-tiered approach. An hourly LSTM model and a 15-minute LSTM model are trained. The four consecutive 15-minute predictions are summed, and this sum is combined with the original 1-hour prediction as input features for a Gradient Boosting Regressor (GBR), which refines the final demand forecast.

Key Contributions

District-Level Profile Integration: The study integrates district-specific features (trip distance, duration, price) with linear regression and data normalization to initialize NMF, providing a more accurate representation of demand dynamics than conventional random initialization.
Enhanced Latent Factor Extraction: The application of White Shark Optimization to NMF improves the model's ability to capture complex demand patterns and correlations, leading to better data imputation.
Relative Hardship Proximity (RHP): The introduction of RHP allows for the simulation of demand relationships based on relative socioeconomic challenges, enabling a fairness-aware grouping of districts that transcends simple absolute hardship metrics.
Fairness-Aware Regularization: The framework explicitly incorporates a regularization mechanism that penalizes unequal error distributions across similar spatial units, promoting balanced performance without sacrificing significant predictive power.

Results
Evaluated on a large-scale Chicago taxi dataset (May–November 2013), the proposed framework achieved a Root Mean Square Error (RMSE) of 5.1 and a Mean Absolute Error (MAE) of 3.8, outperforming benchmark models including ARIMA, MLP, GRU, T-GCN, and ST-GAT.

Imputation: The hybrid NMF-WSO approach successfully reconstructed missing data, with the hourly model achieving an RMSE of 6.9 on held-out test data used for imputation validation.
Fairness Impact: The introduction of fairness regularization ( $\lambda = 0.48$ ) significantly reduced the fairness gap. Specifically, the RMSE for high-hardship (High RHP) districts decreased from 6.2 to 5.4, while low-hardship districts saw a slight increase (4.6 to 4.9). The maximum fairness gap across groups was reduced from 1.2 (without regularization) to 0.5.
Price of Fairness (PoF): The improvement in equity came at a marginal cost to overall accuracy. The PoF was calculated at approximately 2% (increasing overall error from 4.9 to 5.0), demonstrating that substantial fairness gains can be achieved with minimal trade-off in predictive performance.
Statistical Significance: T-tests confirmed that the model's predictions did not exhibit statistically significant deviations from ground truth across different RHP groups, indicating consistent performance.

Significance
The paper argues that incorporating structured fairness constraints into demand forecasting models is both ethically necessary and technically feasible. By prioritizing fairness, the model prevents algorithmic bias that might favor affluent neighborhoods, thereby fostering greater social equity in urban mobility. The findings suggest that "fairness-aware" AI systems can enhance the equitable distribution of transportation resources—reducing wait times and service gaps in vulnerable communities—while maintaining high levels of predictive accuracy. The approach offers a scalable solution for urban planners to address systemic inequities in transportation service provision.

Technical Summary: Spatial Fairness in Taxi Demand Prediction

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