# Recurrent Multi-Graph Neural Networks for Travel Cost Prediction

arXiv: https://arxiv.org/abs/1811.05157 · HTML: https://mlsanity.com/paper/1811.05157/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Nov 2018.

## Built on by (most cited first, 2 of 2)

- [Graph Neural Network for Traffic Forecasting: A Survey](https://mlsanity.com/paper/2101.11174/) (2021)
- [AirRadar: Inferring Nationwide Air Quality in China with Deep Neural Networks](https://mlsanity.com/paper/2501.13141/) (2025)

## Abstract (arXiv)

Origin-destination (OD) matrices are often used in urban planning, where a city is partitioned into regions and an element (i, j) in an OD matrix records the cost (e.g., travel time, fuel consumption, or travel speed) from region i to region j. In this paper, we partition a day into multiple intervals, e.g., 96 15-min intervals and each interval is associated with an OD matrix which represents the costs in the interval; and we consider sparse and stochastic OD matrices, where the elements represent stochastic but not deterministic costs and some elements are missing due to lack of data between two regions. We solve the sparse, stochastic OD matrix forecasting problem. Given a sequence of historical OD matrices that are sparse, we aim at predicting future OD matrices with no empty elements. We propose a generic learning framework to solve the problem by dealing with sparse matrices via matrix factorization and two graph convolutional neural networks and capturing temporal dynamics via recurrent neural network. Empirical studies using two taxi datasets from different countries verify the effectiveness of the proposed framework.