# Grids versus Graphs: Partitioning Space for Improved Taxi Demand-Supply Forecasts

## TL;DR

This paper compares spatial partitioning methods for taxi demand-supply forecasting, proposing a GraphLSTM approach for variable-sized Voronoi partitions and demonstrating its effectiveness against ConvLSTM with ensemble techniques.

## Contribution

Introduces GraphLSTM for variable-sized Voronoi partitions and combines it with ConvLSTM using ensemble learning for improved forecasting performance.

## Key findings

- GraphLSTM performs competitively with ConvLSTM at lower computational cost.
- Voronoi tessellation can be effectively modeled using GraphLSTM.
- Ensemble of GraphLSTM and ConvLSTM yields superior forecasting accuracy.

## Abstract

Accurate taxi demand-supply forecasting is a challenging application of ITS (Intelligent Transportation Systems), due to the complex spatial and temporal patterns. We investigate the impact of different spatial partitioning techniques on the prediction performance of an LSTM (Long Short-Term Memory) network, in the context of taxi demand-supply forecasting. We consider two tessellation schemes: (i) the variable-sized Voronoi tessellation, and (ii) the fixed-sized Geohash tessellation. While the widely employed ConvLSTM (Convolutional LSTM) can model fixed-sized Geohash partitions, the standard convolutional filters cannot be applied on the variable-sized Voronoi partitions. To explore the Voronoi tessellation scheme, we propose the use of GraphLSTM (Graph-based LSTM), by representing the Voronoi spatial partitions as nodes on an arbitrarily structured graph. The GraphLSTM offers competitive performance against ConvLSTM, at lower computational complexity, across three real-world large-scale taxi demand-supply data sets, with different performance metrics. To ensure superior performance across diverse settings, a HEDGE based ensemble learning algorithm is applied over the ConvLSTM and the GraphLSTM networks.