Laurens Arp | Searcharxiv

arXiv2021

A Markov Reward Process-Based Approach to Spatial Interpolation

The interpolation of spatial data can be of tremendous value in various applications, such as forecasting weather from only a few measurements of meteorological or remote sensing data. Existing methods for spatial interpolation, such as variants of kriging and spatial autoregressive models, tend to suffer from at least one of the following limitations: (a) the assumption of stationarity, (b) the assumption of isotropy, and (c) the trade-off between modelling local or global spatial interaction. Addressing these issues in this work, we propose the use of Markov reward processes (MRPs) as a spatial interpolation method, and we introduce three variants thereof: (i) a basic static discount MRP (SD-MRP), (ii) an accurate but mostly theoretical optimised MRP (O-MRP), and (iii) a transferable weight prediction MRP (WP-MRP). All variants of MRP interpolation operate locally, while also implicitly accounting for global spatial relationships in the entire system through recursion. Additionally, O-MRP and WP-MRP no longer assume stationarity and are robust to anisotropy. We evaluated our proposed methods by comparing the mean absolute errors of their interpolated grid cells to those of 7 common baselines, selected from models based on spatial autocorrelation, (spatial) regression, and deep learning. We performed detailed evaluations on two publicly available datasets (local GDP values, and COVID-19 patient trajectory data). The results from these experiments clearly show the competitive advantage of MRP interpolation, which achieved significantly lower errors than the existing methods in 23 out of 40 experimental conditions, or 35 out of 40 when including O-MRP.

cs.AI↗

arXiv2020

Metaheuristic macro scale traffic flow optimisation from urban movement data

How can urban movement data be exploited in order to improve the flow of traffic within a city? Movement data provides valuable information about routes and specific roads that people are likely to drive on. This allows us to pinpoint roads that occur in many routes and are thus sensitive to congestion. Redistributing some of the traffic to avoid unnecessary use of these roads could be a key factor in improving traffic flow. Many proposed approaches to combat congestion are either static or do not incorporate any movement data. In this work, we present a method to redistribute traffic through the introduction of externally imposed variable costs to each road segment, assuming that all drivers seek to drive the cheapest route. We use a metaheuristic optimisation approach to minimise total travel times by optimising a set of road-specific variable cost parameters, which are used as input for an objective function based on traffic flow theory. The optimisation scenario for the city centre of Tokyo considered in this paper was defined using public spatial road network data, and movement data acquired from Foursquare. Experimental results show that our proposed scenario has the potential to achieve a 62.6\% improvement of total travel time in Tokyo compared to that of a currently operational road network configuration, with no imposed variable costs.

physics.soc-ph↗