Road and travel time cross-validation for urban modelling

ABSTRACT

The physical and social processes in urban systems are inherently spatial and hence data describing them contain spatial autocorrelation (a proximity-based interdependency on a variable) that need to be accounted for. Standard k-fold cross-validation (KCV) techniques that attempt to measure the generalisation performance of machine learning and statistical algorithms are inappropriate in this setting due to their inherent i.i.d assumption, which is violated by spatial dependency. As such, more appropriate validation methods have been considered, notably blocking and spatial k-fold cross-validation (SKCV). However, the physical barriers and complex network structures which make up a city’s landscape mean that these methods are also inappropriate, largely because the travel patterns (and hence Spatial Autocorrelation (SAC)) in most urban spaces are rarely Euclidean in nature. To overcome this problem, we propose a new road distance and travel time k-fold cross-validation method, RT-KCV. We show how this outperforms the prior art in providing better estimates of the true generalisation performance to unseen data.

KEYWORDS:

• Road distance
• travel time
• cross-validation
• urban science
• GIS

Acknowledgments

We would like to thank the Engineering and Physical Sciences Research Council (EPSRC) Centre for Doctoral Training in Urban Science (EP/L016400/1) and the Alan Turing Institute (EP/N510129/1) grants. In addition, we are supported by the Lloyds Register Foundation programme on Data Centric Engineering. Finally, our gratitude goes to all the open source mapping contributors.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Engineering and Physical Sciences Research Council [EP/ L016400/ 1,EP/N510129/1];Lloyd’s Register Foundation programme on Data Centric Engineering;

Notes on contributors

Henry Crosby

Henry Crosby completed his PhD as a member of  the Centre for Doctoral Training in Urban Science in the Warwick Institute for the Science of Cities. He received his BSc (Hons) degree in Business and Mathematics from Aston University, United Kingdom, and his MSc in data analysis at the University of Warwick.

Theodoros Damoulas

Theodoros Damoulas an associate professor in Data Science with a joint appointment in the Department of Statistics and Department of Computer Science at the University of Warwick. He is also a Turing Fellow of the Alan Turing Institute and affiliated with NYU as a visiting exchange professor at the Center for Urban Science and Progress (CUSP). Previously, he was a research associate at Cornell University. His studies were undertaken at the University of Edinburgh, Manchester and Paul Scherrer Institut, Switzerland.

Stephen A. Jarvis

Stephen A. Jarvis studied at London, Oxford and Durham Universities before taking his first lectureship at the Oxford University Computing Laboratory. After a short secondment to Microsoft Research in Cambridge, he joined the University of Warwick, rising to professor in 2009. He acted as Director of Research from 2008 to 2013 at which point he was appointed chair of department. Professor Jarvis is a visiting exchange professor at New York University and is engaged with the Alan Turing Institute. He is presently deputy pro vice chancellor (research) at the University of Warwick.