Embedding road networks and travel time into distance metrics for urban modelling

Urban environments are restricted by various physical, regulatory and customary barriers such as buildings, one-way systems and pedestrian crossings. These features create challenges for predictive modelling in urban space, as most proximity-based models rely on Euclidean (straight line) distance metrics which, given restrictions within the urban landscape, do not fully capture spatial urban processes. Here, we argue that road distance and travel time provide effective alternatives, and we develop a new low-dimensional Euclidean distance metric based on these distances using an isomap approach. The purpose of this is to produce a valid covariance matrix for Kriging. Our primary methodological contribution is the derivation of two symmetric dissimilarity matrices ((B ⁺ and B2 ⁺ ), with which it is possible to compute low-dimensional Euclidean metrics for the production of a positive definite covariance matrix with commonly utilised kernels. This new method is implemented into a Kriging predictor to estimate house prices on 3,669 properties in Coventry, UK. We find that a  metric estimating a combination of road distance and travel time, in both R ² and R ³ , produces a superior house price predictor compared with alternative state-of-the-art methods, that is, a standard Euclidean metric in R ^N and a non-restricted road distance metric in  R ² and R ³ . F.