Given the common problem of missing data in real-world applications from various fields, such as remote sensing, ecology and meteorology, the interpolation of missing spatial and spatio-temporal data can be of tremendous value. Existing methods for spatial interpolation, most notably Gaussian processes and spatial autoregressive models, tend to suffer from (a) a trade-off between modelling local or global spatial interaction, (b) the assumption there is only one possible path between two points, and (c) the assumption of homogeneity of intermediate locations between points. Addressing these issues, we propose a value propagation-based spatial interpolation method called VPint, inspired by Markov reward processes (MRPs), and introduce two variants thereof: (i) a static discount (SD-MRP) and (ii) a data-driven weight prediction (WP-MRP) variant. Both these interpolation variants operate locally, while implicitly accounting for global spatial relationships in the entire system through recursion. We evaluated our proposed methods by comparing the mean absolute error, root mean squared error, peak signal-to-noise ratio and structural similarity of interpolated grid cells to those of 8 common baselines. Our analysis involved detailed experiments on a synthetic and two real-world datasets, as well as experiments on convergence and scalability. Empirical results demonstrate the competitive advantage of VPint on randomly missing data, where it performed better than baselines in terms of mean absolute error and structural similarity, as well as spatially clustered missing data, where it performed best on 2 out of 3 datasets.
Keywords: Data imputation; Image inpainting; Missing data; Spatial interpolation; Spatio-temporal interpolation.
© The Author(s) 2022.