A Two-Step Method for Missing Spatio-Temporal Data Reconstruction

Abstract

Abstract:Missing data reconstruction is a critical step in the analysis and mining of spatio-temporal data; however, few studies comprehensively consider missing data patterns, sample selection and spatio-temporal relationships. As a result, traditional methods often fail to obtain satisfactory accuracy or address high levels of complexity. To combat these problems, this study developed an effective two-step method for spatio-temporal missing data reconstruction (ST-2SMR). This approach includes a coarse-grained interpolation method for considering missing patterns, which can successfully eliminate the influence of continuous missing data on the overall results. Based on the results of coarse-grained interpolation, a dynamic sliding window selection algorithm was implemented to determine the most relevant sample data for fine-grained interpolation, considering both spatial and temporal heterogeneity. Finally, spatio-temporal interpolation results were integrated by using a neural network model. We validated our approach using Beijing air quality data and found that the proposed method outperforms existing solutions in term of estimation accuracy and reconstruction rate.

Spatiotemporal Differences of COVID-19 Infection Among Healthcare Workers and Patients in China From January to March 2020

“…The Pearson correlation coefficient [30] was calculated to quantitatively measure the spatiotemporal correlation between healthcare worker infections and patient infections, i.e., the difference in space and time between healthcare worker infections and patient infections. As shown in Figure 5 , the spatial correlation was obtained by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$t_{3}^{h}$ \end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$t_{3}^{p}$ \end{document} , and the temporal correlation was obtained by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$s_{3}^{h}$ \end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$s_{3}^{p}$ \end{document} [31] . The temporal and spatial correlation coefficients of the two series were calculated using Equations (1) and (2) , respectively: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}\begin{align*} r_{temporal} = \frac {{{\mathrm{Cov(}}s_{i}^{p} {\mathrm{,}}s_{i}^{h} {\mathrm{)}}}}{{\sqrt {\rm {D}(s_{i}^{p}) } \sqrt {\rm {D}(s_{i}^{h})} }} \tag{1}\\ r_{spatial} = \frac {{{\mathrm{Cov(}}t_{i}^{p} {\mathrm{,}}t_{i}^{h} {\mathrm{)}}}}{{\sqrt {\rm {D}(t_{i}^{p})} \sqrt {\rm {D}(t_{i}^{h})} }}\tag{2}\end{align*} \end{document} where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$\rm {Cov}(X,Y)$ \end{document} is the covariance of random variables \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$X$ \end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$Y$ \end{document} , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgre...…”

“…The Pearson correlation coefficient [30] was calculated to quantitatively measure the spatiotemporal correlation between healthcare worker infections and patient infections, i.e., the difference in space and time between healthcare worker infections and patient infections. As shown in Figure 5, the spatial correlation was obtained by t h 3 and t p 3 , and the temporal correlation was obtained by s h 3 and s p 3 [31]. The temporal and spatial correlation coefficients of the two series were calculated using Equations (1) and (2), respectively:…”

A Spatiotemporal Multi-View-Based Learning Method for Short-Term Traffic Forecasting

“…Due to equipment failure and other factors, some data were missing from the original traffic-speed data sets. Considering the spatiotemporal characteristics of traffic data, we used the existing spatiotemporal interpolation algorithm to fill in the missing data in order to better reconstruct the original traffic conditions [42]. The basic principle is to consider the missing data pattern in the interpolation process and use coarse-grained interpolation to obtain partial reconstruction results in order to eliminate the effect of missing continuous block data on the subsequent interpolation process.…”

Refining Sparse Cell-ID Trajectory of Public Service Vehicles by Spatiotemporal Modelling

“…e spatial resolution of cell-id trajectory data depends on the service radius of each BTS, which varies in different areas, e.g., of hundred meters in metropolitan cities, and several kilometers in rural areas [5]. Meanwhile, the records of a cell-id trajectory are collected in a relatively long-time interval, which inevitably results in the problem of trajectory discontinuity or sparsity [6][7][8][9][10]. erefore, due to the inconformity between the spatiotemporal sparsity of the cell-id trajectory data and the requirement on fine-scale footprints, the refinement of cell-id trajectories becomes a research hotspot due to its extensive application prospects.…”