An ensemble approach to space–time interpolation

The availability of spatial data on an unprecedented scale as well as advancements in analytical and visualization techniques gives researchers the opportunity to study complex problems over large urban and regional areas. Nevertheless, few individual data sets exist that provide both the requisite spatial and/or temporal observational frequency to truly facilitate detailed investigations. Some data are collected frequently over time but only at a few geographic locations (e.g., weather stations). Similarly, other data are collected with a high level of spatial resolution but not at regular or frequent time intervals (e.g., satellite data). The purpose of this article is to present an interpolation approach that leverages the relative temporal richness of one data set with the relative spatial richness of another to fill in the gaps. Because different interpolation techniques are more appropriate than others for specific types of data, we propose a space–time interpolation approach whereby two interpolation methods – one for the temporal and one for the spatial dimension – are used in tandem to increase the accuracy results.

We call our ensemble approach the space–time interpolation environment (STIE). The primary steps within this environment include a spatial interpolation processor, a temporal interpolation processor, and a calibration processor, which enforces phenomenon-related behavioral constraints. The specific interpolation techniques used within the STIE can be chosen on the basis of suitability for the data and application at hand. In this article, we first describe STIE conceptually including the data input requirements, output structure, details of the primary steps, and the mechanism for coordinating the data within those steps. We then describe a case study focusing on urban land cover in Phoenix, Arizona, using our working implementation. Our empirical results show that our approach increased the accuracy for estimating urban land cover better than a single interpolation technique.     

Geostatistical space–time mapping of house prices using Bayesian maximum entropy

Mapping spatial processes at a small scale is a challenge when observed data are not abundant. The article examines the residential housing market in Fort Worth, Texas, and builds price indices at the inter- and intra-neighborhood levels. To accomplish our objectives, we initially model price variability in the joint space–time continuum. We then use geostatistics to predict and map monthly housing prices across the area of interest over a period of 4 years. For this analysis, we introduce the Bayesian maximum entropy (BME) method into real estate research. We use BME because it rigorously integrates uncertain or secondary soft data, which are needed to build the price indices. The soft data in our analysis are property tax values, which are plentiful, publicly available, and highly correlated with transaction prices. The results demonstrate how the use of the soft data provides the ability to map house prices within a small areal unit such as a subdivision or neighborhood.     

Choice set formation with multiple flexible activities under space–time constraints

In classical time geography, an individual travel path is composed of a chain of visits, with each visit being a flexible activity between two fixed activities at two known stations. In reality, individuals tend to carry out trips with much variation and complexity, with multipurpose trips being a prominent and pervasive phenomenon. There is limited research to date on multipurpose trips in time-geographic analysis by geographic information system (GIS) scientists, or more specifically, multiple flexible activities between two fixed stations. To fill this gap, this article proposes four models for identifying the choice set with multiple flexible activities under space–time constraints. The models are derived through set-theoretic formalism based on the concept of trip chaining. The structure of the four models establishes a theoretical framework for conceptualizing trip-chaining behaviour with respect to the fixity of activities and the number of fixed stations as destinations or origins. They provide fundamental and rigorous apparatus for studying complex individual activity–travel patterns in many applied contexts when multipurpose trips are involved. This article also describes implementation of the models with a real transportation network as a way of validation.     

Modeling of space–time infectious disease spread under conditions of uncertainty

A theoretical model for the spread of infectious diseases in a composite space–time domain is developed. The model has a general form that enables it to account for the basic mechanisms of disease distribution and to incorporate the considerable multisourced uncertainty (caused by physiographic features, disease variability, meteorological conditions, etc.). Starting from the general model formulation regarding the specification of transmission and recovery rates, as well as the population migration dynamics, several subsequent assumptions are introduced that simplify analytical tractability and practical implementation. In particular, linearization involving a deterministic functional representation for the average evolution of the fraction of susceptible individuals allows the formulation of an extended Kalman filter approach for estimation based on the time series observed at a finite set of locations. Different aspects of interest derived from the epidemic space–time model proposed, as well as the performance of the extended Kalman filter procedure, are illustrated through simulations.     

Uncertainty analysis of space–time prisms based on the moment-design method

Space–time prism (STP) is an important concept for the modeling of object movements in space and time. An STP can be conceptualized as the result of the potential path of a moving object revolving around in the three-dimensional space. Though the concept has found applications in time geography, research on the analysis and propagation of uncertainty in STPs, particularly under high degree of nonlinearity, is scanty. Based on the efficiency and effectiveness of the moment-design (M-D) method, this paper proposes an approach to deal with nonlinear error propagation problems in the potential path areas (PPAs) of STPs and their intersections. Propagation of errors to the PPA and its boundary, and to the intersection of two PPAs is investigated. Performance of the proposed method is evaluated via a series of experimental studies. In comparison with the Monte Carlo method and the implicit function method, simulation results show the advantages of the M-D method in the analysis of error propagation in STPs.     

Modelling potential movement in constrained travel environments using rough space–time prisms

The widespread adoption of location-aware technologies (LATs) has afforded analysts new opportunities for efficiently collecting trajectory data of moving individuals. These technologies enable measuring trajectories as a finite sample set of time-stamped locations. The uncertainty related to both finite sampling and measurement errors makes it often difficult to reconstruct and represent a trajectory followed by an individual in space–time. Time geography offers an interesting framework to deal with the potential path of an individual in between two sample locations. Although this potential path may be easily delineated for travels along networks, this will be less straightforward for more nonnetwork-constrained environments. Current models, however, have mostly concentrated on network environments on the one hand and do not account for the spatiotemporal uncertainties of input data on the other hand. This article simultaneously addresses both issues by developing a novel methodology to capture potential movement between uncertain space–time points in obstacle-constrained travel environments.     

Modeling uncertainty of moving objects on road networks via space–time prisms

Moving objects produce trajectories, which are typically observed in a finite sample of time‐stamped locations. Between sample points, we are uncertain about the moving objects's location. When we assume extra information about an object, for instance, a (possibly location‐dependent) speed limit, we can use space–time prisms to model the uncertainty of an object's location.

Until now, space–time prisms have been studied for unconstrained movement in the 2D plane. In this paper, we study space–time prisms for objects that are constrained to travel on a road network. Movement on a road network can be viewed as essentially one‐dimensional. We describe the geometry of a space–time prism on a road network and give an algorithm to compute and visualize space–time prisms. For experiments and illustration, we have implemented this algorithm in MATHEMATICA.

Furthermore, we study the alibi query, which asks whether two moving objects could have possibly met or not. This comes down to deciding if the chains of space–time prisms produced by these moving objects intersect. We give an efficient algorithm to answer the alibi query for moving objects on a road network. This algorithm also determines where and when two moving objects may have met.     

A GIS toolkit for measuring and mapping space–time accessibility from a place-based perspective

This article introduces a novel geographical information system toolkit for measuring and mapping the accessibility of individuals to services. The toolkit contributes to earlier implementations by combining aspects of both place-based and person-based accessibility measures. To this end, place-based accessibility measures are derived from a person-based framework by considering space–time prisms that are centred at service facilities rather than individual anchor points. The implementation is also innovative by explicitly accounting for the opening hours of service delivery in its accessibility measurement. In addition, the toolkit is aimed to be user-friendly and to generate insightful and comprehensible results for non-technically oriented users, which is illustrated in a brief case study about library accessibility in Ghent (Belgium).     

A network Kernel Density Estimation for linear features in space–time analysis of big trace data

ABSTRACT

Kernel Density Estimation (KDE) is an important approach to analyse spatial distribution of point features and linear features over 2-D planar space. Some network-based KDE methods have been developed in recent years, which focus on estimating density distribution of point events over 1-D network space. However, the existing KDE methods are not appropriate for analysing the distribution characteristics of certain kind of features or events, such as traffic jams, queue at intersections and taxi carrying passenger events. These events occur and distribute in 1-D road network space, and present a continuous linear distribution along network. This paper presents a novel Network Kernel Density Estimation method for Linear features (NKDE-L) to analyse the space–time distribution characteristics of linear features over 1-D network space. We first analyse the density distribution of each linear feature along networks, then estimate the density distribution for the whole network space in terms of the network distance and network topology. In the case study, we apply the NKDE-L to analyse the space–time dynamics of taxis’ pick-up events, with real road network and taxi trace data in Wuhan. Taxis’ pick-up events are defined and extracted as linear events (LE) in this paper. We first conduct a space–time statistics of pick-up LE in different temporal granularities. Then we analyse the space–time density distribution of the pick-up events in the road network using the NKDE-L, and uncover some dynamic patterns of people’s activities and traffic condition. In addition, we compare the NKDE-L with quadrat method and planar KDE. The comparison results prove the advantages of the NKDE-L in analysing spatial distribution patterns of linear features in network space.     

An analytic solution to the alibi query in the space–time prisms model for moving object data

Moving objects produce trajectories, which are stored in databases by means of finite samples of time-stamped locations. When speed limitations in these sample points are also known, space–time prisms (also called beads) (Pfoser and Jensen 1999 Pfoser, D. and Jensen, C.S. 1999. “Capturing the uncertainty of moving-object representations”. In Advances in spatial databases (SSD’99), Hong Kong, China, July 20–23, 1999, Vol. 1651, 111–132. Lecture notes in Computer Science.  [Google Scholar], Egenhofer 2003 Egenhofer, M. 2003. “Approximation of geopatial lifelines”. In SpadaGIS, workshop on spatial data and geographic information systsems, 4SpaDaGIS–Workshop on Spatial Data and Geographic Information Systems, Milano, Italy, March 2003. University of Genova.  [Google Scholar], Miller 2005 Miller, H. 2005. A measurement theory for time geography. Geographical Analysis, 37(1): 17–45. [Crossref], [Web of Science ®] , [Google Scholar]) can be used to model the uncertainty about an object's location in between sample points. In this setting, a query of particular interest that has been studied in the literature of geographic information systems (GIS) is the alibi query. This boolean query asks whether two moving objects could have physically met. This adds up to deciding whether the chains of space–time prisms (also called necklaces of beads) of these objects intersect. This problem can be reduced to deciding whether two space–time prisms intersect.

The alibi query can be seen as a constraint database query. In the constraint database model, spatial and spatiotemporal data are stored by boolean combinations of polynomial equalities and inequalities over the real numbers. The relational calculus augmented with polynomial constraints is the standard first-order query language for constraint databases and the alibi query can be expressed in it. The evaluation of the alibi query in the constraint database model relies on the elimination of a block of three exªistential quantifiers. Implementations of general purpose elimination algorithms, such as those provided by QEPCAD, Redlog, and Mathematica, are, for practical purposes, too slow in answering the alibi query for two specific space–time prisms. These software packages completely fail to answer the alibi query in the parametric case (i.e., when it is formulated in terms of parameters representing the sample points and speed constraints).

The main contribution of this article is an analytical solution to the parametric alibi query, which can be used to answer the alibi query on two specific space–time prisms in constant time (a matter of milliseconds in our implementation). It solves the alibi query for chains of space–time prisms in time proportional to the sum of the lengths of the chains. To back this claim up, we implemented our method in Mathematica alongside the traditional quantifier elimination method. The solutions we propose are based on the geometric argumentation and they illustrate the fact that some practical problems require creative solutions, where at least in theory, existing systems could provide a solution.     

Living austerity urbanism: space–time expansion and deepening socio-spatial inequalities for disadvantaged urban youth in Ireland

After the 2008 financial crisis, Ireland implemented a severe austerity program which drastically reshaped the opportunities and constraints experienced by youth living in disadvantaged urban neighborhoods. Rising unemployment, reduced social welfare, and funding cuts for support organizations limited the opportunities of urban life for disadvantaged youth. This article uses the experience of austerity urbanism of young adults from Ballymun (Dublin) and Knocknaheeny (Cork), both among the most disadvantaged neighborhoods of their cities, to argue that austerity, through time-space expansion, removes services, facilities and opportunities from deprived urban neighborhoods, thus reinforcing and intensifying socio-spatial inequalities. In an effort to bring State finances under control and to revitalize the economy the whole urban fabric, and the urban population, is managed for the purpose of economic recovery. Urban life becomes restricted as disadvantaged urban youth becomes socially and spatially excluded from vital urban opportunities and amenities.     

Towards a process-based biogeography of reindeer—scaling space,time, and organizational levels of space use

Due to increasing anthropogenic habitat alteration, fragmentation, and loss, the analysis of how, when, and why animals select particular habitats has become a central issue in ecology and biogeography. Animals adapt to spatiotemporal variability in resources either by tracking these resources or by plasticity in behavior to cover their needs, leading to three important implications: movement, temporal variation, and individual trade-offs leading to intra-species variability, all of which are directly linked to the use of space by animals. Based on GPS-tracking of domesticated reindeer in southern Norway, the authors addressed these issues by analyzing movement patterns and space use simultaneously across different temporal and organizational scales. Emerging information about the space use by reindeer was found explicitly linked to scaling relations, reflecting the matter of scale as having important functional implications rather than solely being a technical question of extent and resolution. Adding movement into the analysis of space use further advances the necessary functional perspective on space use. The authors conclude that scaling not only space but also time and the organizational level, in combination with accounting for different behavioral states, brings biogeography closer to a process-based view, rather than solely pattern-based view.     

Everyday space–time geographies: using mobile phone-based sensor data to monitor urban activity in Harbin,Paris, and Tallinn

This paper proposes a methodology for using mobile telephone-based sensor data for detecting spatial and temporal differences in everyday activities in cities. Mobile telephone-based sensor data has great applicability in developing urban monitoring tools and smart city solutions. The paper outlines methods for delineating indicator points of temporal events referenced as ‘midnight’, ‘morning start’, ‘midday’, and ‘duration of day’, which represent the mobile telephone usage of residents (what we call social time) rather than solar or standard time. Density maps by time quartiles were also utilized to test the versatility of this methodology and to analyze the spatial differences in cities. The methodology was tested with data from cities of Harbin (China), Paris (France), and Tallinn (Estonia). Results show that the developed methods have potential for measuring the distribution of temporal activities in cities and monitoring urban changes with georeferenced mobile phone data.     

The role of visualisation in the choice of stationary non-separable space–time covariance functions: an application to air pollution data

Modelling spatio-temporal dependencies resulting from dynamic processes that evolve in both space and time is essential in many scientific fields. Spatio-temporal Kriging is one of the space–time procedures, which has progressed the most over the last few years. Kriging predictions strongly depend on the covariance function associated with the stochastic process under study. Therefore, the choice of such a covariance function, which is usually based on empirical covariance, is a core aspect in the prediction procedure. As the empirical covariance is not necessarily a permissible covariance function, it is necessary to fit a valid covariance model. Due to the complexity of these valid models in the spatio-temporal case, visualising them is of great help, at least when selecting the set of candidate models to represent the spatio-temporal dependencies suggested by the empirical covariogram. We focus on the visualisation of the most interesting stationary non-separable covariance functions and how they change as their main parameters take different values. We wrote a specialised code for visualisation purposes. In order to illustrate the usefulness of visualisation when choosing the appropriate non-separable spatio-temporal covariance model, we focus on an important pollution problem, namely the levels of carbon monoxide, in the city of Madrid, Spain.     

Space–time interaction of residential burglaries in Wuhan,China

Borrowing methods from epidemiology, studies of spatiotemporal regularities of crime have been booming in various industrialized countries. However, few such attempts are empirical studies using crime data in developing countries due to a lack of data availability. Utilizing a recent burglary dataset in Wuhan, the fourth largest city in China, current research applied the sequential kernel density estimation and the space–time K-function methods to analyze the spatiotemporal changes of hotspots of residential burglaries. The results show that, both spatial and spatiotemporal clustering exists. The hotspots were relatively stable over time. The space–time clustering, however, shows significant concentrations both in space and over time. In addition, analytic results show significant effects of distance decay in terms of occurrences of burglary incidents along the spatial and temporal dimensions. Moreover, findings from the research provide critical information on the space–time rhythm of crime, and therefore can be utilized in crime prevention practice. Finally, the implications of the findings and limitations are discussed.     

Spatio-temporal pattern changes of land space in Hengduan Mountains during 1990–2015

Hengduan Mountains offer land space for a variety of ecological services. However, the sustainable development and management of land space has been challenged by increased human activities in recent years. This paper performs the spatial pattern analysis of the quantitative and structural changes of various landscapes at different altitudes, and uses the land use data in 1990, 2000, 2010 and 2015 to reveal how various land patterns have changed. The results show that, within the production-living-ecological space schema, the ecological space dominates Hengduan Mountains, while the production and living space was mainly distributed in south region. During 1990–2015, the production-living-ecological spatial changes had been gradually accelerated and the regional differences had become more prominent. The agricultural production space had continuously decreased by 1132.31 km², and the industrial and mining production space had rapidly increased by 281.4 km² during 1990–2015. The living space had steadily increased, and the ecological space had increased with fluctuations. The land space pattern in Hengduan Mountains was greatly restricted by the terrain, such as altitude and slope. The implementations of China Western Development Strategy and the Returning Farmland to Forest Program had favorably promoted the changes of land spatial pattern in Hengduan Mountains.     

Space–time multiple regression model for grid-based population estimation in urban areas

We can collect, store, and analyze a huge amount of information about human mobility and social interaction activities due to the emergence of information and communication technologies and location-enabled mobile devices under cyber physical system frameworks. The high spatial resolution of population data on a multi-temporal scale is required by transport planners, human geographers, social scientists, and emergency management teams. In this study, we build a space-time multiple regression model to estimate grid-based (500 m × 500 m) spatial resolution at multi-temporal scale (30-min intervals) population data based on the space-time relationship among geospatially enabled person trip (PT) survey data and incorporate both mobile call (MC) and geotagged Twitter (GT) data. Since using geospatially enabled PT survey data as dependent variables enables us to acquire actual population amounts, which strongly depend on MCs and social interaction activities. Although many grids have a strong correlation between PT and MC/GT, some show fewer correlation results, especially where the grids have factories, schools, and workshops in which fewer MCs are found but a large population is presented. Although GT data are sparser than MCs, people from amusement and tourist areas can be detected by GT data. The space-time multiple regression model can also estimate the different amounts of populations based on human travel behavior that changes over space and time. According to accuracy assessments, the night-time estimated results, especially between 00:00 and 06:30, strongly correlate with national census data except in places where the grids have railway and subway stations.     

Space–time opportunities for multiple agents: a constraint‐based approach

Constraint‐based models and models constructing accessibility measures mainly focus on single agents having only one available transport mode. However, numerous cases exist where multiple agents or groups of individuals with different available transport modes want to participate in a joint activity at a certain location. The aim of this paper is to provide new insights into representing and reasoning about feasible space–time opportunities for multiple agents. Relying on concepts of time geography, we propose a conceptual framework in order to determine interaction spaces for groups of individuals. Besides availability of means of transport and the locations of each individual, minimum activity duration and opening hours of opportunities are taken into account. The reasoning about space and time is visualized in three dimensions using a hybrid (CAD/GIS) system.     

Space–time prism bounds of activity programs: a goal-directed search in multi-state supernetworks

Space–time prism (STP), which envelops the spatial and temporal opportunities for travel and activity participation within a time frame, is a fundamental concept in time geography. Despite many variants, STPs have been mostly modeled for one flexible activity between two anchor points. This study proposes a systemic approach to construct the STP bounds of activity programs that usually include various possible realizations of activity chains. To that effect, multi-state supernetworks are applied to represent the relevant path sets of multi-activity travel patterns. A goal-directed search method in multi-state supernetworks is developed to delineate the potential space–time path areas satisfying the space–time constraints. Particularly, the approximate lower and upper STP bounds are obtained by manipulating the goal-directed search procedure utilizing landmark-based triangular inequalities and spatial characteristics. The suggested approach can in an efficient fashion find the activity state dependent bounds of STP and potential path area. The formalism of goal-directed search through multi-state supernetworks addresses the fundamental shift from constructing STPs for single flexible activities to activity programs of flexible activity chains.