Jed A. Long

A review of quantitative methods for movement data

The collection, visualization, and analysis of movement data is at the forefront of geographic information science research. Movement data are generally collected by recording an objects spatial location (e.g., XY coordinates) at discrete time intervals. Methods for extracting useful information, for example space–time patterns, from these increasingly large and detailed datasets have lagged behind the technology for generating them. In this article we review existing quantitative methods for analyzing movement data. The objective of this article is to provide a synthesis of the existing literature on quantitative analysis of movement data while identifying those techniques that have merit with novel datasets. Seven classes of methods are identified: (1) time geography, (2) path descriptors, (3) similarity indices, (4) pattern and cluster methods, (5) individual–group dynamics, (6) spatial field methods, and (7) spatial range methods. Challenges routinely faced in quantitative analysis of movement data include difficulties with handling space and time attributes together, representing time in GIS, and using classical statistical testing procedures with space–time movement data. Areas for future research include investigating equivalent distance comparisons in space and time, measuring interactions between moving objects, developing predictive frameworks for movement data, integrating movement data with existing geographic layers, and incorporating theory from time geography into movement models. In conclusion, quantitative analysis of movement data is an active research area with tremendous opportunity for new developments and methods.

Analysis of human mobility patterns from GPS trajectories and contextual information

ABSTRACT Human mobility is important for understanding the evolution of size and structure of urban areas, the spatial distribution of facilities, and the provision of transportation services. Until recently, exploring human mobility in detail was challenging because data collection methods consisted of cumbersome manual travel surveys, space-time diaries, or interviews. The development of location-aware sensors has significantly altered the possibilities for acquiring detailed data on human movements. Although this has spurred many methodological developments in identifying human movement patterns, many of these methods operate solely from the analytical perspective and ignore the environmental context within which the movement takes place. In this paper we attempt to widen this view and present an integrated approach to the analysis of human mobility using a combination of volunteered GPS trajectories and contextual spatial information. We propose a new framework for the identification of dynamic (travel modes) and static (significant places) behaviour using trajectory segmentation, data mining, and spatio-temporal analysis. We are interested in examining if and how travel modes depend on the residential location, age, or gender of the tracked individuals. Further, we explore theorised ‘third places’, which are spaces beyond main locations (home/work) where individuals spend time to socialise. Can these places be identified from GPS traces? We evaluate our framework using a collection of trajectories from 205 volunteers linked to contextual spatial information on the types of places visited and the transport routes they use. The result of this study is a contextually enriched data set that supports new possibilities for modelling human movement behaviour.

Regionalization of Landscape Pattern Indices Using Multivariate Cluster Analysis

Regionalization, or the grouping of objects in space, is a useful tool for organizing, visualizing, and synthesizing the information contained in multivariate spatial data. Landscape pattern indices can be used to quantify the spatial pattern (composition and configuration) of land cover features. Observable patterns can be linked to underlying processes affecting the generation of landscape patterns (e.g., forest harvesting). The objective of this research is to develop an approach for investigating the spatial distribution of forest pattern across a study area where forest harvesting, other anthropogenic activities, and topography, are all influencing forest pattern. We generate spatial pattern regions (SPR) that describe forest pattern with a regionalization approach. Analysis is performed using a 2006 land cover dataset covering the Prince George and Quesnel Forest Districts, 5.5 million ha of primarily forested land base situated within the interior plateau of British Columbia, Canada. Multivariate cluster analysis (with the CLARA algorithm) is used to group landscape objects containing forest pattern information into SPR. Of the six generated SPR, the second cluster (SPR2) is the most prevalent covering 22% of the study area. On average, landscapes in SPR2 are comprised of 55.5% forest cover, and contain the highest number of patches, and forest/non-forest joins, indicating highly fragmented landscapes. Regionalization of landscape pattern metrics provides a useful approach for examining the spatial distribution of forest pattern. Where forest patterns are associated with positive or negative environmental conditions, SPR can be used to identify similar regions for conservation or management activities.

Measuring Dynamic Interaction in Movement Data

The emergence of technologies capable of storing detailed records of object locations has presented scientists and researchers with a wealth of data on object movement. Yet analytical methods for investigating more advanced research questions from such detailed movement datasets remain limited in scope and sophistication. Recent advances in the study of movement data has focused on characterizing types of dynamic interactions, such as single-file motion, while little progress has been made on quantifying the degree of such interactions. In this article, we introduce a new method for measuring dynamic interactions (termed DI) between pairs of moving objects. Simulated movement datasets are used to compare DI with an existing correlation statistic. Two applied examples, team sports and wildlife, are used to further demonstrate the value of the DI approach. The DI method is advantageous in that it measures interaction in both movement direction (termed azimuth) and displacement. Also, the DI approach can be applied at local, interval, episodal, and global levels of analysis. However the DI method is limited to situations where movements of two objects are recorded at simultaneous points in time. In conclusion, DI quantifies the level of dynamic interaction between two moving objects, allowing for more thorough investigation of processes affecting interactive moving objects.

A critical examination of indices of dynamic interaction for wildlife telemetry studies

Wildlife scientists continue to be interested in studying ways to quantify how the movements of animals are interdependent - dynamic interaction. While a number of applied studies of dynamic interaction exist, little is known about the comparative effectiveness and applicability of available methods used for quantifying interactions between animals. We highlight the formulation, implementation and interpretation of a suite of eight currently available indices of dynamic interaction. Point- and path-based approaches are contrasted to demonstrate differences between methods and underlying assumptions on telemetry data. Correlated and biased correlated random walks were simulated at a range of sampling resolutions to generate scenarios with dynamic interaction present and absent. We evaluate the effectiveness of each index at identifying different types of interactive behaviour at each sampling resolution. Each index is then applied to an empirical telemetry data set of three white-tailed deer (Odocoileus virginianus) dyads. Results from the simulated data show that three indices of dynamic interaction reliant on statistical testing procedures are susceptible to Type I error, which increases at fine sampling resolutions. In the white-tailed deer examples, a recently developed index for quantifying local-level cohesive movement behaviour (the di index) provides revealing information on the presence of infrequent and varying interactions in space and time. Point-based approaches implemented with finely sampled telemetry data overestimate the presence of interactions (Type I errors). Indices producing only a single global statistic (7 of the 8 indices) are unable to quantify infrequent and varying interactions through time. The quantification of infrequent and variable interactive behaviour has important implications for the spread of disease and the prevalence of social behaviour in wildlife. Guidelines are presented to inform researchers wishing to study dynamic interaction patterns in their own telemetry data sets. Finally, we make our code openly available, in the statistical software R, for computing each index of dynamic interaction presented herein.

Toward a kinetic-based probabilistic time geography

Time geography represents a powerful framework for the quantitative analysis of individual movement. Time geography effectively delineates the space–time boundaries of possible individual movement by characterizing movement constraints. The goal of this paper is to synchronize two new ideas, probabilistic time geography and kinetic-based time geography, to develop a more realistic set of movement constraints that consider movement probabilities related to object kinetics. Using random-walk theory, the existing probabilistic time geography model characterizes movement probabilities for the space–time cone using a normal distribution. The normal distribution has a symmetric probability density function and is an appropriate model in the absence of skewness – which we relate to an object’s initial velocity. Moving away from a symmetric distribution for movement probabilities, we propose the use of the skew-normal distribution to model kinetic-based movement probabilities, where the degree and direction of skewness is related to movement direction and speed. Following a description of our model, we use a set of case-studies to demonstrate the skew-normal model: a random walk, a correlated random walk, wildlife data, cyclist data, and athlete movement data. Our results show that for objects characterized by random movement behavior, the existing model performs well, but for object movement with kinetic properties (e.g., athletes), the proposed model provides a substantial improvement. Future work will look to extend the proposed probabilistic framework to the space–time prism.

Visual analytics of delays and interaction in movement data

ABSTRACT The analysis of interaction between movement trajectories is of interest for various domains when movement of multiple objects is concerned. Interaction often includes a delayed response, making it difficult to detect interaction with current methods that compare movement at specific time intervals. We propose analyses and visualizations, on a local and global scale, of delayed movement responses, where an action is followed by a reaction over time, on trajectories recorded simultaneously. We developed a novel approach to compute the global delay in subquadratic time using a fast Fourier transform (FFT). Central to our local analysis of delays is the computation of a matching between the trajectories in a so-called delay space. It encodes the similarities between all pairs of points of the trajectories. In the visualization, the edges of the matching are bundled into patches, such that shape and color of a patch help to encode changes in an interaction pattern. To evaluate our approach experimentally, we have implemented it as a prototype visual analytics tool and have applied the tool on three bidimensional data sets. For this we used various measures to compute the delay space, including the directional distance, a new similarity measure, which captures more complex interactions by combining directional and spatial characteristics. We compare matchings of various methods computing similarity between trajectories. We also compare various procedures to compute the matching in the delay space, specifically the Fréchet distance, dynamic time warping (DTW), and edit distance (ED). Finally, we demonstrate how to validate the consistency of pairwise matchings by computing matchings between more than two trajectories.

Kinematic interpolation of movement data

Mobile tracking technologies are facilitating the collection of increasingly large and detailed data sets on object movement. Movement data are collected by recording an object’s location at discrete time intervals. Often, of interest is to estimate the unknown position of the object at unrecorded time points to increase the temporal resolution of the data, to correct erroneous or missing data points, or to match the recorded times between multiple data sets. Estimating an object’s unknown location between known locations is termed path interpolation. This paper introduces a new method for path interpolation termed kinematic interpolation. Kinematic interpolation incorporates object kinematics (i.e. velocity and acceleration) into the interpolation process. Six empirical data sets (two types of correlated random walks, caribou, cyclist, hurricane and athlete tracking data) are used to compare kinematic interpolation to other interpolation algorithms. Results showed kinematic interpolation to be a suitable interpolation method with fast-moving objects (e.g. the cyclist, hurricane and athlete tracking data), while other algorithms performed best with the correlated random walk and caribou data. Several issues associated with path interpolation tasks are discussed along with potential applications where kinematic interpolation can be useful. Finally, code for performing path interpolation is provided (for each method compared within) using the statistical software R.

Mapping areas of spatial-temporal overlap from wildlife tracking data.

BackgroundThe study of inter-individual interactions (often termed spatial-temporal interactions, or dynamic interactions) from remote tracking data has focused primarily on identifying the presence of such interactions. New datasets and methods offer opportunity to answer more nuanced questions, such as where on the landscape interactions occur. In this paper, we provide a new approach for mapping areas of spatial-temporal overlap in wildlife from remote tracking data. The method, termed the joint potential path area (jPPA) builds from the time-geographic movement model, originally proposed for studying human movement patterns.ResultsThe jPPA approach can be used to delineate sub-areas of the home range where inter-individual interaction was possible. Maps of jPPA regions can be integrated with existing geographic data to explore landscape conditions and habitat associated with spatial temporal-interactions in wildlife. We apply the jPPA approach to simulated biased correlated random walks to demonstrate the method under known conditions. The jPPA method is then applied to three dyads, consisting of fine resolution (15 minute sampling interval) GPS tracking data of white-tailed deer (Odocoileus virginianus) collected in Oklahoma, USA. Our results demonstrate the ability of the jPPA to identify and map jPPA sub-areas of the home range. We show how jPPA maps can be used to identify habitat differences (using percent tree canopy cover as a habitat indicator) between areas of spatial-temporal overlap and the overall home range in each of the three deer dyads.ConclusionsThe value of the jPPA approach within current wildlife habitat analysis workflows is highlighted along with its simple and straightforward implementation and interpretation. Given the current emphasis on remote tracking in wildlife movement and habitat research, new approaches capable of leveraging both the spatial and temporal information content contained within these data are warranted. We make code (in the statistical software R) for implementing the jPPA approach openly available for other researchers.

A Bayesian space-time model for discrete spread processes on a lattice

In this article we present a Bayesian Markov model for investigating environmental spread processes. We formulate a model where the spread of a disease over a heterogeneous landscape through time is represented as a probabilistic function of two processes: local diffusion and random-jump dispersal. This formulation represents two mechanisms of spread which result in highly peaked and long-tailed distributions of dispersal distances (i.e., local and long-distance spread), commonly observed in the spread of infectious diseases and biological invasions. We demonstrate the properties of this model using a simulation experiment and an empirical case study - the spread of mountain pine beetle in western Canada. Posterior predictive checking was used to validate the number of newly inhabited regions in each time period. The model performed well in the simulation study in which a goodness-of-fit statistic measuring the number of newly inhabited regions in each time interval fell within the 95% posterior predictive credible interval in over 97% of simulations. The case study of a mountain pine beetle infestation in western Canada (1999-2009) extended the base model in two ways. First, spatial covariates thought to impact the local diffusion parameters, elevation and forest cover, were included in the model. Second, a refined definition for translocation or jump-dispersal based on mountain pine beetle ecology was incorporated improving the fit of the model. Posterior predictive checks on the mountain pine beetle model found that the observed goodness-of-fit test statistic fell within the 95% posterior predictive credible interval for 8 out of 10 years. The simulation study and case study provide evidence that the model presented here is both robust and flexible; and is therefore appropriate for a wide range of spread processes in epidemiology and ecology.