FlowAMOEBA: Identifying Regions of Anomalous Spatial Interactions

Definition:Spatial interaction refers to all cases in which a relationship (a flow of persons, goods, communications, citations, and so on) is observed between pairs of spatial units. Differently from the standard areal or point units often analyzed in spatial science, spatial interaction data are denoted by their bilateral nature. They have an origin and a destination (in the particular case, the two being the same). Such origins and destinations may have observable characteristics. Moreover, each pair of spatial units may be described according to some measures of separation (such as distance) or of commonality (e.g., the presence of a common language). Such descriptors are typically employed in spatial interaction models, the most commonly used analytical framework for modeling flow data. Problems occur when the aforementioned descriptors exhibit correlation between the values of different spatial units or dyads which is due to the spatial configuration of the units themselves (e.g., ...This is an excerpt from the content.

This paper addresses the theme of spatial autocorrelation impacting spatial equilibria, and hence an understanding of economic network resilience and vulnerability. It exploits the notion that spatial autocorrelation in the geographic distribution of origin and destination attributes and network autocorrelation in the flows between origins and destinations constitute two spatial autocorrelation components contained in spatial interaction data. It illustrates that a spatial interaction model specification needs to incorporate both components in order to furnish sound implications about associated economic network resilience and vulnerability. Such models also need to undergo sensitivity analyses in terms of changes in geographic scale and resolution. And, it furnishes a novel 3-D visualization of geographic flows, such as journey-to-work trips, in order to achieve a better comprehension of economic network resilience and vulnerability.

In the era of big data, large amounts of detailed spatial interaction data are readily available due to the increasing pervasiveness of location-aware devices and techniques. Such data are often applied in the research of spatial structures, land use characteristics, and human activity regularities. However, visualizing such data on maps is a great challenge. Existing approaches either encounter overlapping and intersection problems, which may cause information loss or distortion, or are unable to present interaction characteristics. Consequently, the functional and positional features of places and human mobility trends are not fully demonstrated. We propose direction-based pattern maps, a new visualization method to display the spatial interaction pattern of every place by aggregating spatial interaction data in cardinal directions. This approach can well represent local interaction characteristics and is applicable to different spatial scales. Owing to regular hexagonal tessellations, it can avoid cluttering problems and maintain a geographical context. A case study using Beijing taxi trip data is conducted to validate the usefulness of our approach.

For many years, effective model‐based representations of the dynamics and evolution of urban spatial structure have proved elusive. While some progress has been made through the deployment of spatial interaction models, these approaches have been limited by the difficulty of representing behavioural mechanisms and processes. In this paper, it is demonstrated that evolutionary models grounded in the principles of spatial interaction are compatible with the more novel approaches of agent‐based modelling. The incorporation of agents provides a much more flexible means for the representation of behavioural mechanisms. The paper illustrates the way in which three more complicated situations can be handled through the fusion of spatial interaction and agent modelling perspectives. These situations comprise discontinuous evolution (in which structural adjustment takes place in discrete steps, and not as a continuously smooth process); nonequilibrium dynamics (in which the underlying system parameters continue to evolve through time); the incorporation of new decision variables (which we illustrate through the addition of land rents into the model). The conclusion of the paper is that the combination of spatial interaction and agent‐based modelling methods provides encouraging prospects for the social simulation of real urban systems.

This paper attempts to develop a mathematically rigid and unified framework for neural spatial interaction modeling. Families of classical neural network models, but also less classical ones such as product unit neural network ones are considered for the cases of unconstrained and singly constrained spatial interaction flows. Current practice appears to suffer from least squares and normality assumptions that ignore the true integer nature of the flows and approximate a discrete‐valued process by an almost certainly misrepresentative continuous distribution. To overcome this deficiency we suggest a more suitable estimation approach, maximum likelihood estimation under more realistic distributional assumptions of Poisson processes, and utilize a global search procedure, called Alopex, to solve the maximum likelihood estimation problem. To identify the transition from underfitting to overfitting we split the data into training, internal validation, and test sets. The bootstrapping pairs approach with replacement is adopted to combine the purity of data splitting with the power of a resampling procedure to overcome the generally neglected issue of fixed data splitting and the problem of scarce data. In addition, the approach has power to provide a better statistical picture of the prediction variability. Finally, a benchmark comparison against the classical gravity models illustrates the superiority of both, the unconstrained and the origin constrained neural network model versions in terms of generalization performance measured by Kullback and Leibler's information criterion.

Spatial scale is a fundamental issue for geographical phenomena because the size of the spatial unit adopted for analysis can have a significant effect on aggregated spatial data and the corresponding analytical results. There exists much research on the scale issue of spatial distribution data while a few has paid attention to the scale effect on spatial interactions. Big geo-data with micro-level individual movements provide an unprecedented opportunity to explore spatial interactions from the bottom up and to understand the scale effect from the perspective of interaction patterns. In this paper, we introduced an empirical framework to explore spatial interaction data across scales. By incorporating two data sets of taxi trajectories in Beijing and Shanghai, we aggregated the taxi O-D trips under multiple regular grids with different cell sizes and analyzed the properties of spatial interactions in three aspects: the statistical distribution, the distance decay mechanism, and the structure pattern. Our research demonstrated the feasibility of analyzing spatial interactions from a multi-scale view and offered a basic empirical framework for future geographical research that is interested in scale and spatial interactions.

Les interactions spatiales entre les régions traduisent l’existence d’une dépendance spatiale également appelée autocorrélation spatiale. La modélisation de ces interactions nécessite l’utilisation de matrices de poids permettant d’imposer une structure sur leur étendue. Dans la littérature, les matrices de contiguïté et des k-plus proches voisins sont les plus couramment utilisées. Afin de dépasser ces deux approches, jugées insuffisantes d’un point de vue théorique à l’heure d’expliquer les relations économiques interrégionales, nous introduisons les trois éléments suivants au sein de matrices de pondération construites en analogie au modèle gravitationnel : la distance temps, la population et les infrastructures routières. L’analyse montre, d’une part, que ces matrices semblent plus aptes à capter le phénomène de concentration globale de l’espace européen et d’autre part, qu’elles modifient l’étendue des interactions spatiales, mettant en exergue la discontinuité de celles-ci dans l’espace.

Conventional gravity-model estimates of spatial interactions assume that spatial interactions or flows from all locations to all other locations are independent of other flows and, therefore, overlook the latent multilateral influences in play. This research developed a novel application of Self-Organizing Map (SOM) to retrospectively examine historical spatial interactions among multiple locations for new insights into the spatial and temporal dependence of flows across locations. We built a SOM with units of spatial interaction patterns and traced changes in spatial interactions patterns for each location over time. By tracing the changes, we created new trajectories of spatial interactions on the SOM to contextualize spatial interactions at individual locations and among all locations over time. We used international trade data among 207 countries from 1900 to 2014 to demonstrate the proposed data-driven approach for retrospective analysis of spatial interactions. We created a SOM of international trade patterns, mapped each country’s trading trajectory, and compared the trajectories among all 207 countries. We showed that the SOM application could answer questions about multilateral spatial interactions over time. Our findings extended earlier network analyses of the global system with an integrated space-time view of spatial interactions. The SOM approach is adaptable to other domains of spatial interactions (e.g., urban transportation, immigrations) to characterize spatial interactions among locations change over time individually or contextually among all locations.

Spatial interaction and spatial structure are foundational geographical abstractions, though there is often variation in how they are conceptualized and deployed in quantitative models. In particular, the last five decades have produced an exceptional diversity regarding the role of spatial structure within spatial interaction models. This is explored by outlining the initiation and development of the notion of spatial structure within spatial interaction modeling and critically reviewing four methodological approaches that emerged from ongoing debate about the topic. The outcome is a comprehensive coverage of the past and a sketch of one potential path forward for advancing this long-standing inquiry.

For decades, gravitational analysis has been a key instrument in analyzing spatial flows. Time and again, it has prompted new and challenging research questions. This paper provides a concise overview of the foundation, the conceptualization and empirical relevance of gravitational principles in regional science and spatial economics. Attention is also given to general “social physics” interpretations of gravity in spatial interaction models and to the impact of intangible distance frictions. The main emphasis in the study is placed on the significance of spatial impedance functions and gravity potential analysis. In particular, the paper focuses on cross-border trade and has three main goals: (i) to address the robustness of distance friction parameters related to trade borders, employing, inter alia, quantitative results from meta-analyses on trade models in spatial economics; (ii) to present a promising methodology based on gravity potential and the related gravitational gradient models that include directional intensities of flows; (iii) to test the validity of the latter approach on the basis of a vector gradient analysis of export patterns of the Netherlands. The paper argues that—despite the space-reducing impact of the modern digital technologies—gravitational principles still have an uncontested relevance in an analysis of spatial flows in regional science.

Until recently, considerable effort has been devoted to the estimation of panel data regression models without adequate attention being paid to the drivers of interaction amongst cross-section and spatial units. We discuss some new methodologies in this emerging area and demonstrate their use in measurement and inferences on cross-section and spatial interactions. Specifically, we highlight the important distinction between spatial dependence driven by unobserved common factors and those based on a spatial weights matrix. We argue that purely factor-driven models of spatial dependence may be inadequate because of their connection with the exchangeability assumption. The three methods considered are appropriate for different asymptotic settings; estimation under structural constraints when N is fixed and T → ∞, whilst the methods based on GMM and common correlated effects are appropriate when T ≫ N → ∞. Limitations and potential enhancements of the existing methods are discussed, and several directions for new research are highlighted.

Spatial spillover effect on land conveyance fee—A multi-scheme investigation in Wuhan agglomeration

This chapter is an introduction to the study of migration flows. It starts with a review of major definition and measurement issues. Comparative studies of migration are particularly difficult because different countries define migration differently and measurement methods are not harmonized. Insight in data collection practices is a first requirement to study flows. In the paper, several migration indicators are presented that describe the level and direction of migration. Scientists attempt to model migration flows since Ravenstein presented his migration laws at the end of the nineteenth century. Initially theories and models were borrowed from physics. The gravity model, based on Newton’s law of gravitation, has been the main model of migration flows for decades and continues to be popular today. Gradually human behaviour replaced the laws of physics and spatial interaction models the gravity model. Spatial interaction models emphasize interaction between geographically dispersed populations. Initially the gravity model had a strong influence on spatial interaction models, but the interest shifted gradually to probability theory and probability models. A parallel development was the life course perspective on migration, resulting from the increased awareness that some life events trigger migration and that during some stages of life, a person has an elevated propensity to migrate. These links produce the typical and universal age patterns of migration. Today, population projection models incorporate models of these typical age patterns (model schedules) and models of spatial interaction. Projection models may be turned into policy models to infer the migration flows required to meet demographic objectives, i.e. to offset population decline resulting from low fertility.

Spatial heterogeneity in spatial interaction of human movements—Insights from large-scale mobile positioning data

The gravity model which is based on Newton’s gravitational law, has been widely used as a spatial interaction model in the past few decades. Spatial interactions are important in epidemic modeling as different populations in the world are interconnected by them. Human dispersal behaviors are spatial interactions and they are crucial aspects of infectious disease spread. However, many existing compartmental models model epidemics in a single area. Hence, a gravity model approach to model epidemics incorporated with a multipatch compartmental model is studied here. Both human dispersal behaviors within a patch and between patches are considered. When the human dispersal behaviors within a patch are modeled, the denominator of the general gravity model becomes zero. An alternative power-based distance decay function is introduced to the gravity model to address that research gap. The parameters of the modified gravity model are estimated using a hybrid method combining ordinary least squares (OLS) and nonlinear least squares (NLS) methods (Hybrid OLS-NLS method).