Qualitative spatial reasoning: cardinal directions as an example

ABSTRACT

Abstract. Geographers use spatial reasoning extensively in large-scale spaces, i.e., spaces that cannot be seen or understood from a single point of view. Spatial reasoning differentiates several spatial relations, e.g. topological or metric relations, and is typically formalized using a Cartesian coordinate system and vector algebra. This quantitative processing of information is clearly different from the ways human draw conclusions about spatial relations. Formalized qualitative reasoning processes are shown to be a necessary part of Spatial Expert Systems and Geographical Information Systems.

Addressing a subset of the total problem, namely reasoning with cardinal directions, a completely qualitative method, without recourse to analytical procedures, is introduced and a method for its formal comparison with quantitative formula is defined. The focus is on the analysis of cardinal directions and their properties. An algebraic method is used to formalize the meaning of directions. The standard directional symbols (N, W, etc.) are supplemented with a symbol corresponding to an undetermined direction between points too close to each other which greatly increases the power of the inference rules. Two specific systems to determine and reason with cardinal directions are discussed in some detail.

From this example and some other previous work, a comprehensive set of research steps is laid out, following a mathematically based taxonomy. It includes the extension of distance and direction reasoning to extended objects and the definitions of other metric relations that characterize situations when objects are not disjointed. The conclusions compare such an approach with other concepts.     

A new approach to quantifying spatial contiguity using graph theory and spatial interaction

Spatial contiguity is an important and fundamental landscape property in land allocation, habitat design, and forest management. The agreed upon notion of contiguity in the literature suggests shapelessness. However, existing approaches for measuring/promoting contiguity use proxies that either favour a particular shape or ignore inter‐patch relationships in fragmented landscapes. We propose an unbiased relative measure of contiguity ranging from zero to one based on graph theory and spatial interaction. The new measure reflects intra‐patch and inter‐patch relationships by quantifying contiguity within patches and potential contiguity among patches. Empirical analysis suggests that this measure of contiguity is reliable, consistent, and insensitive to sub‐region shape.     

New spatial dimensions of global cityscapes: From reviewing existing concepts to a conceptual spatial approach

Current global urbanisation processes are leading to new forms of massive urban constellations. The conceptualisations and classifications of these, however, are often ambiguous, overlap or lag behind in scientific literature. This article examines whether there is a common denominator to define and delimitate–and ultimately map–these new dimensions of cityscapes. In an extensive literature review we analysed and juxtaposed some of the most common concepts such as megacity, megaregion or megalopolis. We observed that many concepts are abstract or unspecific, and for those concepts for which physical parameters exist, the parameters are neither properly defined nor used in standardised ways. While understandably concepts originate from various disciplines, the authors identify a need for more precise definition and use of parameters. We conclude that often, spatial patterns of large urban areas resemble each other considerably but the definitions vary so widely that these differences may surpass any inconsistencies in the spatial delimitation process. In other words, today we have tools such as earth observation data and Geographic Information Systems to parameterise if clear definitions are provided. This appears not to be the case. The limiting factor when delineating large urban areas seems to be a commonly agreed ontology.     

A spatial zoning approach to calibrate and validate urban growth models

Calibration and validation of models predicting urban growth have been largely developed using internal variables. Further investigation is required to improve model’s calibration and validation mixing internal and external variables. To reach this objective, a spatial zoning approach simulating long-term expansion of Mashhad, the second largest city of Iran, was presented in this study. Spatial zoning approaches distinguish local-scale urban dynamics in districts with different socioeconomic characteristics. Thiessen polygons were used to identify districts with different morphology and functional attributes. Urban growth was subsequently simulated for each district using a Multi-Layer Perceptron (MLP) neural network and Markov chains (MC) analysis. MLP and MC algorithms were respectively used to derive transition maps from non-urban to urban use of land and to determine spatial evolution of built-up areas at the metropolitan scale. Results of simulations based on spatial zoning were compared with outcomes of traditional urban growth models. Spatial zoning improved significantly model’s accuracy in respect to more traditional simulation modes. The approach proposed here is appropriate when simulating land-use changes under discontinuous urban expansion.     

A relative spatial access assessment approach for analyzing potential spatial access to colorectal cancer services in Texas

The usefulness of gravity-based spatial access models is limited because of the uncertainty introduced by the range of values of the impedance coefficient. To solve this problem, this paper proposes the concept of spatial access ratio (SPAR) derived from the enhanced 2-step floating catchment area (E2SFCA) method — a recent extension of the gravity model — to assess potential spatial access. First, a sensitivity assessment is conducted to verify the effectiveness of SPAR and its advantages in overcoming the uncertainty problem. Then, the E2SFCA method and the shortest travel time method are employed to measure potential spatial access to colorectal cancer (CRC) prevention and treatment services in Texas based on data at the census tract level. The socio-demographic and geographic distributions of potential spatial access to CRC services are also examined. The sensitivity assessment reveals substantial fluctuations in the values of the spatial access index calculated directly by the E2SFCA method under different values of the impedance coefficient. However, the values of SPAR remain stable under different values of the coefficient. A comparative analysis indicates that potential spatial access to primary care physicians (PCPs), CRC screening facilities, and oncologists varied among different racial/ethnic and socioeconomic population groups as well as in different geographic regions in Texas. Non-Hispanic blacks, Asians, and people in affluent areas had a geographical advantage in accessing CRC services than other groups. The urban/rural difference was more obvious and serious than those of different racial/ethnic groups and groups with different socio-economic statuses, as metropolitan residents had more than three times the potential spatial access than isolated rural residents.     

A rough set approach to the discovery of classification rules in spatial data

This paper proposes a novel rough set approach to discover classification rules in real‐valued spatial data in general and remotely sensed data in particular. A knowledge induction process is formulated to select optimal decision rules with a minimal set of features necessary and sufficient for a remote sensing classification task. The approach first converts a real‐valued or integer‐valued decision system into an interval‐valued information system. A knowledge induction procedure is then formulated to discover all classification rules hidden in the information system. Two real‐life applications are made to verify and substantiate the conceptual arguments. It demonstrates that the proposed approach can effectively discover in remotely sensed data the optimal spectral bands and optimal rule set for a classification task. It is also capable of unraveling critical spectral band(s) discerning certain classes. The framework paves the road for data mining in mixed spatial databases consisting of qualitative and quantitative data.     

A citizen data-based approach to predictive mapping of spatial variation of natural phenomena

The vast accumulation of environmental data and the rapid development of geospatial visualization and analytical techniques make it possible for scientists to solicit information from local citizens to map spatial variation of geographic phenomena. However, data provided by citizens (referred to as citizen data in this article) suffer two limitations for mapping: bias in spatial coverage and imprecision in spatial location. This article presents an approach to minimizing the impacts of these two limitations of citizen data using geospatial analysis techniques. The approach reduces location imprecision by adopting a frequency-sampling strategy to identify representative presence locations from areas over which citizens observed the geographic phenomenon. The approach compensates for the spatial bias by weighting presence locations with cumulative visibility (the frequency at which a given location can be seen by local citizens). As a case study to demonstrate the principle, this approach was applied to map the habitat suitability of the black-and-white snub-nosed monkey (Rhinopithecus bieti) in Yunnan, China. Sightings of R. bieti were elicited from local citizens using a geovisualization platform and then processed with the proposed approach to predict a habitat suitability map. Presence locations of R. bieti recorded by biologists through intensive field tracking were used to validate the predicted habitat suitability map. Validation showed that the continuous Boyce index (B_cont(0.1)) calculated on the suitability map was 0.873 (95% CI: [0.810, 0.917]), indicating that the map was highly consistent with the field-observed distribution of R. bieti. B_cont(0.1) was much lower (0.173) for the suitability map predicted based on citizen data when location imprecision was not reduced and even lower (?0.048) when there was no compensation for spatial bias. This indicates that the proposed approach effectively minimized the impacts of location imprecision and spatial bias in citizen data and therefore effectively improved the quality of mapped spatial variation using citizen data. It further implies that, with the application of geospatial analysis techniques to properly account for limitations in citizen data, valuable information embedded in such data can be extracted and used for scientific mapping.     

A GIS-based approach to identify the spatial variability of social vulnerability to seismic hazard in Italy

This paper argues for a multidisciplinary framework to assess the relationship between environmental processes and social sciences that can be adapted to any geographic location. This includes both physical (earthquake hazard) and human (social vulnerability) dimensions in the context of disaster risk reduction. Disasters varies drastically depending on the local context. Indeed, the probability of a natural disaster having more devastating effects in one place than in another depends on the local vulnerability components of the affected society (cultural, social and economic). Therefore, there is an important correlation between the potential risk and the social resistance and resilience of a specific place, thus the disaster response varies according to the social fabric. In this context, the evaluation of social vulnerability is a crucial point in order to understand the ability of a society (studied at individual, household or community level) to anticipate, cope with, resist and recover from the impact of natural disaster events. Within this framework, the paper discusses how it is possible to integrate social vulnerability into the seismic risk analysis in Italy. Specifically, socioeconomic indicators were used to assess and mapping social vulnerability index. Afterwards, a Geographic Information System (GIS) approach was applied to identify the spatial variability of social vulnerability to seismic hazard. Through the use of a risk matrix, the classes of a social vulnerability index map were combined with those of a seismic hazard map proposed by INGV (National Institute of Geophysics and Volcanology). Finally, a qualitative social vulnerability exposure map to an earthquake hazard was produced, highlighting areas with high seismic and social vulnerability levels. Results suggest the importance of the integration of social vulnerability studies into seismic risk mitigation policies, emergency management and territorial planning to reduce the impact of disasters.     

建国以来国家城市化空间过程研究

建国以来,中国大陆城市体系空间格局发生了深刻的变化.传统的空间分析方法很难深入刻画城市体系空间格局的空间演化过程.运用Kernel空间密度分析方法,就建国以来国家城市化空间过程进行系统研究.结果显示:①中国城市空间分布密度在省区间存在明显的空间差异,且在1949～2003年间不断扩大.②中国城市空间分布具有"东密西疏/南密北疏"的基本倾向没有发生根本性变更.③中国城市空间分布在省区尺度上表现为"先减弱(1949～1965)、后增强(1965～1984)、再减弱并趋于稳定(1984～2003)"的趋势.④国家城市分布空间的节点结构发育逐渐趋于完善.⑤中国大陆城市空间从1949年的3个城市集聚区发育至2003年的20个.     

Population landscape: a geometric approach to studying spatial patterns of the US urban hierarchy

We present a geometric and graphic approach to studying spatial patterns of urban hierarchy in the US. The multiplicatively weighted Voronoi diagram is found to be effective for visualizing theoretical regions delineated by socio‐economic variables. The population landscape of the continental US demonstrates overall and stepwise patterns reflecting population, neighborhood and distance, with overwhelming influence from huge metropolitan areas. Stepwise exploration and cluster analysis of the spatial pattern reveal an urban hierarchy. Attributes and arrangement are the two important factors of urban hierarchy, with attribute having a stronger local influence and arrangement having a stronger global influence. The study also presents a variation of Zipf's law to visualize the rank‐size distribution from tabular and statistical space to map space.     

GeoVisuals: a visual analytics approach to leverage the potential of spatial videos and associated geonarratives

ABSTRACT

Videos embedded with spatial coordinates, especially when combined with additional expert insights, offer the potential to acquire fine-scale multi-time period contextualized data for a variety of different environments. However, while these geospatial multimedia (GSMM) data include abundant spatiotemporal, semantic and visual information, the means to fully leverage their potential using a suite of visual and interactive analysis techniques and tools has thus far been lacking. In this paper, we address this gap by first identifying the types of tasks required of GSMM data, and then presenting a solution platform. This GeoVisuals system utilizes a visual analysis approach built on semantic data points that can be integrated spatially, which in turn enables management in a unified database with combined spatio-temporal and text querying. A set of visualization functions are integrated in two investigation modes: geo-video analysis and geo-location analysis.     

A representativeness-directed approach to mitigate spatial bias in VGI for the predictive mapping of geographic phenomena

Volunteered geographic information (VGI) contains valuable field observations that represent the spatial distribution of geographic phenomena. As such, it has the potential to provide regularly updated low-cost field samples for predictively mapping the spatial variations of geographic phenomena. The predictive mapping of geographic phenomena often requires representative samples for high mapping accuracy, but samples consisting of VGI observations are often not representative as they concentrate on specific geographic areas (i.e. spatial bias) due to the opportunistic nature of voluntary observation efforts. In this article, we propose a representativeness-directed approach to mitigate spatial bias in VGI for predictive mapping. The proposed approach defines and quantifies sample representativeness by comparing the probability distributions of sample locations and the mapping area in the environmental covariate space. Spatial bias is mitigated by weighting the sample locations to maximize their representativeness. The approach is evaluated using species habit suitability mapping as a case study. The results show that the accuracy of predictive mapping using weighted sample locations is higher than using unweighted sample locations. A positive relationship between sample representativeness and mapping accuracy is also observed, suggesting that sample representativeness is a valid indicator of predictive mapping accuracy. This approach mitigates spatial bias in VGI to improve predictive mapping accuracy.     

A spatial cognition-based urban building clustering approach and its applications

This article presents a spatial cognition analysis technique for automated urban building clustering based on urban morphology and Gestalt theory. The proximity graph is selected to present the urban mrphology. The proximity graph considers the local adjacency among buildings, providing a large degree of freedom in object displacement and aggregation. Then, three principles of Gestalt theories, proximity, similarity, and common directions, are considered to extract potential Gestalt building clusters. Next, the Gestalt features are further characterized with seven indicators, that is, area difference, height difference, similarity difference, orientation difference, linear arrangement difference, interval difference, and oblique degree of arrangement. A support vector machine (SVM)-based approach is employed to extract the Gestalt building clusters. This approach transforms the Gestalt cluster extraction into a supervised discrimination process. The method presents a generalized approach for clustering buildings of a given street block into groups, while maintaining the spatial pattern and adjacency of buildings during the displacement operation. In applications of urban building generalization and three-dimensional (3D) urban panoramic-like view, the method presented in this article adequately preserves the spatial patterns, distributions, and arrangements of urban buildings. Moreover, the final 3D panoramic-like views ensure the accurate appearance of important features and landscapes.     

An integrated approach for addressing geographic uncertainty in spatial optimization

There exist many facets of error and uncertainty in digital spatial information. As error or uncertainty will not likely ever be completely eliminated, a better understanding of its impacts is necessary. Spatial analytical approaches, in particular, must somehow address data-quality issues. This can range from evaluating impacts of potential data uncertainty in planning processes that make use of methods to devising methods that explicitly account for error/uncertainty. To date, little has been done to structure methods accounting for error. This article develops an integrated approach to address data uncertainty in spatial optimization. We demonstrate that it is possible to characterize uncertainty impacts by constructing and solving a new multi-objective model that explicitly incorporates facets of data uncertainty. Empirical findings indicate that the proposed approaches can be applied to evaluate the impacts of data uncertainty with statistical confidence, which moves beyond popular practices of simulating errors in data.     

A fuzzy formal concept analysis-based approach to uncovering spatial hierarchies among vague places extracted from user-generated data

The spatial hierarchy of part-whole relationships is an essential characteristic of the platial world. Constructing spatial hierarchies of places is valuable in association analysis and qualitative spatial reasoning. The emergence of large amounts of geotagged user-generated content provides strong support for modelling places. However, the vague nature of places and the complex spatial relationships among places make it intractable to understand and represent the hierarchies among places. In this paper, we introduce a fuzzy formal concept analysis-based approach to uncovering the spatial hierarchies among vague places. Each place is represented as a concept that consists of its extent and its intent. Based on the place concepts, the spatial hierarchies are generated and expressed as a graph that is easy to comprehend and contains abundant information on spatial relations. We also demonstrate the rationality of our result by comparing it with the result of a questionnaire survey.     

Modelling residential fire incident response times: A spatial analytic approach

Rapid response to fire incidents is critical as delays in the departure and arrival at the scene can have significant consequences in terms of damage, injury and death. Research on the dynamics of residential fire incident response times has barely begun, a situation arguably underpinned by limited access to disaggregate command and control data. In this paper we draw on unit record data and employ quantile regression to examine the role that socio-demographic, infrastructure characteristics and temporal factors play on response times. Results reveal that response times are slower during the winter, in locales with larger numbers of children (aged 14 years and below) and low socioeconomic households, and in areas that have more complex street layouts. We conclude through emphasising the importance of these findings in their capacity to contribute to a new evidence base to inform policy decisions from a resource allocation perspective through the spatial allocation of finite fire resources.     

Reconstructing pre-erosion topography using spatial interpolation techniques:A validation-based approach

Understanding the topographic context preceding the development of erosive landforms is of major relevance in geomorphic research, as topography is an important factor on both water and mass movement-related erosion, and knowledge of the original surface is a condition for quantifying the volume of eroded material. Although any reconstruction implies assuming that the resulting surface reflects the original topography, past works have been dominated by linear interpolation methods, incapable of generating curved surfaces in areas with no data or values outside the range of variation of inputs. In spite of these limitations, impossibility of validation has led to the assumption of surface representativity never being challenged. In this paper, a validation-based method is applied in order to define the optimal interpolation technique for reconstructing pre-erosion topography in a given study area. In spite of the absence of the original surface, different techniques can be nonetheless evaluated by quantifying their capacity to reproduce known topography in unincised locations within the same geomorphic contexts of existing erosive landforms. A linear method (Triangulated Irregular Network, TIN) and 23 parameterizations of three distinct Spline interpolation techniques were compared using 50 test areas in a context of research on large gully dynamics in the South of Portugal. Results show that almost all Spline methods produced smaller errors than the TIN, and that the latter produced a mean absolute error 61.4% higher than the best Spline method, clearly establishing both the better adjustment of Splines to the geomorphic context considered and the limitations of linear approaches. The proposed method can easily be applied to different interpolation techniques and topographic contexts, enabling better calculations of eroded volumes and denudation rates as well as the investigation of controls by antecedent topographic form over erosive processes.     

A density-based approach for detecting network-constrained clusters in spatial point events

Existing spatial clustering methods primarily focus on points distributed in planar space. However, occurrence locations and background processes of most human mobility events within cities are constrained by the road network space. Here we describe a density-based clustering approach for objectively detecting clusters in network-constrained point events. First, the network-constrained Delaunay triangulation is constructed to facilitate the measurement of network distances between points. Then, a combination of network kernel density estimation and potential entropy is executed to determine the optimal neighbourhood size. Furthermore, all network-constrained events are tested under a null hypothesis to statistically identify core points with significantly high densities. Finally, spatial clusters can be formed by expanding from the identified core points. Experimental comparisons performed on the origin and destination points of taxis in Beijing demonstrate that the proposed method can ascertain network-constrained clusters precisely and significantly. The resulting time-dependent patterns of clusters will be informative for taxi route selections in the future.