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1.
This article introduces a new classification scheme—head/tail breaks—to find groupings or hierarchy for data with a heavy-tailed distribution. The heavy-tailed distributions are heavily right skewed, with a minority of large values in the head and a majority of small values in the tail, commonly characterized by a power law, a lognormal, or an exponential function. For example, a country's population is often distributed in such a heavy-tailed manner, with a minority of people (e.g., 20 percent) in the countryside and the vast majority (e.g., 80 percent) in urban areas. This new classification scheme partitions all of the data values around the mean into two parts and continues the process iteratively for the values (above the mean) in the head until the head part values are no longer heavy-tailed distributed. Thus, the number of classes and the class intervals are both naturally determined. I therefore claim that the new classification scheme is more natural than the natural breaks in finding the groupings or hierarchy for data with a heavy-tailed distribution. I demonstrate the advantages of the head/tail breaks method over Jenks's natural breaks in capturing the underlying hierarchy of the data.  相似文献   

2.
According to Christopher Alexander’s theory of centers, a whole comprises numerous, recursively defined centers for things or spaces surrounding us. Wholeness is a type of global structure or life-giving order emerging from the whole as a field of the centers. The wholeness is an essential part of any complex system and exists, to some degree or other, in spaces. This paper defines wholeness as a hierarchical graph, in which individual centers are represented as the nodes and their relationships as the directed links. The hierarchical graph gets its name from the inherent scaling hierarchy revealed by the head/tail breaks, which is a classification scheme and visualization tool for data with a heavy-tailed distribution. We suggest that (1) the degrees of wholeness for individual centers should be measured by PageRank (PR) scores based on the notion that high-degree-of-life centers are those to which many high-degree-of-life centers point, and (2) that the hierarchical levels, or the ht-index of the PR scores induced by the head/tail breaks, can characterize the degree of wholeness for the whole: the higher the ht-index, the more life or wholeness in the whole. Three case studies applied to the Alhambra building complex and the street networks of Manhattan and Sweden illustrate that the defined wholeness captures fairly well human intuitions on the degree of life for the geographic spaces. We further suggest that the mathematical model of wholeness be an important model of geographic representation, because it is topological oriented, which enables us to see the underlying scaling structure. The model can guide geodesign, which should be considered as the wholeness-extending transformations that are essentially like the unfolding processes of seeds or embryos, for creating built and natural environments of beauty or with a high degree of wholeness.  相似文献   

3.
A fractal can be simply understood as a set or pattern in which there are far more small things than large ones, for example, far more small geographic features than large ones on the earth surface, or far more large-scale maps than small-scale maps for a geographic region. This article attempts to argue and provide evidence for the fractal nature of maps and mapping. It is the underlying fractal structure of geographic features, either natural or man-made, that make reality mappable, large-scale maps generalizable, and cities imageable. The fractal nature is also what underlies the beauty of maps. After introducing some key fractal concepts such as recursion, self-similarity, scaling ratio, and scaling exponent, this article demonstrates that fractal thought is rooted in long-standing map-making practices such as series maps subdivision, visual hierarchy, and Töpfer’s radical law. Drawing on previous studies on head/tail breaks, mapping can be considered a head/tail breaks process; that is to divide things around an average, according to their geometric, topological and/or semantic properties, into the head (for those above the average) and the tail (for those below the average), and recursively continue the dividing process for the head for map generalization, statistical mapping, and cognitive mapping. Given the fractal nature of maps and mapping, cartography should be considered a perfect combination of science and art, and scaling must be formulated as a law of cartography or that of geography in general.  相似文献   

4.
Geographical entities are characterized by rather complex structures. They involve space and thematic information, which is subject to change in time, while history should be maintained. On the other hand, these structures may be irregular (i.e. they do not necessarily conform to a fixed schema), because associated data is usually collected based on different specifications and multiple resolutions. Hence, the representation of geographical entities in traditional data models, such as the relational or object-oriented, is not always feasible. In this respect, this paper investigates the use of semi-structured data (SSD) models—an innovative approach recently developed in Information Technology—for modelling dynamic geographical entities. A framework for the representation of geographic entities in Object Exchange Model (OEM), a popular model for semi-structured data, is introduced. Additionally, it is shown how useful information can be extracted from such a representation using the LOREL query language for SSD. A simplified case study in the application domain of cadastre involving SSD is examined closely.  相似文献   

5.
Abstract

The point-vector representation for line segments offers several advantages over other more familiar representations for lines and line segments, such as the point-slope form, the slope-intercept form and the two-point form. With the point-vector form, line segment intersection routines and related cartographic computations, such as point-in-polygon routines and detection of near-intersections, can be streamlined, simplified and more easily understood geometrically. The point-vector segment representation retains information on the line segment and not just the line. Special case handling for vertical lines is not necessary as with some other representations and several computational short cuts can be derived directly from the segment end-point coordinates.  相似文献   

6.
Abstract

Multiresolution data structures provide a means of retrieving geographical features from a database at levels of detail which are adaptable to different scales of representation. A database design is presented which integrates multi-scale storage of point, linear and polygonal features, based on the line generalization tree, with a multi-scale surface model based on the Delaunay pyramid. The constituent vertices of topologically-structured geographical features are thus distributed between the triangulated levels of a Delaunay pyramid in which triangle edges are constrained to follow those features at differing degrees of generalization. Efficient locational access is achieved by imposing a spatial index on each level of the pyramid.  相似文献   

7.
Environmental simulation models need automated geographic data reduction methods to optimize the use of high-resolution data in complex environmental models. Advanced map generalization methods have been developed for multiscale geographic data representation. In the case of map generalization, positional, geometric and topological constraints are focused on to improve map legibility and communication of geographic semantics. In the context of environmental modelling, in addition to the spatial criteria, domain criteria and constraints also need to be considered. Currently, due to the absence of domain-specific generalization methods, modellers resort to ad hoc methods of manual digitization or use cartographic methods available in off-the-shelf software. Such manual methods are not feasible solutions when large data sets are to be processed, thus limiting modellers to the single-scale representations. Automated map generalization methods can rarely be used with confidence because simplified data sets may violate domain semantics and may also result in suboptimal model performance. For best modelling results, it is necessary to prioritize domain criteria and constraints during data generalization. Modellers should also be able to automate the generalization techniques and explore the trade-off between model efficiency and model simulation quality for alternative versions of input geographic data at different geographic scales. Based on our long-term research with experts in the analytic element method of groundwater modelling, we developed the multicriteria generalization (MCG) framework as a constraint-based approach to automated geographic data reduction. The MCG framework is based on the spatial multicriteria decision-making paradigm since multiscale data modelling is too complex to be fully automated and should be driven by modellers at each stage. Apart from a detailed discussion of the theoretical aspects of the MCG framework, we discuss two groundwater data modelling experiments that demonstrate how MCG is not just a framework for automated data reduction, but an approach for systematically exploring model performance at multiple geographic scales. Experimental results clearly indicate the benefits of MCG-based data reduction and encourage us to continue expanding the scope of and implement MCG for multiple application domains.  相似文献   

8.
Abstract

This study examines the role of surface geomorphic features in tree establishment at the alpine treeline in Glacier National Park, Montana, through the presentation of a multiscale, conceptual model of biogeomorphic relationships at alpine treeline. Empirical observations gathered through a multiscale field methodology over three summers serve as a base for the model. The model highlights the importance of surface geomorphic features, specifically boulders and terrace risers, in creating favorable local site conditions, largely by protecting seedlings from wind. The sheltering effect of surface features enables initial seedling establishment, and in some cases survival, above current treeline locations, thereby initiating a positive feedback effect that encourages subsequent tree establishment. Geomorphic features are therefore important in linking scales of pattern and process at the alpine treeline ecotone.  相似文献   

9.
Abstract

Recent changes in information technology offer the opportunity to explore alternative architectures for geographical information systems (GIS) which might better support advanced applications. This paper describes the architecture and implementation of the environmental decision support system (EDSS), a prototype GIS tool kit. The architecture is based on a simple yet powerful systems model using only data collections, views and operations as the basic entity types. The design of the user interface, data management and data analysis within the model are outlined, with particular emphasis on the advanced facilities for which implementation is simplified by the architecture. A prototype applications system, BANKSIA, is also described.  相似文献   

10.
Abstract

The field of geographical information systems (GIS) is reviewed from the viewpoint of spatial analysis which is the key component of the familiar four-part model of input, storage, analysis and output Input is constrained by the limits of manual methods and problems of ambiguity in scanning. The potential for developments in output is seen to be limited to the query mode of GIS operation, and to depend on abandoning the cartographic model. Discussion of storage methods is organized around the raster versus vector debate and the need to represent two spatial dimensions in one. A taxonomy of GIS spatial analysis operations is presented together with a generic data model. Prospects for implementation are discussed and seen to depend on appropriate scales of organization in national and international academic research.  相似文献   

11.
Linear features are represented on paper or digital maps with polyline geometries. Sampling, discretization, and generalization processes result in polylines of a length smaller than that of the actual features. In addition, semantics associated to the original line features may be lost. This becomes more significant for coarse sampling and/or high degree of generalization. This paper introduces a data structure that can alleviate this problem, by preserving the attributes and semantic characteristics associated to the original features in cartographic representation. The structure can handle both linear features and polygon outlines. Various compression methods have been examined. The structure has been implemented and tested with both synthetic and real datasets. Extensions to spatiotemporal features, like trajectories, have also been considered.  相似文献   

12.
The ht-index is a recently proposed tool for capturing dynamic views of the evolution process of geographic features, but the ht-index is not sensitive to small changes during this process. To address this problem, an improved ht-index, a cumulative rate of growth (CRG) index, was proposed. Compared to the ht-index, the CRG index is more sensitive to changes during the evolution process of geographic features, and the process is better captured by the CRG index as a result. In addition, the head/tail breaks method (used to derive the ht-index) was adjusted, making the CRG index a universal tool for capturing the dynamic views of both increasingly heterogeneous and increasingly homogeneous geographic features.  相似文献   

13.
As a basic and significant operator in map generalization, polyline simplification needs to work across scales. Perkal’s ε-circle rolling approach, in which a circle with diameter ε is rolled on both sides of the polyline so that the small bend features can be detected and removed, is considered as one of the few scale-driven solutions. However, the envelope computation, which is a key part of this method, has been difficult to implement. Here, we present a computational method that implements Perkal’s proposal. To simulate the effects of a rolling circle, Delaunay triangulation is used to detect bend features and further to construct the envelope structure around a polyline. Then, different connection methods within the enveloping area are provided to output the abstracted result, and a strategy to determine the best connection method is explored. Experiments with real land-use polygon data are implemented, and comparison with other algorithms is discussed. In addition to the scale-specificity inherited from Perkal’s proposal, the results show that the proposed algorithm can preserve the main shape of the polyline and meet the area-maintaining constraint during large-scale change. This algorithm is also free from self-intersection.  相似文献   

14.
《The Journal of geography》2012,111(5):208-219
ABSTRACT

Geography textbooks contain chapter or review questions that may engage students in spatial thinking. This research used Jo and Bednarz’s (2009) Taxonomy of Spatial Thinking to evaluate the percentage of spatial thinking questions in four university-level world geography course textbooks. The results from this study were then compared to the findings in Jo and Bednarz’s (2009) analysis of high school geography textbooks. Thirty-five percent of university level textbook questions are related to spatial thinking compared to twenty-four percent in high school geography textbooks. The results provide information useful to stakeholders, such as teachers, administrators, and textbook writers and may help these stakeholders to consciously incorporate the three components of spatial thinking as defined by the National Research Council (2006). A simplified taxonomy for identifying spatial-thinking concepts in textbook review questions is also suggested.  相似文献   

15.
On the density distribution within the Earth   总被引：1，自引：0，他引：1  
The distribution of density as a function of position within the Earth is much less well constrained than the seismic velocities. The primary information comes from the mass and moment of inertia of the Earth and this information alone requires that there be a concentration of mass towards the centre of the globe. Additional information is to be found in the frequencies of the graver normal modes of the Earth which are sensitive to density through self-gravitation effects induced in deformation.
  The present generation of density models has been constructed using linearized inversion techniques from earlier models, which ultimately relate back to models developed by Bullen and based in large part on physical arguments. A number of experiments in non-linear inversion have been conducted using the PREM reference model, with fixed velocity and attenuation, but with the density model constrained to lie within fixed bounds on both density and density gradient. A set of models is constructed from a uniform probability density within the bound and slope constraints. Each of the resultant density models is tested against the mass and moment of inertia of the Earth, and for successful models a comparison is made with observed normal mode frequencies. From the misfit properties of the ensemble of models the robustness of the density profile in different portions of the Earth can be assessed, which can help with the design of parametrization for future reference models. In both the lower mantle and the outer core it would be desirable to allow a more flexible representation than the single cubic polynomial employed in PREM.  相似文献   

16.
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17.
The distinctive data management needs of transportation agencies in developing transportation-based applications dictate the presence of essential elements that are beyond existing transportation location referencing system data models. These elements include multi-dimensional location referencing, multiscale representation, navigation, and temporal GIS. This paper looks at the foundation for these elements, describes the characteristics of these elements and offers solutions through a transportation-based multi-dimensional data model. By managing data expressed in one to four dimensions, the Multi-Dimensional Location Referencing System (MDLRS) data model allows organizations to implement improved solutions for transportation systems using advanced spatial technologies (e.g. GPS).  相似文献   

18.
Summary. Three Fast Fourier Transform numerical methods for computing the Hilbert transform have been evaluated for their accuracy by numerical examples. All three methods employ the property that the Hdbert transform is a convolution. The first method uses the result that the Fourier transform of 1/π x is — isgn(ω). The second method is based on a discrete Hilbert transform introduced by Saito. The third method, introduced in this research note, uses linear interpolation to transform the Hilbert transform integral into a discrete convolution. The last method is shown by numerical examples from fault dislocation models to be more accurate than the other two methods when the Hilbert transform integral has high-frequency components.  相似文献   

19.
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20.

In traditional, constrained spatial interaction models, the number of predicted movers leaving origins and entering destinations is constrained to match exactly the observed number. In relaxed models, these constraints are allowed to vary over a range of values in order to provide greater flexibility in calibration. This paper identifies a new, seven-member family of relaxed spatial interaction models, based upon the generalization of the constraint sets used in model derivation. Three categories are suggested, including single and doubly relaxed models, cost-relaxed models, and totally relaxed models. This paper introduces these relaxed models as entropy-maximizing ones, proposes a terminology for them, and describes empirical situations in which they are useful.  相似文献   

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