Approximation of Gaussian spatial autoregressive models for massive regular square tessellation data

Most of the literature to date proposes approximations to the determinant of a positive definite n × n spatial covariance matrix (the Jacobian term) for Gaussian spatial autoregressive models that fail to support the analysis of massive georeferenced data sets. This paper briefly surveys this literature, recalls and refines much simpler Jacobian approximations, presents selected eigenvalue estimation techniques, summarizes validation results (for estimated eigenvalues, Jacobian approximations, and estimation of a spatial autocorrelation parameter), and illustrates the estimation of the spatial autocorrelation parameter in a spatial autoregressive model specification for cases as large as n = 37,214,101. The principal contribution of this paper is to the implementation of spatial autoregressive model specifications for any size of georeferenced data set. Its specific additions to the literature include (1) new, more efficient estimation algorithms; (2) an approximation of the Jacobian term for remotely sensed data forming incomplete rectangular regions; (3) issues of inference; and (4) timing results.     

Efficient regionalization techniques for socio‐economic geographical units using minimum spanning trees

Regionalization is a classification procedure applied to spatial objects with an areal representation, which groups them into homogeneous contiguous regions. This paper presents an efficient method for regionalization. The first step creates a connectivity graph that captures the neighbourhood relationship between the spatial objects. The cost of each edge in the graph is inversely proportional to the similarity between the regions it joins. We summarize the neighbourhood structure by a minimum spanning tree (MST), which is a connected tree with no circuits. We partition the MST by successive removal of edges that link dissimilar regions. The result is the division of the spatial objects into connected regions that have maximum internal homogeneity. Since the MST partitioning problem is NP‐hard, we propose a heuristic to speed up the tree partitioning significantly. Our results show that our proposed method combines performance and quality, and it is a good alternative to other regionalization methods found in the literature.     

Query processing in spatial databases containing obstacles

Despite the existence of obstacles in many database applications, traditional spatial query processing assumes that points in space are directly reachable and utilizes the Euclidean distance metric. In this paper, we study spatial queries in the presence of obstacles, where the obstructed distance between two points is defined as the length of the shortest path that connects them without crossing any obstacles. We propose efficient algorithms for the most important query types, namely, range search, nearest neighbours, e‐distance joins, closest pairs and distance semi‐joins, assuming that both data objects and obstacles are indexed by R‐trees. The effectiveness of the proposed solutions is verified through extensive experiments.     

Integration of genetic algorithms and GIS for optimal location search

Optimal location search is frequently required in many urban applications for siting one or more facilities. However, the search may become very complex when it involves multiple sites, various constraints and multiple‐objectives. The exhaustive blind (brute‐force) search with high‐dimensional spatial data is infeasible in solving optimization problems because of a huge combinatorial solution space. Intelligent search algorithms can help to improve the performance of spatial search. This study will demonstrate that genetic algorithms can be used with Geographical Information systems (GIS) to effectively solve the spatial decision problems for optimally sitting n sites of a facility. Detailed population and transportation data from GIS are used to facilitate the calculation of fitness functions. Multiple planning objectives are also incorporated in the GA program. Experiments indicate that the proposed method has much better performance than simulated annealing and GIS neighborhood search methods. The GA method is very convenient in finding the solution with the highest utility value.     

Computational reproducibility in geoscientific papers: Insights from a series of studies with geoscientists and a reproduction study

Reproducibility is a cornerstone of science and thus for geographic research as well. However, studies in other disciplines such as biology have shown that published work is rarely reproducible. To assess the state of reproducibility, specifically computational reproducibility (i.e. rerunning the analysis of a paper using the original code), in geographic research, we asked geoscientists about this topic using three methods: a survey (n = 146), interviews (n = 9), and a focus group (n = 5). We asked participants about their understanding of open reproducible research (ORR), how much it is practiced, and what obstacles hinder ORR. We found that participants had different understandings of ORR and that there are several obstacles for authors and readers (e.g. effort, lack of openness). Then, in order to complement the subjective feedback from the participants, we tried to reproduce the results of papers that use spatial statistics to address problems in the geosciences. We selected 41 open access papers from Copernicus and Journal of Statistical Software and executed the R code. In doing so, we identified several technical issues and specific issues with the reproduced figures depicting the results. Based on these findings, we propose guidelines for authors to overcome the issues around reproducibility in the computational geosciences.     

社会经济统计数据空间化研究进展

社会经济统计数据通常是以各级行政区为单位的汇总数据,它虽然能反映统计单元之间的差异但却不能反映统计单元内部的异质性,在实际应用中,无法满足统计任意区域内的社会经济数据的需求,而社会经济统计数据空间化则是有效解决该问题的一条重要途径。本文对现有社会经济统计数据的空间化方法、社会经济统计数据空间化过程所依赖的辅助数据、现有主要的社会经济空间化数据产品进行了归纳总结,并从空间化方法的制约因素和改进方向、新型辅助数据的探索和多源辅助数据的综合利用、高时空分辨率和高精度数据产品研发3个方面展望了社会经济统计数据空间化的未来发展趋势。研究结果可为社会经济统计数据空间化方法的选择与改进、辅助数据的选择与综合利用、社会经济空间化数据产品的选择与改进提供参考。     

Spatial and Longitudinal Patterns in County Age-Specific Net Migration in the United States 1950–2010

Many migration studies describe various counties by adopting a priori county typologies, such as the U.S. Department of Agriculture Economic Research Service county typology, which might not be suitable for identifying different age migration patterns of the U.S. counties. This study employs a spatial clustering method that exhaustively compares all U.S. counties on their age migration similarity and spatial proximity to investigate signature age-specific net migration profiles across six decades of U.S. county age-specific net migration data from 1950 to 2010. All of the six-decade data are integrated into a common spatial county boundary on which counties below a population threshold are merged with the nearest county to mitigate the small population problem in net migration rates. As counties are merged by increasing large population thresholds, the Getis-Ord Gi* spatial autocorrelation statistic is applied to examine how the spatial migration patterns are affected. It is found that U.S. county age-specific net migration profiles exhibit four signature patterns. Although these patterns are persistent across the past six decades, their spatial distributions have experienced dramatic variation. The small population problem in net migration rates affects the extent and location of the significant spatial migration patterns.     

Finding community structure in spatially constrained complex networks

One feature discovered in the study of complex networks is community structure, in which vertices are gathered into several groups where more edges exist within groups than between groups. Many approaches have been developed for identifying communities; these approaches essentially segment networks based on topological structure or the attribute similarity of vertices, while few approaches consider the spatial character of the networks. Many complex networks are spatially constrained such that the vertices and edges are embedded in space. In geographical space, nearer objects are more related than distant objects. Thus, the relations among vertices are defined not only by the links connecting them but also by the distance between them. In this article, we propose a geo-distance-based method of detecting communities in spatially constrained networks to identify communities that are both highly topologically connected and spatially clustered. The algorithm is based on the fast modularity maximisation (CNM) algorithm. First, we modify the modularity to geo-modularity Q^geo by introducing an edge weight that is the inverse of the geographic distance to the power of n. Then, we propose the concept of a spatial clustering coefficient as a measure of clustering of the network to determine the power value n of the distance. The algorithm is tested with China air transport network and BrightKite social network data-sets. The segmentation of the China air transport network is similar to the seven economic regions of China. The segmentation of the BrightKite social network shows the regionality of social groups and identifies the dynamic social groups that reflect users’ location changes. The algorithm is useful in exploring the interaction and clustering properties of geographical phenomena and providing timely location-based services for a group of people.     

Progressive vector compression for high-accuracy vector map data

With the increase in the number of applications using digital vector maps and the development of surveying techniques, a large volume of GIS (geographic information system) vector maps having high accuracy and precision is being produced. However, to achieve their effective transmission while preserving their high positional quality, these large amounts of vector map data need to be compressed. This paper presents a compression method based on a bin space partitioning data structure, which preserves a high-level accuracy and exact precision of spatial data. To achieve this, the proposed method a priori divides a map into rectangular local regions and classifies the bits of each object in the local regions to three types of bins, defined as category bin (CB), direction bin (DB), and accuracy bin (AB). Then, it encodes objects progressively using the properties of the classified bins, such as adjacency and orientation, to obtain the optimum compression ratio. Experimental results verify that our method can encode vector map data constituting less than 20% of the original map data at a 1-cm accuracy degree and that constituting less than 9% at a 1-m accuracy degree. In addition, its compression efficiency is greater than that of previous methods, whereas its complexity is lower for close to real-time applications.     

A modified binary space partitioning tree for geographic information systems

We present a reactive data structure, that is, a spatial data structure with detail levels. The two properties, spatial organization and detail levels, are the basis for a geographic information system (GIS) with a multi-scale database. A reactive data structure is a novel type of data structure catering to multiple detail levels with rapid responses to spatial queries. It is presented here as a modification of the binary space partitioning tree that includes the levels of detail. This tree is one of the few spatial data structures that does not organize space in a rectangular manner. A prototype system has been implemented. An important result of this implementation is that it shows that binary space partitioning trees of real maps have O(n) storage space complexity in contrast to the theoretical worst case O(n² ), with n the number of line segments in the map.     

Multi-objective spatially constrained clustering for regionalization with particle swarm optimization

Regionalization is an important part of the spatial analysis process, and the solution should be contiguity-constrained in each region. In general, several objectives need to be optimized in practical regionalization, such as the homogeneity of regions and the heterogeneity among regions. Therefore, multi-objective techniques are more suitable for solving regionalization problems. In this paper, we design a multi-objective particle swarm optimization algorithm for solving regionalization problems. Towards this goal, a novel particle representation for regionalization is proposed, which can be expressed in continuous space and has flexible constraints on the number of regions. In the process of optimization, a contiguous-region method is designed that satisfies the constraints and improves the efficiency. The decision solution is selected in the Pareto set based on a trade-off between the objective functions, and the number of regions can be automatically determined. The proposed method outperforms six regionalization algorithms in terms of both the number and the quality of the solutions.     

Mining urban land-use patterns from volunteered geographic information by means of genetic algorithms and artificial neural networks

In the context of OpenStreetMap (OSM), spatial data quality, in particular completeness, is an essential aspect of its fitness for use in specific applications, such as planning tasks. To mitigate the effect of completeness errors in OSM, this study proposes a methodological framework for predicting by means of OSM urban areas in Europe that are currently not mapped or only partially mapped. For this purpose, a machine learning approach consisting of artificial neural networks and genetic algorithms is applied. Under the premise of existing OSM data, the model estimates missing urban areas with an overall squared correlation coefficient (R ²) of 0.589. Interregional comparisons of European regions confirm spatial heterogeneity in the model performance, whereas the R ² ranges from 0.129 up to 0.789. These results show that the delineation of urban areas by means of the presented methodology depends strongly on location.     

General multidimensional cloud model and its application on spatial clustering in Zhanjiang, Guangdong

Traditional spatial clustering methods have the disadvantage of “hardware division”, and can not describe the physical characteristics of spatial entity effectively. In view of the above, this paper sets forth a general multi-dimensional cloud model, which describes the characteristics of spatial objects more reasonably according to the idea of non-homogeneous and non-symmetry. Based on infrastructures’ classification and demarcation in Zhanjiang, a detailed interpretation of clustering results is made from the spatial distribution of membership degree of clustering, the comparative study of Fuzzy C-means and a coupled analysis of residential land prices. General multi-dimensional cloud model reflects the integrated characteristics of spatial objects better, reveals the spatial distribution of potential information, and realizes spatial division more accurately in complex circumstances. However, due to the complexity of spatial interactions between geographical entities, the generation of cloud model is a specific and challenging task.     

广义多维云模型及在空间聚类中的应用

传统的空间聚类方法难于脱离"硬划分"的束缚,且不能有效描述空间对象的复杂特征.一维云模型无法准确反映现实世界的多属性特征.简单的数据融合丢失了空间对象的必要信息.标准二维云模型克服了一维云的不足,但是在模拟复杂地理现象的非齐性和非对称性方面显得捉襟见肘.基于以上考虑,提出了广义多维云模型,以分段特性来体现空间对象的综合特征,并推导出模型的数学表达式.在实证研究的基础上,从空间聚类的隶属程度空间分布特征、与模糊C均值的对比研究及与住宅地价的耦合分析三个视角,详实解读了聚类结果.分析发现,广义多维云模型更能体现空间对象的综合特征,空间聚类结果能够反映出空间分布的潜在信息.更为准确的实现了复杂情况下的空间划分.该模型在刻画地理现象中更为合理,但由于地理实体的空间作用极其复杂.建立模型是一项既具体又充满挑战的任务.     

Multi-level method for discovery of regional co-location patterns

Regional co-location patterns represent subsets of feature types that are frequently located together in sub-regions in a study area. These sub-regions are unknown a priori, and instances of these co-location patterns are usually unevenly distributed across a study area. Regional co-location patterns remain challenging to discover. This study developed a multi-level method to identify regional co-location patterns in two steps. First, global co-location patterns were detected, and other non-prevalent co-location patterns were identified as candidates for regional co-location patterns. Second, an adaptive spatial clustering method was applied to detect the sub-regions where regional co-location patterns are prevalent. To improve computational efficiency, an overlap method was developed to deduce the sub-regions of (k + 1)-size co-location patterns from the sub-regions of k-size co-location patterns. Experiments based on both synthetic and ecological data sets showed that the proposed method is effective in the detection of regional co-location patterns.     

线性抽样及分形理论在景观异质性研究中的应用

景观异质性是景观生态学研究的核心,对景观格局、动态和功能具有决定作用。将线性抽样与分形理论相结合的方法应用于景观空间异质性的表达中,相比于传统方法,可以定量表达景观类型在空间序列中的组合规律,而该组合规律可以作为指标来测度景观空间异质性的高低。景观类型在空间序列中的组合越复杂,则景观的空间异质性越高。该方法以景观类型空间序列的线形图像为基础,利用分形理论计算线形图像的分维,以分维数值的大小来表达景观空间异质性的高低。但样线的布设方法、分维计算方法以及景观分类系统的不同都会对分维数值产生影响。以妫水河流域为试验区,对该方法的适用性进行验证,结果表明,该方法可以有效表达景观空间异质性的高低。     

Network-constrained bivariate clustering method for detecting urban black holes and volcanoes

ABSTRACT

Urban black holes and volcanoes are typical traffic anomalies that are useful for optimizing urban planning and maintaining public safety. It is still challenging to detect arbitrarily shaped urban black holes and volcanoes considering the network constraints with less prior knowledge. This study models urban black holes and volcanoes as bivariate spatial clusters and develops a network-constrained bivariate clustering method for detecting statistically significant urban black holes and volcanoes with irregular shapes. First, an edge-expansion strategy is proposed to construct the network-constrained neighborhoods without the time-consuming calculation of the network distance between each pair of objects. Then, a network-constrained spatial scan statistic is constructed to detect urban black holes and volcanoes, and a multidirectional optimization method is developed to identify arbitrarily shaped urban black holes and volcanoes. Finally, the statistical significance of multiscale urban black holes and volcanoes is evaluated using Monte Carlo simulation. The proposed method is compared with three state-of-the-art methods using both simulated data and Beijing taxicab spatial trajectory data. The comparison shows that the proposed method can detect urban black holes and volcanoes more accurately and completely and is useful for detecting spatiotemporal variations of traffic anomalies.     

A comparative analysis of DEM‐based models to estimate the solar radiation in mountainous terrain

Daily solar radiation estimates of four up‐to‐date solar radiation models (Solar Analyst, r.sun, SRAD and Solei‐32), based on a digital elevation model (DEM), have been evaluated and compared in a Mediterranean environment characterized by a complex topography. The models' estimates were evaluated against 40 days of radiometric data collected in 14 stations. Analyzed sky conditions ranged from completely overcast conditions to clear skies. Additionally, the role of the spatial resolution of the DEM has been evaluated through the use of two different resolutions: 20 and 100 m. Results showed that, under clear‐sky conditions, the daily solar radiation variability in the study area may be reasonably estimated with mean bias errors under 10% and root mean square error values of around 15%. On the other hand, results proved that the reliability of the estimates substantially decreases under overcast conditions for some of the solar radiation models. Regarding the role of the DEM spatial resolution, results suggested that the reliability of the estimates for complex topography areas under clear‐sky conditions improves using a higher spatial resolution.     

Visualizing and quantifying the movement of vegetative drought using remote-sensing data and GIS

Remote-sensing-based drought monitoring methods provide fast and useful information for a sustainable management strategy of drought impact over a region. Common pixel-based monitoring methods are limited in the analysis of the dynamics of this impact at regional scale. For instance, these hardly allow us to quantify the movement of drought in space and time and to compare drought with rainfall deficits without losing the variability of these events within a region. This study proposed an object-based approach that allowed us to visualize and quantify the spatio-temporal movement of drought impact on vegetation, called vegetative drought, in a region. The GIS software Dynomap was used to extract and track objects. Measures of distance and angle were used for determining the speed and direction of vegetative drought and rainfall deficit objects, calculated from the National Oceanic and Atmospheric Administration's (NOAA's) normalized difference vegetation index and rainfall estimates data. The methods were applied to the two rainy seasons during the drought year 1999 in East Africa. Results showed that vegetative drought objects moved into the southwestern direction at an average angle of??138.5° during the first season and??144.5° during the second season. The speed of objects varied between 38 km dekad^?1 and 185 km dekad^?1 during the first season and between 33 km dekad^?1 and 144 km dekad^?1 during the second season, reflecting the rate of spread between dekads. Vegetative drought objects close to rainfall deficit objects showed similar trajectories and sometimes regions overlapped. This indicated that the two events are related. We conclude that a spatiotemporal relationship existed between the two types of events and that this could be quantified.     

Image‐based quality assessment of road databasesX

In this paper an approach to the automatic quality assessment of existing geo‐spatial data is presented. The necessary reference information is derived automatically from up‐to‐date digital remotely sensed images using image analysis methods. The focus is on the quality assessment of roads as these are among the most frequently changing objects in the landscape. In contrast to existing approaches for quality control of road data, the data to be assessed and the objects extracted from the images are modelled and processed together. A geometric‐topologic relationship model for the roads and their surroundings is defined. Context objects such as rows of trees support the quality assessment of road vector data as they may explain gaps in road extraction. The extraction and explicit incorporation of these objects in the assessment of a given road database give stronger support for or against its correctness.

During the assessment existing relations between road objects from the database and extracted objects are compared to the modelled relations. The certainty measures of the objects are integrated into this comparison. Normally, more than one extracted object gives evidence for a road database object; therefore, a reasoning algorithm which combines evidence given by the extracted objects is used. If the majority of the total evidence argues for the database object and if a certain amount of this database object is covered by extracted objects, the database object is assumed to be correct, i.e. it is accepted, otherwise it is rejected. The procedure is embedded into a two‐stage graph‐based approach which exploits the connectivity of roads and results in a reduction of false alarms. The algorithms may be incorporated into a semi‐automatic environment, where a human operator only checks those objects that have been rejected.

The experimental results confirm the importance of the employed advanced statistical modelling. The overall approach can reliably assess the roads from the given database, using road and context objects which have been automatically extracted from remotely sensed imagery. Sensitivity analysis shows that in most cases the chosen two‐stage graph‐approach reduces the number of false decisions. Approximately 66% of the road objects have been accepted by the developed approach in an extended test area, 1% has been accepted though incorrect. Those false decisions are mainly related to the lack of modelling road junction areas.