中图分类号: P208
文献标识码: A
文章编号: 1000-0690(2016)12-1843-07
收稿日期: 2015-11-9
修回日期: 2016-03-25
网络出版日期: 2016-12-20
版权声明: 2016 《地理科学》编辑部 本文是开放获取期刊文献,在以下情况下可以自由使用:学术研究、学术交流、科研教学等,但不允许用于商业目的.
基金资助:
作者简介:
作者简介:王结臣(1973-),男,安徽太湖人,教授,博导,主要研究GIS理论与应用、地理空间分析。E-mail:wangjiechen@nju.edu.cn
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摘要
运用Ripley’s K函数的相关理论,以南京市ATM网点为研究对象,分别从平面与网络空间两种视角,在中心城区范围与主城区范围两种空间尺度上,通过单变量
关键词:
Abstract
Since distributions of many types of urban objects are not random but in some particular patterns, analyzing and revealing the spatial distribution pattern of these points in urban space are essential to understand social, economic and geographical factors behind the distributions, and analysis results are conductive to wide applications such as facility layout and aided decision support. In point pattern analysis, the results may be biased by merely calculating the nearest neighbor distance. The Ripley’s K-function was therefore proposed with advantages of considering the distance between any pair of points. Because many urban points associated with human activities are constrained by road networks, a network K-function, as an extension of traditional planar K-function, is then presented by applying a network distance, i.e., the shortest path distance between any pair of two points. In this article, the Ripley’s K-function was applied to analyze the spatial distribution characteristics of ATMs in Nanjing City. First of all, we used both planar univariate K-function and network univariate K-function to analyze the distribution pattern of ATMs at spatial scales of downtown areas and main urban districts. Then we used planar bivariate K-function and network bivariate K-function to investigate the spatial correlation between ATMs and metro stations in main urban districts. Local bivariate (cross) K-functionwas finally applied to explore the impact of metro stations on the ATMs in local areas. The results show that ATMs are highly clustered in both planar and network space and the cluster characteristic is more significant in downtown areas than in main urban areas. Besides, ATMs and metro stations are highly correlated in the study area. With the increase of the measuring distance, the relationship between ATM and metro station distributions shows more obvious characteristic of spatial aggregation within a certain distance. In the analysis of local cross K-function method, ATMs are clustered with metro stations in downtown areas while there is no significant clustering characteristic between ATMs and metro stations on the outskirts. It implies that the distribution of ATMs is mainly determined by the regional commercial development. In addition, for spatial pattern analysis on point objects distributed along road networks, network K-function method is more practical than planar K-function in terms of revealing appropriate distribution pattern and relationship between two types of point objects.
Keywords:
城市中很多事件的发生地点往往不是随机分布,而是在特定空间呈现一定的集聚状态。如果将事件抽象成点,则可应用空间点模式的相关理论进行分析。
城市ATM网点作为重要的便民设施,数量巨大并广泛服务于商业及购物消费场所,然而其空间分布模式等信息仍有待研究挖掘。本文针对南京市ATM网点,基于平面和网络空间两种视角,分别采用单变量、双变量以及局部
对实际的地理对象点集进行集聚模式分析时,仅仅使用最邻近距离会掩盖结果中的其他模式。为了解决这一问题,Ripley对事件之间的所有距离进行研究,提出了
在“完全空间随机”(Completely Spatial Random, CSR)的零假设条件下,即观测模式与随机模式之间不存在统计上显著的差异[13],很容易确定
作为对平面
式中,
接下来考虑
为了检验零假设,需要计算
本研究采用的数据包括:南京市主城区范围及中心城区边界范围、道路网络、各大中型银行ATM网点数据等。主城区边界是以南京市区影像图(2012版)为底图,以绕城公路和长江岸线为界通过屏幕数字化方法获取的,如图1中外边界所示;中心城区范围主要参照南京城墙分布范围绘制形成,即图1中内部区域的边界。对影像图上标注的主要道路经矢量化和拓扑构建,获得主城区的简单道路网络模型(不考虑道路等级、通行状况等)。银行ATM数据主要选择了南京市主城区内网点数量超过50的大中型商业银行ATM网点,包括工商银行、建设银行等合计749个ATM网点,网点分布与数量见图1与表1。
表1 银行ATM网点数量统计
Table 1 Statistics of ATMs in Nanjing City
银行名称 | ATM网点数量 | 银行名称 | ATM网点数量 |
---|---|---|---|
中国工商银行 | 130 | 中国邮政储蓄银行 | 96 |
中国建设银行 | 117 | 中国银行 | 86 |
中国农业银行 | 102 | 中国民生银行 | 62 |
交通银行 | 97 | 招商银行 | 59 |
在南京市主城区范围内,ATM网点的单变量
图2 ATM网点单变量K函数分析
Obs曲线为观测的
a. 主城区平面; b.主城区网络; c.中心城区平面; d.中心城区网络
Fig.2 Univariate K function analysis for ATMs
在中心城区范围内,ATM网点的平面和网络单变量
总体而言,平面
ATM网点在空间上的集聚规律主要与商业设施的分布相关。对于商业中心而言,为有效吸引客流量,更好地实现其商业效益,在进行区位规划时最看重的因素之一就是交通可达性,因此商业中心一般选址于交通便捷的城市道路主干道上。南京市于2005年开始铺设并逐步完善城市轨道交通线路网络,沿路所设的地铁站点位置也主要参考了商业中心所在的位置,因此地铁站点与商业中心之间存在较大程度上的关联。为此,我们进一步针对ATM网点与地铁站点之间关系进行双变量
平面和网络双变量
图3 ATM网点与地铁站点的双变量K函数分析
a.平面; b.网络 (
Fig.3 Bivariate cross-K function analysis along ATM networks and metro stations
局部
图4 单个地铁站点的局部网络
a.新街口; b.奥体东站; c.孝陵卫; d.迈皋桥 (
Fig.4 The local K function for single metro station
从图4可以看出,位于不同位置的地铁站点表现出来的分布模式有较大差异。其中,位于城区中心地带的新街口地铁站点,其局部
综合平面与网络的双变量
本文以南京市ATM网点为研究对象,在平面和网络空间两种视角下,采用单变量和双变量
The authors have declared that no competing interests exist.
[1] |
Methods for analysing spatial processes of several types of points [J]. .
Two approaches are described to the analysis of spatial patterns consisting of several types of points. The first approach uses a method of asymptotically unbiased estimation of the second moment distribution; the second uses methods based on regions of empty space in the patterns. Some distributional results are given in each case, and a method of Monte Carlo testing conditional on the marginal structure is described. The methods are illustrated by being applied to some physiological data.
|
[2] |
Ripley’s K function [J]. ,https://doi.org/10.1002/9780470057339.var046 URL [本文引用: 2] 摘要
Ripley's K function summarizes spatial point process data. It can be used to describe a set of locations, test hypotheses about patterns, and estimate parameters in a spatial point process model. For a stationary point process, K ( t ) is the expected number of additional points within distance t of a focal point divided by the intensity of the process. A univariate version is used for one set of locations and a multivariate version is used when points can be labeled by a small number of groups. This article reviews the properties of Ripley's K function and two related functions, then illustrates the computation and interpretation using data on the locations of trees in a swamp hardwood forest.
|
[3] |
Spatial statistics [M]. , |
[4] |
基于Ripley’s K函数的武汉市景观格局特征及其变化 [J]. ,
基于1987、1996和2007年武汉市tm遥感影像,应用点格局分析方法之一的ripley-k函数,分析了武汉市市域景观格局的特征及其变化.结果表明:1987—2007年间,耕地是武汉市的景观基质,而林地、水体、草地、城乡建设用地和其他未利用地则以斑块或廊道的形式镶嵌其中;林地、水体、草地和城乡建设用地在所有研究尺度下均呈现出显著的聚集空间格局,且林地、草地和城乡建设用地的空间聚集性强于水体;耕地在小尺度下呈现出聚集的空间格局,随着尺度的增大,逐渐变为随机、均匀的空间格局.研究期间,武汉市林地、城乡建设用地面积逐次增大,水体、草地和耕地面积逐次减少;各景观类型的空间格局特征也发生了改变,总体表现为林地和城乡建设用地空间聚集度降低,分布的均匀程度增加,而草地、水体和耕地的空间分布变得更加不均匀,聚集程度增加.与样方法、样线(带)法相比,利用样点分析景观格局具有简单、准确、易用等优点.ripleyk函数是多尺度景观格局分析的有效手段,是景观指数法的支持和补充.
Characteristics and changes of landscape pattern in Wuhan City based on Ripley’s K function .,
基于1987、1996和2007年武汉市tm遥感影像,应用点格局分析方法之一的ripley-k函数,分析了武汉市市域景观格局的特征及其变化.结果表明:1987—2007年间,耕地是武汉市的景观基质,而林地、水体、草地、城乡建设用地和其他未利用地则以斑块或廊道的形式镶嵌其中;林地、水体、草地和城乡建设用地在所有研究尺度下均呈现出显著的聚集空间格局,且林地、草地和城乡建设用地的空间聚集性强于水体;耕地在小尺度下呈现出聚集的空间格局,随着尺度的增大,逐渐变为随机、均匀的空间格局.研究期间,武汉市林地、城乡建设用地面积逐次增大,水体、草地和耕地面积逐次减少;各景观类型的空间格局特征也发生了改变,总体表现为林地和城乡建设用地空间聚集度降低,分布的均匀程度增加,而草地、水体和耕地的空间分布变得更加不均匀,聚集程度增加.与样方法、样线(带)法相比,利用样点分析景观格局具有简单、准确、易用等优点.ripleyk函数是多尺度景观格局分析的有效手段,是景观指数法的支持和补充.
|
[5] |
Market area delimitation within networks using geographic information systems [J]. ,
Abstract Market area delimitation is important for assessing a commercial facility's performance or for identifying candidates for new facility location. However, current market area delimitation methods rely on an unrealistic representation of space as planar and isotropic. This paper develops generic procedures for conducting market area delimitation within street network structures using geographic information systems (GIS). First, this paper formulates network based versions of the Huff visit probability model. Then, restatement of these models in the format of relational databases and structured query language (SQL) provides a generic algorithm that bridges the gap between mathematics and the capabilities of a computerized information system. Finally, this paper discusses general implementation issues and a case study using a commercial GIS package. -Author
|
[6] |
The K-function method on a network and its computational implementation [J]. ,https://doi.org/10.1111/j.1538-4632.2001.tb00448.x URL [本文引用: 1] 摘要
Abstract This paper proposes two statistical methods, called the network K-function method and the network cross K-function method, for analyzing the distribution of points on a network. First, by extending the ordinary K-function method defined on a homogeneous infinite plane with the Euclidean distance, the paper formulates the K-function method and the cross K-function method on a finite irregular network with the shortest-path distance. Second, the paper shows advantages of the network K-function methods, such as that the network K-function methods can deal with spatial point processes on a street network in a small district, and that they can exactly take the boundary effect into account. Third, the paper develops the computational implementation of the network K-functions, and shows that the computational order of the K-function method is O(n2Q log nQ) and that of the network cross K-function is O(nQ log U3Q), where nQ is the number of nodes of a network.
|
[7] |
Spatial Statistics along Networks: Statistical and Computational Methods [M]. , |
[8] |
On the false alarm of planar K-function when analyzing urban crime distributed along streets [J]. ,https://doi.org/10.1016/j.ssresearch.2006.05.003 URL [本文引用: 1] 摘要
Abstract Many social and economic activities, especially those in urban areas, are subject to location restrictions imposed by existing street networks. To analyze the spatial patterns of these urban activities, the restrictions imposed by the street networks need to be taken into account. K-function is a method commonly used for general point pattern analysis as well as crime pattern study. However, applying the planar K-function to analyze the spatial autocorrelation patterns of urban activities that are typically distributed along streets could result in false alarm problems. Depending on the nature of the urban street networks and the distribution of the urban activities, either positive or negative false alarm might be introduced. Acknowledging that many urban crimes are typically distributed along streets, this paper compares the traditional planar K-function with a network K-function for crime pattern analysis. The patterns of vehicle thefts in San Antonio, Texas are examined as a case study.
|
[9] |
Calculating Intraurban Agglomeration of Economic Units with Planar and Network K-Functions: A Comparative Analysis [J]. ,https://doi.org/10.1080/02723638.2013.778655 URL [本文引用: 1] 摘要
ABSTRACT According to recent research, one of the most promising strategies for intraurban job growth lies promoting localized clusters that produce goods and services which are primarily sold within a single city, metropolitan area, or urban region. However, in order to design urban policies to create or reinforce local clusters, the first challenge is to measure in a reliable way the clustering tendencies of different kinds of economic units in intraurban space. The aim is to compare the similarities and differences in results obtained from two methods designed to measure global clustering tendencies (the planar and network K-functions) in terms of characterization, scale, and intensity of intraurban localization patterns for tertiary economic units in a Latin American metropolis. It is concluded that the network K-function is a more appropriate method for measuring agglomeration patterns, scale, and intensity at the intra-urban level.
|
[10] |
基于网络K函数法的地理对象分布模式分析——以香港岛餐饮业空间格局为例 [J]. ,https://doi.org/10.7702/dlydlxxkx20130502 URL [本文引用: 1] 摘要
很多地理对象的空间分布与空间上呈现网状结构的地理现象高度相 关,分析这些地理对象的分布模式,在地理研究中有重要意义.该文采用由平面空间扩展到网状结构空间的网络K函数法,以香港岛餐饮业地理空间格局为例开展研 究.应用单变量K函数法分析餐饮店在网状结构空间中的分布模式,应用双变量交叉K函数法分析餐饮店分布是否受交通站点及旅游景点影响,并对不同尺度下餐饮 店地理选址和空间分布规律进行探索与分析.
Spatial Pattern Analysis of Geographic Feature Using Network K—Function Methods with a Case Study of Restaurant Distribution in Hong Kong Island. Geography and ,https://doi.org/10.7702/dlydlxxkx20130502 URL [本文引用: 1] 摘要
很多地理对象的空间分布与空间上呈现网状结构的地理现象高度相 关,分析这些地理对象的分布模式,在地理研究中有重要意义.该文采用由平面空间扩展到网状结构空间的网络K函数法,以香港岛餐饮业地理空间格局为例开展研 究.应用单变量K函数法分析餐饮店在网状结构空间中的分布模式,应用双变量交叉K函数法分析餐饮店分布是否受交通站点及旅游景点影响,并对不同尺度下餐饮 店地理选址和空间分布规律进行探索与分析.
|
[11] |
基于边际K函数的长三角地区城市群经济空间划分 [J]. ,https://doi.org/10.11821/dlxb201504002 URL [本文引用: 1] 摘要
基于空间点模式分析的Ripley's K函数,结合微观经济学的边际分析法,通过集聚度和边际集聚两个指标,从理论上探索城市群集聚效应的定量测度方法,提出一种城市群的经济空间划分方法。本 文的不同在于,多尺度估算城市的集聚度和边际集聚,以城市的边际集聚极值点时的城市区域布局模式为最优,据此划分城市群的经济空间,并以长江三角洲地区为 例,对本文提出的方法进行实证。研究结果表明:①城市的集聚度估计显示,长三角地区2010年城市空间布局为随机分布型,但随着观测尺度的增加,城市的集 聚度呈快速上升趋势。②边际集聚估计揭示,当城市区位和城市规模的集聚尺度分别为173 km和185 km时,城市区位或规模的集聚效应达到峰值,此时长三角地区城市空间布局出现最优模式。③空间聚类分析展示,在城市区域布局的最优空间模式下,长三角地区 呈现“中心—外围”的经济空间结构,高集聚度子群是区域经济发展中心,全部位于上海经济辐射圈,而低集聚度子群是外围欠发达地区,全部位于区际行政边界, 暗示边际负效应仍阻碍着地区内外人员的往来。
Dividing economic space into urban agglomerations usingthe marginal K-function:A case study of the Yangtze River Delta region . ,https://doi.org/10.11821/dlxb201504002 URL [本文引用: 1] 摘要
基于空间点模式分析的Ripley's K函数,结合微观经济学的边际分析法,通过集聚度和边际集聚两个指标,从理论上探索城市群集聚效应的定量测度方法,提出一种城市群的经济空间划分方法。本 文的不同在于,多尺度估算城市的集聚度和边际集聚,以城市的边际集聚极值点时的城市区域布局模式为最优,据此划分城市群的经济空间,并以长江三角洲地区为 例,对本文提出的方法进行实证。研究结果表明:①城市的集聚度估计显示,长三角地区2010年城市空间布局为随机分布型,但随着观测尺度的增加,城市的集 聚度呈快速上升趋势。②边际集聚估计揭示,当城市区位和城市规模的集聚尺度分别为173 km和185 km时,城市区位或规模的集聚效应达到峰值,此时长三角地区城市空间布局出现最优模式。③空间聚类分析展示,在城市区域布局的最优空间模式下,长三角地区 呈现“中心—外围”的经济空间结构,高集聚度子群是区域经济发展中心,全部位于上海经济辐射圈,而低集聚度子群是外围欠发达地区,全部位于区际行政边界, 暗示边际负效应仍阻碍着地区内外人员的往来。
|
[12] |
Spatial distributions of tree species in a subtropical forest of China [J]. ,https://doi.org/10.1111/j.1600-0706.2009.16753.x URL [本文引用: 1] 摘要
ABSTRACT The spatial dispersion of individuals in a species is an important pattern that is controlled by many mechanisms. In this study we analyzed spatial distributions of tree species in a large-scale (20 ha) stem-mapping plot in a species-rich subtropical forest of China. O-ring statistic was used to measure spatial patterns of species with abundance >10. 惟0鈥10, the mean conspecific density within 10 m of a tree, was used as a measure of the intensity of aggregation of a species. Our results showed: (1) aggregated distribution was the dominant pattern in the plot. The percentage of aggregated species decreased with increased spatial scale. (2) The percentages of significantly aggregated species decreased from abundant to intermediate and to rare species. Rare species was more strongly aggregated than common species. Aggregation was weaker in larger diameter classes. (3) Seed traits determined the spatial patterns of trees. Seed dispersal mode can influence spatial patterns of species, with species dispersed by both modes being less clumped than species dispersed by animal or wind, respectively. Considering these results, we concluded that seed dispersal limitation, self-thinning and habitat heterogeneity primarily contributed to spatial patterns and species coexistence in the forest.
|
[13] |
Extending point pattern analysis for objects of finite size and irregular shape [J]. ,https://doi.org/10.1111/j.1365-2745.2006.01113.x URL [本文引用: 1] 摘要
1 We use a grid- and simulation-based approach to extend point pattern analysis to deal with plants of finite size and irregular shape, and compare the results of our approach with that of the conventional point approximation. The plants are approximated by using an underlying grid and may occupy several adjacent grid cells depending on their size and shape. Null models correspond to that of point pattern analysis but need to be modified to account for the finite size and irregular shape of plants.
|
[14] |
Rings, circles, and null-models for point pattern analysis in ecology [J]. , |
[15] |
Simple Monte Carlo tests for spatial pattern [J]. ,https://doi.org/10.2307/2346974 URL [本文引用: 1] 摘要
ABSTRACT The Monte Carlo approach to testing a simple null hypothesis is reviewed briefly and several examples of its application to problems involving spatial distributions are presented. These include spatial point pattern, pattern similarity, space-time interaction and scales of pattern. The aim is not to present specific “recommended tests” but rather to illustrate the value of the general approach, particularly at a preliminary stage of analysis.
|
[16] |
Spatial analysis of roadside Acacia populations on a road network using the network K-function [J]. ,https://doi.org/10.1023/B:LAND.0000036114.32418.d4 URL [本文引用: 1] 摘要
Spatial patterning of plant distributions has long been recognised as being important in understanding underlying ecological processes. Ripley’s K-function is a frequently used method for studying the
|
[17] |
A computational method for market area analysis on a network [J]. ,https://doi.org/10.1111/j.1538-4632.1996.tb00939.x URL [本文引用: 1] 摘要
ABSTRACT This paper shows a computational method for market area analysis assuming that stores and consumers are distributed over a network and the distance between two points on the network is given by the route distance. First, we consider five basic questions often raised in market area analysis, and show a general method, called the network transformation method, that gives an intuitive way of looking at computational methods for solving these questions. Second, assuming that consumers follow the Huff model, we consider four questions concerning market area delineation and market potential often discussed in market area analysis in practice. We show that the network transformation method is also useful to develop computational methods for solving these questions. One of the notable results is that market area delineation of the Huff model (which is analytically difficult to obtain on a plane) can be exactly obtained on a network.
|
[18] |
基于网络K函数的西双版纳人工林空间格局及动态 [J]. ,
Abstract 区域植被格局的分布特征受诸多要素影响,但其空间格局和动态具有一定规律或自相关性,道路网络作为景观中显著的人工线性要素,在很大程度上影响着区域的植被格局特征,特别是人工植被的分布特征。运用网络K函数,分析了道路网络和人工林空间格局分布的相互关系,并且用二元网络K函数研究了人工林扩展对针叶林和阔叶林的影响。结果表明:人工林在1970—2000年间种群分布格局有非常明显的变化,特别是从1990到2000年,种群面积不断扩大,主要从北部地区扩展到西北和东南地区。1970—1990年人工林扩展主要集中在低海拔的道路网络附近,沿道路网络呈现明显的集聚分布,公路效应明显。但后期逐渐向距公路较远、海拔较高的地区扩展,到2000年在大尺度下人工林斑块呈显著随机分布。同时,人工林面积的增长对针叶林影响显著,对阔叶林有影响但是并不显著。二元网络K函数表明,在1970到1990年人工林与针叶林沿道路网络在小尺度为负关联,在局部地区存在着竞争,但在大尺度上对环境条件的要求具有一致性为正关联。到2000年,在大尺度上人工林与针叶林的种群分布格局呈显著负相关,人工林面积的不断扩展导致了针叶林面积的下降。
Spatial and dynamic analysis of plantations in Xishuangbanna using network K-function . ,
Abstract 区域植被格局的分布特征受诸多要素影响,但其空间格局和动态具有一定规律或自相关性,道路网络作为景观中显著的人工线性要素,在很大程度上影响着区域的植被格局特征,特别是人工植被的分布特征。运用网络K函数,分析了道路网络和人工林空间格局分布的相互关系,并且用二元网络K函数研究了人工林扩展对针叶林和阔叶林的影响。结果表明:人工林在1970—2000年间种群分布格局有非常明显的变化,特别是从1990到2000年,种群面积不断扩大,主要从北部地区扩展到西北和东南地区。1970—1990年人工林扩展主要集中在低海拔的道路网络附近,沿道路网络呈现明显的集聚分布,公路效应明显。但后期逐渐向距公路较远、海拔较高的地区扩展,到2000年在大尺度下人工林斑块呈显著随机分布。同时,人工林面积的增长对针叶林影响显著,对阔叶林有影响但是并不显著。二元网络K函数表明,在1970到1990年人工林与针叶林沿道路网络在小尺度为负关联,在局部地区存在着竞争,但在大尺度上对环境条件的要求具有一致性为正关联。到2000年,在大尺度上人工林与针叶林的种群分布格局呈显著负相关,人工林面积的不断扩展导致了针叶林面积的下降。
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[19] |
Detecting traffic accident clusters with network kernel density estimation and local spatial statistics: An integrated approach [J]. ,https://doi.org/10.1016/j.jtrangeo.2013.05.009 URL [本文引用: 1] 摘要
Kernel density estimation (KDE) has long been used for detecting traffic accident hot spots and network kernel density estimation (NetKDE) has proven to be useful in accident analysis over a network space. Yet, both planar KDE and NetKDE are still used largely as a visualization tool, due to the missing of quantitative statistical inference assessment. This paper integrates NetKDE with local Moran’I for hot spot detection of traffic accidents. After density is computed for road segments through NetKDE, it is then used as the attribute for computing local Moran’s I. With an NetKDE-based approach, conditional permutation, combined with a 100-m neighbor for Moran’s I computation, leads to fewer statistically significant “high-high” (HH) segments and hot spot clusters. By conducting a statistical significance analysis of density values, it is now possible to evaluate formally the statistical significance of the extensiveness of locations with high density values in order to allocate limited resources for accident prevention and safety improvement effectively.
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