Urban multi-center phenomenon is very common in many countries, which challenges urban models with the assumption of single center. Although there are literatures trying to explain the mechanism of multi-center urban system using models based on multi-center, the lack of empirical research makes the models being questioned. Under the pattern of multi-center, does the traditional classical geographic model like law of distance decay exist? What factors will disturb the model? This study aims to analyze and validate the spatio-temporal discipline of attration and mutual relationship between two commercial centers, based on spatio-temporal data mining of floating cars' GPS data and the recognition of two important commercial centers in Shenzhen City, China. The study reveals that the attraction between two commercial centers shows distinct power function relationship, which validates the law of geographic spatial decay. At the same time, the spatial decay's law shows some local disturbances due to a series of causes, such as the mutual attraction from other important and crowded areas, the influence of infrastructure to accessibility, urban spatial layout factor like landform and humanity factors like consumer behavior and preference etc.

城市与区域多中心化已经成为全球性的现象,作为快速城市化地区,城市新中心建设和多中心现象在中国尤为普遍。把握城市中心发展客观规律,探讨多中心的相互作用关系,将有助于补充传统基于单中心假设的城市空间结构相关理论和模型的研究,同时,对指导城市商业中心选址和城市空间结构规划具有良好的现实意义。以深圳为案例,通过海量浮动车 (FCD) GPS数据的时空挖掘,在识别出深圳市两个重要商业中心的基础上,分析和验证了双商业中心的交通吸引时空规律以及相互作用关系。发现城市商业中心的交通吸引存在显著的幂函数关系,验证了传统的地理空间衰减规律。同时,这种衰减规律受到一系列因素的影响而在局部发生扰动,主要扰动因素包括城市其他人流密集的主要功能区之间的相互吸引、基础设施对可达性的影响、地形地貌等城市空间布局因素和消费者行为、偏好等人文因素等。

Expand intensity index (EII) is an index commonly used to characterize the extent and speed of urban expansion. In other words, it is simply used to describe and analyze the physical spatial change from the perspective of urban area. But this index only represents the result of urban expansion neglecting the feeling of people to space and the underlying mechanisms of urban expansion. Moreover, an in-depth study is ignored on the evolving pattern of urban space and cannot reflect human activities in urban space. This paper presents a new expansion intensity index based on space syntax by considering the driving effect of transport network on urban expansion, namely space syntax expand intensity Index (SS-EII). SS-EII can reflect the syntactic variables about spatial clustering and dispersion and analyze the changes of spatial accessibility. Compared to the conventional expand intensity index, SS-EII not only cares about the result of urban expansion, but also captures the effect of transportation on the pattern and direction of urban expansion as well as the feeling of human to urban space. With Cotton Lake Town in Guangdong Province, China as an example, SS-EII is utilized to compare expansion speeds of built-up areas in different directions. It can be concluded that the result based on SS-EII is consistent to the actual situation of urban expansion and the correlation coefficient with EII is higher than 0.95.

扩张强度指数（Expand Intensity Index, EII）是目前城市扩展数量特征研究的常用指标,用以表征城市扩张程度和速度,但该指标是从城市扩张的结果,即从城市用地面积变化角度对物质空间变化的简单描述与分析,忽略了人在空间中的感受,未能从城市扩张的动因角度揭示城市扩张特征,缺乏对城市外部空间形态演变模式的深入研究,不能反映人在城市扩展空间上的活动。本文从交通网络对城市扩张的驱动作用入手,基于空间句法,提出一种新的扩张强度指数——基于空间句法的扩张强度指数（Space Syntax Expand Intensity Index, SS-EII）,SS-EII包涵可反映空间集聚和离散程度的句法变量,可用于分析空间可达性的变化等情况。与传统扩张强度指数相比,SS-EII是基于空间句法从城市扩张的驱动力方面计算扩张强度,不仅关注城市扩张的结果,同时关注交通对城市扩张模式、方向的导向作用和人主观感知下城市空间的变化。将SS-EII应用于广东省棉湖镇2002-2014年期间的城镇扩展特征分析中,研究结果表明,SS-EII可用于分析比较建成区不同方向的扩张速率与建设状况,其计算结果与棉湖镇建成区实际扩张情况相符,与EII相关度R²达0.95以上。

Polycentric structure is an important method of dispersing urban population, relieving traffic congestion, adjusting the imbalance of job-housing, and dealing with "big city disease". First of all, word vector is used to describe the spatial characteristics and behavior rules of the trajectory big data, and vector operation is used to reflect the correlation between the origin points and destination points of the trajectories. In addition, the spatial grid of Zhengzhou city is divided, the gravity of grid units to mobile targets is measured by using the gravitational model of data field theory, and the recognition of polycentric structure is completed. At last, the interaction rules of the polycentric structure are explored with the assistance of the complex network theory, and the relationships between the polycentric nodes are reflected by the in-and-out intensity, net flow ratio and chain weight. The results show that: (1) The gravity strength of trajectories presents a circular spatial pattern with a strong core and weak peripheries, and the region with high gravity spreads along the main roads. There are significant differences in the unbalanced gravity of trajectories among the identified 21 centers. Urban elements and moving targets spread from the saturated core urban area to the periphery along the main traffic routes. The spatial distribution of polycentric structure presents a typical overflow pattern of dense inside and sparse outside. (2) The regional gravity intensity and interaction frequency of the peripheral sub-centers are low, and the interaction direction mainly goes towards the primary centers in the core urban area. Although the planning prospect of the peripheral centers is broad, due to the late planning, remote location and insufficient supporting facilities, their attraction to the surrounding areas is limited. And it will take a long time to achieve the planning objectives. In order to make the sub-centers decentralize better, it is necessary to strengthen the overall planning and guide the scientific development of the sub-centers. A polycentric structure recognition method and spatial interaction analysis method based on the trajectory gravity of word vector data field are proposed. The trajectory word vector describes the spatial information and travel pattern information in a comprehensive way, the trajectory gravity intensity expressed by the potential value of data field is more accurate, and the polycentric spatial interaction structure analyzed in a complex network is clearer. The evolution mechanism of polycentric structure is presented from the perspective of flow. This is a more suitable polycentric analysis method for trajectory data, which provides a new idea for urban planning.

多中心化是分散城市人口,疏解交通拥堵,调节职住失衡,应对“大城市病”的重要手段。针对轨迹大数据,先利用词向量描述其空间特征和行为规律,再结合数据场理论表达城市区域对轨迹的吸引强度,并完成多中心识别,最后借鉴复杂网络理论对多中心空间交互规律进行探索和挖掘。结果表明：① 郑州市轨迹吸引强度呈核心强、外围弱、沿线蔓延的圈层空间分布形态,识别出的21个多中心轨迹引力差异较大,区域吸引能力不均衡;② 外围次级中心的区域引力强度和交互频次低,交互方向主要指向一级中心,呈现出外溢型多中心结构,为了实现其应有的分散疏解作用,还需加强统筹规划,带动其科学发展。提出基于词向量数据场轨迹引力的多中心识别分析方法,对于轨迹隐含的出行规律描述更加完整,对轨迹引力的表达更准确,从流动角度呈现了多中心的演化机理,为城市规划实践提供了新思路。

Due to the lack of empirical studies of scale variables and distance exponents, the effective application of the gravity model in urban study is challenging. With the development of multi-centralized Chinese cities, the gravity model must be validated because several relevant external conditions have changed. The purpose of this study is to validate Huff's Gravity Model using an individual mobile trajectory of mobile communication user in 2015. We follow Huff's two-step validation method: variable validation and parameter correction. Our main conclusions are as follows. First, attractions of commercial and employment centres conform to the law of the gravity model in which the attraction is proportional to the scale of a centre and inversely proportional to the distance from a centre. Second, in the spatial scale of Shanghai central city with spatial units in a 200-m grid, the mean distance exponent for commercial centres is 2.5 and that for employment centres is 3.0. The distance decay for commuting is greater than that for shopping trips, which means commuting is more sensitive to distance. Third, the gravity model can be used to predict the influence areas of adjusted commercial and employment centres based on validated variables and corrected parameters. Our results indicate that the prediction accuracies can reach 78.5% and 71.9% for the commercial and employment centres, respectively. The prediction accuracy for employment centres is slightly lower. This is because the attraction of employment centres is influenced not only by distance but also by factors such as family and housing prices, which will affect the prediction results. Lastly, in this study, we verify the spatial stratified heterogeneity of distance decay and determine that the distance exponent is not a unique constant because it has different values in different areas. Factors such as accessibility, distance to each centre, distance to a subway station and population density will affect distance decay.

长期以来由于规模变量、距离衰减系数取值缺乏依据,引力模型在城市研究中的应用容易受到质疑,加之中国城市的多中心化使得模型应用的外部条件发生改变,模型验证工作的必要性再次显现。本文使用2015年移动通信用户的个体移动轨迹数据,使用Huff当年的验证方法,通过变量检验、参数校正两个步骤,验证Huff的引力模型。研究发现：① 城市内部商业中心和就业中心的吸引力与中心的规模呈正比,与距中心的距离呈反比,符合引力模型规律。② 在上海中心城区空间尺度、200 m网格空间单元下,商业中心吸引力的距离衰减系数平均值为2.5,就业中心吸引力的距离衰减系数平均值为3.0,表明居民就业通勤对距离更加敏感,距离衰减比购物出行更加显著。③ 经变量检验、参数校正后的引力模型可用于对商业中心、就业中心优化调整后的势力范围进行预测,预测准确率可分别达到78.5%和71.9%。就业中心势力范围预测准确性略低,这是由于就业中心吸引力衰减除受距离影响外,还受家庭、房价等因素影响,会对预测结果产生扰动。最后,研究还证实了距离衰减系数存在空间分层异质性：距离衰减系数不是唯一值,受道路可达性、至就业（商业）中心距离、至地铁站距离、人口密度影响,不同地区的距离衰减系数存在较显著差异。

Before the emergence of modern transport modes, the traditional road infrastructure and road transport (carriage) was a widely used land transport mode, and became a major approach to complete the nationwide social and economic exchanges throughout all historical periods. But the long-term evolution of transport infrastructure is an important studying topic, which has received little research attention. Under this background, this paper, choosing the national road as the studying subject, and taking 3500 years from 1600 BC to 1900 AD as the studying period and designing the model of shortest distance path, aims to examine the developing regularities of traditional road network in a long-term dimension, involving the expansion of spatial network, network structure and accessibility, and developing dynamics. Our analysis reveals long-term regularities: the continuously expanding road network, which experiences four phases with different developing features and spatial pattern, follows a path of inland expansion especially to border areas and brings the peripheral region much closer to the core area of China's homeland, but its coverage and accessibility is characterized by 'concentric rings' and 'core-peripheral' configuration, and the middle and lower reaches of the Yellow River has been the core region. The development and evolution of traditional road network has close relationship with the national defense and warfare, centralization of national power around the capital, homeland governance, the postal transport, and specialized cargo and trade transport. This research pays attention to a long-term pattern and attempts to fill the gap of extant literatures, to deeply and better understand the evolving regularities of transport infrastructure network and China's homeland development.

现代交通方式产生之前,传统道路设施及道路运输是主要交通方式,成为各历史时期社会经济联系的主要途径,本文力图探究道路设施网络的长期演化规律。为此,本文以具有国家意义的“国道”为研究对象,以商周以来3500年为时间尺度,设计了道路网发育指标和可达性—最短距离模型;刻画了中国道路网的拓展和演化过程,总结各时期的发展特征、空间格局及模式,揭示演变规律;评价了道路网的结构特征、成熟水平与连通性,分析各时期的可达性格局及演变,识别可达性优势与劣势区域;考察了道路网演变与中国社会—经济系统的关系机制。研究发现,中国道路网遵循了“内陆扩张”模式尤其从内陆向边疆拓展,可达性形成明显的“核心—边缘”中心圈层格局,并同国防建设和国家集权、邮驿系统、贸易运输有紧密关系。