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Yanguang Chen

Publications and source records attributed to Yanguang Chen.

At least 37 records · Page 2Linked to original sources
arXiv2022

Reconstruction and Normalization of Anselin's Local Indicators of Spatial Association (LISA)

The local indicators of spatial association (LISA) are significant measures for spatial autocorrelation analysis. However, there is an inadvertent fault in Anselin's mathematical processes so that the local Moran and Geary indicators do not satisfy his second basic requirement, i.e., the sum of the local indicators is proportional to a global indicator. Based on Anselin's original intention, this paper is devoted to reconstructing the calculation formulae of the local Moran indexes and Geary coefficients through mathematical derivation and empirical evidence. Two sets of LISAs were clarified by mathematical reasoning. One set of LISAs is based on no normalized weights and centralized variable (MI1 and GC1), and the other set is but the second the set cannot. Then, the third set of LISA was proposed, treated as canonical forms (MI3 and GC3). The local Moran indexes are based on global normalized weights and standardized variable based on population standard deviation, while the local Geary coefficients are based on global normalized weights and standardized variable based on sample standard deviation. This set of LISAs satisfies the second requirement of based on row normalized weights and standardized variable (MI2 and GC2). The results show that the first set of LISAs satisfy Anselin's second requirement,Anselin's. The observational data of city population and traffic mileage in Beijing-Tianjin-Hebei region of China were employed to verify the theoretical results. This study helps to clarify the misunderstandings about LISAs in the field of geospatial analysis.

stat.AP↗
arXiv2022

Defining Urban Boundaries by Characteristic Scales

Defining an objective boundary for a city is a difficult problem, which remains to be solved by an effective method. Recent years, new methods for identifying urban boundary have been developed by means of spatial search techniques (e.g. CCA). However, the new algorithms are involved with another problem, that is, how to determine the characteristic radius of spatial search. This paper proposes new approaches to looking for the most advisable spatial searching radius for determining urban boundary. We found that the relationships between the spatial searching radius and the corresponding number of clusters take on an exponential function. In the exponential model, the scale parameter just represents the characteristic length that we can use to define the most objective urban boundary objectively. Two sets of China's cities are employed to test this method, and the results lend support to the judgment that the characteristic parameter can well serve for the spatial searching radius. The research may be revealing for making urban spatial analysis in methodology and implementing identification of urban boundaries in practice.

physics.soc-ph↗
arXiv2022

Exploring Spatial Patterns of Interurban Passenger Flows Using Dual Gravity Models

Passenger flows in a traffic network reflect spatial interaction patterns in an urban systems. Gravity models can be employed to quantitatively describe and predict spatial flows. However, how to model passenger flows and reveal the deep structure of urban and traffic networks in the case of missing partial data is still a problem to be solved. This paper is devoted to characterizing the interurban passenger flows in the Beijing-Tianjin-Hebei region of China by means of dual gravity models and Tencent location big data. The method of parameter estimation is the least squares regression. The main results are as follows. First, both railway and highway passenger flows can be effectively described by the dual gravity model. A small part of missing spatial data can be made up by the predicted values. Second, the fractal properties of traffic flows can be revealed. The railway passenger flows more follow gravity scaling law than the highway passenger flows. Third, the prediction residuals indicate the changing trend of interurban connections in the study area in recent years. The center of gravity of spatial dynamics seems to shift from the Beijing-Tianjin-Tangshan triangle to the Beijing-Baoding-Shijiazhuang axis. A conclusion can be reached that the dual gravity models is an effective tools of for analyzing spatial structures and dynamics of traffic networks and flows. Moreover, the models provide a new approach to estimate fractal dimension of traffic network and spatial flow patterns.

physics.soc-ph↗
arXiv2021

Modeling Growth Process of \b{eta} index of Transport Network Based on Nonlinear Spatial Dynamics

The \b{eta} index is one of important measurements reflecting development level of traffic networks. However, how to explain and predict the \b{eta} index growth for a geographical region is a pending problem. With the help of mathematical reasoning and empirical analysis, this paper is devoted to modeling the growing curve of \b{eta} index. A new measurement termed δ index is introduced and a set of new models are constructed. Suppose there is a nonlinear relation between human settlements and roads. A pair differential equations are built for describing the nonlinear dynamics of traffic networks. A logistic function of \b{eta} index growth is derived from the two spatial dynamic equations. On the other hand, based on verified empirical models about urbanization level, economic development level, and \b{eta} index of traffic network, a Boltzmann equation of \b{eta} index growth can be derived. Normalizing the \b{eta} index, Boltzmann equation will become logistic function. This lends an indirect support to the theoretical model of \b{eta} index from the prospective of positive studies. The models proposed in this work provided new approaches for explanation and prediction of spatio-temporal evolution of traffic networks.

physics.soc-ph↗
arXiv2021

Demonstration of Duality of Fractal Gravity Models by Scaling Symmetry

A pair of fractal gravity models can be derived from the spatial interaction models based on entropy maximizing principle and allometric scaling law. The models can be expressed as dual form in mathematics and are important for analyzing and predicting spatial flows in network of cities. However, the dual relationship of urban gravity parameters has been an empirical relationship for a long time and lacks theoretical proof. This paper is devoted to proving the duality of fractal gravity models by means of ideas from scaling invariance. The results show that a fractal gravity model can be derived from its dual form. The observational data of interurban spatial flows of Beijing-Tianjin-Hebei region of China are employed to make a case study, lending a further support to the theoretical derivation. A conclusion can be reached that the duality of gravity models rests with scaling symmetry of fractal structure. This work may be helpful for understanding the theoretical essence and application direction of spatial interaction modeling.

physics.soc-ph↗
arXiv2021

Stage Division of Urban Growth Based on Logistic Model of Fractal Dimension Curves

The time series of fractal dimension values of urban form always take on sigmoid curves. The basic model of these curves is logistic function. From the logistic model of fractal dimension curves, we can derive the growth rate formula and acceleration formula of city development. Using the inflexions of the fractal parameter curves, we can identify the different phases of urban evolution. The main results are as follows. (1) Based on the curve of fractal dimension of urban form, urban growth can be divided into four stages: initial slow growth, accelerated fast growth, decelerated fast growth, and terminal slow growth. The three dividing points are 0.2113Dmax, 0.5Dmax, and 0.7887Dmax, where Dmax is the capacity of fractal dimension. When the fractal dimension reaches half of its capacity value, 0.5Dmax, the urban growth rate reaches its peak. (2) Based on the curve of fractal dimension odds, urban growth can also be divided into four stages: initial slow filling, accelerated fast filling, decelerated fast filling, terminal slow filling. The three dividing points are 0.2113Zmax, 0.5Zmax, and 0.7887Zmax, where Zmax=/(2-Dmax) denotes the capacity of fractal dimension odds (Dmax<2). Empirical analyses show that the first scheme based fractal dimension is suitable for the young cities and the second scheme based on fractal dimension odds can be applied to mature cities. A conclusion can be reached that logistic function is one of significant model for the stage division of urban growth based on fractal parameters of cities. The results of this study provide a new way of understanding the features and mechanism of urban phase transition.

physics.soc-ph↗
arXiv2021

Derivation of Correlation Dimension from Spatial Autocorrelation Functions

Spatial autocorrelation coefficients such as Moran's index proved to be an eigenvalue of the spatial correlation matrixes. An eigenvalue represents a kind of characteristic length for quantitative analysis. However, if a spatial correlation is based on self-organized evolution, complex structure, and the distributions without characteristic scale, the eigenvalue will be ineffective. In this case, the single Moran index cannot lead to reliable statistic inferences. This paper is devoted to finding advisable approach to measure spatial autocorrelation for the scale-free processes of complex systems by means of mathematical reasoning and empirical analysis. Based on relative step function as spatial contiguity function, a series of ordered spatial autocorrelation coefficients are converted into the corresponding spatial autocorrelation functions. Then the mathematical relation between spatial correlation dimension and spatial autocorrelation functions is derived by decomposition of spatial autocorrelation functions. As results, a set of useful mathematical models are constructed for spatial analysis. Using these models, we can utilize spatial correlation dimension to make simple spatial autocorrelation analysis, and use spatial autocorrelation functions to make complex spatial autocorrelation analysis for geographical phenomena. This study reveals the inherent association of fractal patterns with spatial autocorrelation processes in nature and society. The work may inspire new ideas of spatial modeling and analysis for complex geographical systems.

physics.soc-ph↗
arXiv2021

An Analytical Process of Spatial Autocorrelation Functions Based on Moran's Index

A number of spatial statistic measurements such as Moran's I and Geary's C can be used for spatial autocorrelation analysis. Spatial autocorrelation modeling proceeded from the 1-dimension autocorrelation of time series analysis, with time lag replaced by spatial weights so that the autocorrelation functions degenerated to autocorrelation coefficients. This paper develops 2-dimensional spatial autocorrelation functions based on the Moran index using the relative staircase function as a weight function to yield a spatial weight matrix with a displacement parameter. The displacement bears analogy with time lag of time series analysis. Based on the spatial displacement parameter, two types of spatial autocorrelation functions are constructed for 2-dimensional spatial analysis. Then the partial spatial autocorrelation functions are derived by Yule-Walker recursive equation. The spatial autocorrelation functions are generalized to the autocorrelation functions based on Geary's coefficient and Getis' index. As an example, the new analytical framework was applied to the spatial autocorrelation modeling of Chinese cities. A conclusion can be reached that it is an effective method to build an autocorrelation function based on the relative step function. The spatial autocorrelation functions can be employed to reveal deep geographical information and perform spatial dynamic analysis, and lay the foundation for the scaling analysis of spatial correlation.

physics.soc-ph↗
arXiv2021

Multifractal scaling analyses of urban street network structure: the cases of twelve megacities in China

Traffic networks have been proved to be fractal systems. However, previous studies mainly focused on monofractal networks, while complex systems are of multifractal structure. This paper is devoted to exploring the general regularities of multifractal scaling processes in the street network of 12 Chinese cities. The city clustering algorithm is employed to identify urban boundaries for defining comparable study areas; box-counting method and the direct determination method are utilized to extract spatial data; the least squares calculation is employed to estimate the global and local multifractal parameters. The results showed multifractal structure of urban street networks. The global multifractal dimension spectrums are inverse S-shaped curves, while the local singularity spectrums are asymmetric unimodal curves. If the moment order q approaches negative infinity, the generalized correlation dimension will seriously exceed the embedding space dimension 2, and the local fractal dimension curve displays an abnormal decrease for most cities. The scaling relation of local fractal dimension gradually breaks if the q value is too high, but the different levels of the network always keep the scaling reflecting singularity exponent. The main conclusions are as follows. First, urban street networks follow multifractal scaling law, and scaling precedes local fractal structure. Second, the patterns of traffic networks take on characteristics of spatial concentration, but they also show the implied trend of spatial deconcentration. Third, the development space of central area and network intensive areas is limited, while the fringe zone and network sparse areas show the phenomenon of disordered evolution. This work may be revealing for understanding and further research on complex spatial networks by using multifractal theory.

physics.soc-ph↗
arXiv2020

Gravitational and Autoregressive Analysis Spatial Diffusion of COVID-19 in Hubei Province, China

The spatial diffusion of epidemic disease follows distance decay law in geography, but different diffusion processes may be modeled by different mathematical functions under different spatio-temporal conditions. This paper is devoted to modeling spatial diffusion patterns of COVID-19 stemming from Wuhan city to Hubei province. The methods include gravity and spatial auto-regression analyses. The local gravity model is derived from allometric scaling and global gravity model, and then the parameters of the local gravity model are estimated by observational data and linear regression. The main results are as below. The local gravity model based on power law decay can effectively describe the diffusion patterns and process of COVID-19 in Hubei Province, and the goodness of fit of the gravity model based on negative exponential decay to the observation data is not satisfactory. Further, the goodness of fit of the model to data entirely became better and better over time, the size elasticity coefficient increases first and then decreases, and the distance attenuation exponent decreases first and then increases. Moreover, the significance of spatial autoregressive coefficient in the model is low, and the confidence level is less than 80%. The conclusions can be reached as follows. (1) The spatial diffusion of COVID-19 of Hubei bears long range effect, and the size of a city and the distance of the city to Wuhan affect the total number of confirmed cases. (2) Wuhan direct transmission is the main process in the spatial diffusion of COVID-19 in Hubei at the early stage, and the horizontal transmission between regions is not significant. (3) The effect of spatial isolation measures taken by Chinese government against the transmission of COVID-19 is obvious. This study suggests that the role of gravity should be taken into account to prevent and control epidemic disease.

physics.soc-ph↗
arXiv2020

Modeling Urban Growth and Socio-Spatial Dynamics of Hangzhou: 1964-2010

Urban population density provides a good perspective for understanding urban growth and socio-spatial dynamics. Based on sub-district data of the five times of national population censuses in 1964, 1982, 1990, 2000, and 2010, this paper is devoted to making analyses of urban growth and the spatial restructuring of population in the city of Hangzhou, China. Research methods are based on mathematical modeling and field investigation. The modeling result shows that the negative exponential function and the power-exponential function can be well fitted to Hangzhou's observational data of urban density. The negative exponential model reflect the expected state, while the power-exponential model reflects the real state of urban density distribution. The parameters of these models are linearly correlated to the spatial information entropy of population distribution. The density gradient in the negative exponential function flattened in the 1990s and 2000s is closely related to the development of suburbanization. In terms of investigation materials and the changing trend of model parameters, we can reveal the spatio-temporal features of Hangzhou's urban growth. The main conclusions can be reached as follows. The policy of reformation and opening-up and the establishment of a market economy improved the development mode of Hangzhou. As long as a city has a good social and economic environment, it will automatically tend to the optimal state through self-organization.

physics.soc-ph↗
arXiv2020

Spatial Signal Analysis based on Wave-Spectral Fractal Scaling: A Case of Urban Street Networks

For a long time, many methods are developed to make temporal signal analyses based on time series. However, for geographical systems, spatial signal analyses are as important as temporal signal analyses. Nonstationary spatial and temporal processes are associated with nonlinearity, and cannot be effectively analyzed by conventional analytical approaches. Fractal theory provides a powerful tool for exploring complexity and is helpful for spatio-temporal signal analysis. This paper is devoted to researching spatial signals of geographical systems by means of wave-spectrum scaling. The traffic networks of 10 Chinese cities are taken as cases for positive studies. Fast Fourier transform and least squares regression analysis are employed to calculate spectral exponents. The results show that the wave-spectral density distribution of all these urban traffic networks follows scaling law, and the spectral scaling exponents can be converted to fractal dimension values. Using the fractal parameters, we can make spatial analyses for the geographical signals. The analytical process can be generalized to temporal signal analyses. The wave-spectrum scaling methods can be applied to both self-similar fractal signals and self-affine fractal signals in the geographical world.

physics.soc-ph↗
arXiv2020

Exploring the Level of Urbanization Based on Zipf's Scaling Exponent

The rank-size distribution of cities follows Zipf's law, and the Zipf scaling exponent often tends to a constant 1. This seems to be a general rule. However, a recent numerical experiment shows that there exists a contradiction between the Zipf exponent 1 and high urbanization level in a large population country. In this paper, mathematical modeling, computational analysis, and the method of proof by contradiction are employed to reveal the numerical relationships between urbanization level and Zipf scaling exponent. The main findings are as follows. (1) If Zipf scaling exponent equals 1, the urbanization rate of a large populous country can hardly exceed 50%. (2) If Zipf scaling exponent is less than 1, the urbanization level of large populous countries can exceeds 80%. A conclusion can be drawn that the Zipf exponent is the control parameter for the urbanization dynamics. In order to improve the urbanization level of large population countries, it is necessary to reduce the Zipf scaling exponent. Allometric growth law is employed to interpret the change of Zipf exponent, and scaling transform is employed to prove that different definitions of cities do no influence the above analytical conclusion essentially. This study provides a new way of looking at Zipf's law of city-size distribution and urbanization dynamics.

physics.soc-ph↗
arXiv2020

Modeling Urban Growth and Form with Spatial Entropy

Entropy is one of physical bases for fractal dimension definition, and the generalized fractal dimension was defined by Renyi entropy. Using fractal dimension, we can describe urban growth and form and characterize spatial complexity. A number of fractal models and measurements have been proposed for urban studies. However, the precondition for fractal dimension application is to find scaling relations in cities. In absence of scaling property, we can make use of entropy function and measurements. This paper is devoted to researching how to describe urban growth by using spatial entropy. By analogy with fractal dimension growth models of cities, a pair of entropy increase models can be derived and a set of entropy-based measurements can be constructed to describe urban growing process and patterns. First, logistic function and Boltzmann equation are utilized to model the entropy increase curves of urban growth. Second, a series of indexes based on spatial entropy are used to characterize urban form. Further, multifractal dimension spectrums are generalized to spatial entropy spectrums. Conclusions are drawn as follows. Entropy and fractal dimension have both intersection and different spheres of application to urban research. Thus, for a given spatial measurement scale, fractal dimension can often be replaced by spatial entropy for simplicity. The models and measurements presented in this work are significant for integrating entropy and fractal dimension into the same framework of urban spatial analysis and understanding spatial complexity of cities.

physics.soc-ph↗
arXiv2020

Fractal-based modeling and spatial analysis of urban form and growth: a case study of Shenzhen in China

Fractal dimension curves of urban growth can be modeled with sigmoid functions, including logistic function and quadratic logistic function. Different types of logistic functions indicate different spatial dynamics. The fractal dimension curves of urban growth in western countries follows the common logistic function, while these curves of cities in northern China follows quadratic logistic function. Now we want to know whether all Chinese cities follow the same rules of urban evolution. This paper is devoted to exploring the fractals and fractal dimension properties of the city of Shenzhen in southern China. The urban region is divided into four subareas, ArcGIS technology, box-counting method is adopted to extract spatial datasets, and the least squares regression is employed to estimate fractal parameters. The results show that: (1) The urban form of Shenzhen city has clear fractal structure, but fractal dimension values of different subareas are different; (2) The fractal dimension growth curves of all the four study areas can only be modeled by the common logistic function, and the goodness of fit increases over time; (3) The peak of urban growth in Shenzhen had passed before 1986, the fractal dimension growth is approaching its maximum capacity. Conclusions can be reached that the urban form of Shenzhen bears characteristics of multifractals, the fractal structure has been becoming better gradually through self-organization, but its land resources are reaching the limits of growth. The fractal dimension curves of Shenzhen's urban growth are similar to those of European and American cities, but differ from those of the cities in northern China. This suggests that there is subtle different dynamic mechanisms of city development between northern and southern China.

physics.soc-ph↗
arXiv2020

Fractal Modeling and Fractal Dimension Description of Urban Morphology

The conventional mathematical methods are based on characteristic length, while urban form has no characteristic length in many aspects. Urban area is a measure of scale dependence, which indicates the scale-free distribution of urban patterns. Thus, the urban description based on characteristic lengths should be replaced by urban characterization based on scaling. Fractal geometry is one powerful tool for scaling analysis of cities. Fractal parameters can be defined by entropy and correlation functions. However, how to understand city fractals is still a pending question. By means of logic deduction and ideas from fractal theory, this paper is devoted to discussing fractals and fractal dimensions of urban landscape. The main points of this work are as follows. First, urban form can be treated as pre-fractals rather than real fractals, and fractal properties of cities are only valid within certain scaling ranges. Second, the topological dimension of city fractals based on urban area is 0, thus the minimum fractal dimension value of fractal cities is equal to or greater than 0. Third, fractal dimension of urban form is used to substitute urban area, and it is better to define city fractals in a 2-dimensional embedding space, thus the maximum fractal dimension value of urban form is 2. A conclusion can be reached that urban form can be explored as fractals within certain ranges of scales and fractal geometry can be applied to the spatial analysis of the scale-free aspects of urban morphology.

physics.soc-ph↗
arXiv2020

Characteristic Scales, Scaling, and Geospatial Analysis

Geographical phenomena fall into two categories: scaleful phenomena and scale-free phenomena. The former bears characteristic scales, and the latter has no characteristic scale. The conventional quantitative and mathematical methods can only be effectively applied to scaleful geographical phenomena rather than the scale-free geographical phenomena. In this paper, a comparison between scaleful geographical systems and scale-free geographical systems are drawn by means of simple geographical mathematical models. The main viewpoints are as below. First, the scaleful phenomena can be researched by conventional mathematical methods, while the scale-free phenomena should be studied using the theory based on scaling such as fractal geometry; Second, the scaleful phenomena belong to distance-based geo-space, while the scale-free phenomena belong to dimension-based geo-space; Third, four approaches to distinguish scale-free phenomena from scaleful phenomena are presented, including scaling transform, probability distribution, autocorrelation and partial autocorrelation functions, and ht-index. In practice, a complex geographical system usually possesses scaleful aspects and scale-free aspects. Different methodologies must be adopted for different types of geographic systems or different aspects of the same geographic system.

physics.soc-ph↗
arXiv2020

New Framework of Getis-Ord's Indexes Associating Spatial Autocorrelation with Interaction

Spatial autocorrelation and spatial interaction are two important analytical processes for geographical analyses. However, the internal relations between the two types of models have not been brought to light. This paper is devoted to integrating spatial autocorrelation analysis and spatial interaction analysis into a logic framework by means of Getis-Ord's indexes. Based on mathematical derivation and transform, the spatial autocorrelation measurements of Getis-Ord's indexes are reconstructed in a new and simple form. A finding is that the local Getis-Ord's indexes of spatial autocorrelation are equivalent to the rescaled potential energy indexes of spatial interaction theory based on power-law distance decay. The normalized scatterplot is introduced into the spatial analysis based on Getis-Ord's indexes, and the potential energy indexes are proposed as a complementary measurement. The global Getis-Ord's index proved to be the weighted sum of the potential energy indexes and the direct sum of total potential energy. The empirical analysis of the system of Chinese cities are taken as an example to illustrate the effect of the improved methods and measurements. The mathematical framework newly derived from Getis-Ord's work is helpful for further developing the methodology of geographical spatial modeling and quantitative analysis.

physics.soc-ph↗