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  1. AU="Chen, Yanguang"
  2. AU="Sakizono, Kenji"
  3. AU="Romero-Daza, Nancy"
  4. AU="Jean-Pierre Thomé"
  5. AU=Narayanan Naveen
  6. AU=Azam Faizul
  7. AU="Özdog˘ru, Asil Ali"
  8. AU="Emami, Hajar"
  9. AU="Cimino, R."
  10. AU="Judith R. Stabel"
  11. AU="Takeuchi, Kazuto"
  12. AU="Mirzaei, Samira"
  13. AU="Carolina Salgado"
  14. AU="Mate, Sebastian"
  15. AU="Hou, Tian-Yang Liu"
  16. AU=Nino Gustavo
  17. AU="Lydon, Myra"
  18. AU="Jain, Nibha"
  19. AU="David A Schwartz"
  20. AU="Swart, Jonathan"
  21. AU="Karol, Agnieszka"
  22. AU="Reilly, Brittni"
  23. AU="Arfaatabar, Maryam"
  24. AU="Kumar Pandey, Anand"

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  1. Artikel ; Online: Spatial autocorrelation equation based on Moran's index.

    Chen, Yanguang

    Scientific reports

    2023  Band 13, Heft 1, Seite(n) 19296

    Abstract: Moran's index is an important spatial statistical measure used to determine the presence or absence of spatial autocorrelation, thereby determining the selection orientation of spatial statistical methods. However, Moran's index is chiefly a statistical ... ...

    Abstract Moran's index is an important spatial statistical measure used to determine the presence or absence of spatial autocorrelation, thereby determining the selection orientation of spatial statistical methods. However, Moran's index is chiefly a statistical measurement rather than a mathematical model. This paper is devoted to establishing spatial autocorrelation models by means of linear regression analysis. Using standardized vector as independent variable, and spatial weighted vector as dependent variable, we can obtain a set of normalized linear autocorrelation equations based on quadratic form and vector inner product. The inherent structure of the models' parameters are revealed by mathematical derivation. The slope of the equation gives Moran's index, while the intercept indicates the average value of standardized spatial weight variable. The square of the intercept is negatively correlated with the square of Moran's index, but omitting the intercept does not affect the estimation of the slope value. The datasets of a real urban system are taken as an example to verify the reasoning results. A conclusion can be reached that the inner product equation of spatial autocorrelation based on Moran's index is effective. The models extend the function of spatial analysis, and help to understand the boundary values of Moran's index.
    Sprache Englisch
    Erscheinungsdatum 2023-11-07
    Erscheinungsland England
    Dokumenttyp Journal Article
    ZDB-ID 2615211-3
    ISSN 2045-2322 ; 2045-2322
    ISSN (online) 2045-2322
    ISSN 2045-2322
    DOI 10.1038/s41598-023-45947-x
    Datenquelle MEDical Literature Analysis and Retrieval System OnLINE

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  2. Artikel ; Online: An analytical process of spatial autocorrelation functions based on Moran's index.

    Chen, Yanguang

    PloS one

    2021  Band 16, Heft 4, Seite(n) e0249589

    Abstract: 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 ... ...

    Abstract 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 the time lag in 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 using the 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.
    Mesh-Begriff(e) China ; Cities/statistics & numerical data ; Geography ; Humans ; Models, Statistical ; Spatial Analysis
    Sprache Englisch
    Erscheinungsdatum 2021-04-14
    Erscheinungsland United States
    Dokumenttyp Journal Article ; Research Support, Non-U.S. Gov't
    ISSN 1932-6203
    ISSN (online) 1932-6203
    DOI 10.1371/journal.pone.0249589
    Datenquelle MEDical Literature Analysis and Retrieval System OnLINE

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  3. Artikel ; Online: New framework of Getis-Ord's indexes associating spatial autocorrelation with interaction.

    Chen, Yanguang

    PloS one

    2020  Band 15, Heft 7, Seite(n) e0236765

    Abstract: 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 ...

    Abstract 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.
    Mesh-Begriff(e) Geography ; Humans ; Models, Statistical ; Spatial Analysis
    Sprache Englisch
    Erscheinungsdatum 2020-07-30
    Erscheinungsland United States
    Dokumenttyp Journal Article ; Research Support, Non-U.S. Gov't
    ISSN 1932-6203
    ISSN (online) 1932-6203
    DOI 10.1371/journal.pone.0236765
    Datenquelle MEDical Literature Analysis and Retrieval System OnLINE

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  4. Artikel ; Online: Fractal Modeling and Fractal Dimension Description of Urban Morphology.

    Chen, Yanguang

    Entropy (Basel, Switzerland)

    2020  Band 22, Heft 9

    Abstract: The conventional mathematical methods are based on characteristic length, while urban form has no characteristic length in many aspects. Urban area is a scale-dependence measure, which indicates the scale-free distribution of urban patterns. Thus, the ... ...

    Abstract The conventional mathematical methods are based on characteristic length, while urban form has no characteristic length in many aspects. Urban area is a scale-dependence measure, 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 the scaling analysis of cities. Fractal parameters can be defined by entropy and correlation functions. However, the question of how to understand city fractals is still pending. 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. Firstly, urban form can be treated as pre-fractals rather than real fractals, and fractal properties of cities are only valid within certain scaling ranges. Secondly, the topological dimension of city fractals based on the urban area is 0; thus, the minimum fractal dimension value of fractal cities is equal to or greater than 0. Thirdly, the fractal dimension of urban form is used to substitute the urban area, and it is better to define city fractals in a two-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.
    Sprache Englisch
    Erscheinungsdatum 2020-08-30
    Erscheinungsland Switzerland
    Dokumenttyp Journal Article
    ZDB-ID 2014734-X
    ISSN 1099-4300 ; 1099-4300
    ISSN (online) 1099-4300
    ISSN 1099-4300
    DOI 10.3390/e22090961
    Datenquelle MEDical Literature Analysis and Retrieval System OnLINE

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  5. Artikel ; Online: Characterizing the Spatio-Temporal Variations of Urban Growth with Multifractal Spectra.

    Fu, Meng / Chen, Yanguang

    Entropy (Basel, Switzerland)

    2023  Band 25, Heft 8

    Abstract: Urban morphology exhibits fractal characteristics, which can be described by multifractal scaling. Multifractal parameters under positive moment orders primarily capture information about central areas characterized by relatively stable growth, while ... ...

    Abstract Urban morphology exhibits fractal characteristics, which can be described by multifractal scaling. Multifractal parameters under positive moment orders primarily capture information about central areas characterized by relatively stable growth, while those under negative moment orders mainly reflect information about marginal areas that experience more active growth. However, effectively utilizing multifractal spectra to uncover the spatio-temporal variations of urban growth remains a challenge. To addresses this issue, this paper proposes a multifractal measurement by combining theoretical principles and empirical analysis. To capture the difference between growth stability in central areas and growth activity in marginal areas, an index based on generalized correlation dimension
    Sprache Englisch
    Erscheinungsdatum 2023-07-27
    Erscheinungsland Switzerland
    Dokumenttyp Journal Article
    ZDB-ID 2014734-X
    ISSN 1099-4300 ; 1099-4300
    ISSN (online) 1099-4300
    ISSN 1099-4300
    DOI 10.3390/e25081126
    Datenquelle MEDical Literature Analysis and Retrieval System OnLINE

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  6. Artikel ; Online: The Solutions to the Uncertainty Problem of Urban Fractal Dimension Calculation.

    Chen, Yanguang

    Entropy (Basel, Switzerland)

    2019  Band 21, Heft 5

    Abstract: Fractal geometry provides a powerful tool for scale-free spatial analysis of cities, but the fractal dimension calculation results always depend on methods and scopes of the study area. This phenomenon has been puzzling many researchers. This paper is ... ...

    Abstract Fractal geometry provides a powerful tool for scale-free spatial analysis of cities, but the fractal dimension calculation results always depend on methods and scopes of the study area. This phenomenon has been puzzling many researchers. This paper is devoted to discussing the problem of uncertainty of fractal dimension estimation and the potential solutions to it. Using regular fractals as archetypes, we can reveal the causes and effects of the diversity of fractal dimension estimation results by analogy. The main factors influencing fractal dimension values of cities include prefractal structure, multi-scaling fractal patterns, and self-affine fractal growth. The solution to the problem is to substitute the real fractal dimension values with comparable fractal dimensions. The main measures are as follows. First, select a proper method for a special fractal study. Second, define a proper study area for a city according to a study aim, or define comparable study areas for different cities. These suggestions may be helpful for the students who take interest in or have already participated in the studies of fractal cities.
    Sprache Englisch
    Erscheinungsdatum 2019-04-30
    Erscheinungsland Switzerland
    Dokumenttyp Journal Article
    ZDB-ID 2014734-X
    ISSN 1099-4300 ; 1099-4300
    ISSN (online) 1099-4300
    ISSN 1099-4300
    DOI 10.3390/e21050453
    Datenquelle MEDical Literature Analysis and Retrieval System OnLINE

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  7. Buch ; Online: Derivation of Relations between Scaling Exponents and Standard Deviation Ratios

    Chen, Yanguang

    2020  

    Abstract: The law of allometric growth is one of basic rules for understanding urban evolution. The general form of this law is allometric scaling law. However, the deep meaning and underlying rationale of the scaling exponents remain to be brought to light. In ... ...

    Abstract The law of allometric growth is one of basic rules for understanding urban evolution. The general form of this law is allometric scaling law. However, the deep meaning and underlying rationale of the scaling exponents remain to be brought to light. In this paper, the theories of linear algebra and regression analysis are employed to reveal the mathematical and statistic essence of allometric scaling exponents. Suppose that the geometric measure relations between a set of elements in an urban system follow the allometric growth law. An allometric scaling exponent is proved to equal in theory to the ratio of the standard deviation of one logarithmic measure to the standard deviation of another logarithmic measure. In empirical analyses based on observational data, the scaling exponent is equal to the product between the standard deviation ratio and the corresponding Pearson correlation coefficient. The mathematical derivation results can be verified by empirical analysis: the scaling exponent values based on the standard deviation ratios are completely identical to those based on the conventional method. This finding can be generalized to city fractals and city size distribution to explain fractal dimensions of urban space and Zipf scaling exponent of urban hierarchy. A conclusion can be reached that scaling exponents reflect the ratios of characteristic lengths. This study may be helpful for comprehending scaling from a new perspective and the connections and distinctions between scaling and characteristic scales.

    Comment: 23 pages, 3 figures, 5 tables
    Schlagwörter Physics - Physics and Society
    Thema/Rubrik (Code) 612
    Erscheinungsdatum 2020-04-03
    Erscheinungsland us
    Dokumenttyp Buch ; Online
    Datenquelle BASE - Bielefeld Academic Search Engine (Lebenswissenschaftliche Auswahl)

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  8. Buch ; Online: Geographical Modeling

    Chen, Yanguang

    from Characteristic Scale to Scaling

    2020  

    Abstract: Geographical research was successfully quantified through the quantitative revolution of geography. However, the succeeding theorization of geography encountered insurmountable difficulties. The largest obstacle of geography's theorization lies in scale- ... ...

    Abstract Geographical research was successfully quantified through the quantitative revolution of geography. However, the succeeding theorization of geography encountered insurmountable difficulties. The largest obstacle of geography's theorization lies in scale-free distributions of geographical phenomena which exist everywhere. The first paradigm of scientific research is mathematical theory. The key of a quantitative measurement and mathematical modeling is to find a valid characteristic scale. Unfortunately, for many geographical systems, there is no characteristic scale. In this case, the method of scaling should be employed to make a spatial measurement and carry out mathematical modeling. The basic idea of scaling is to find a power exponent using the double logarithmic linear relation between a variable scale and the corresponding measurement results. The exponent is a characteristic parameter which follows a scaleful distribution and can be used to characterize the scale-free phenomena. The importance of the scaling analysis in geography is becoming more and more evident for scientists.

    Comment: 19 pages, 2 figures, 5 tables
    Schlagwörter Physics - Physics and Society
    Thema/Rubrik (Code) 910
    Erscheinungsdatum 2020-01-28
    Erscheinungsland us
    Dokumenttyp Buch ; Online
    Datenquelle BASE - Bielefeld Academic Search Engine (Lebenswissenschaftliche Auswahl)

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  9. Buch ; Online: Geographical Analysis

    Chen, Yanguang

    from Distance-based Space to Dimension-based Space

    2020  

    Abstract: The traditional concept of space in geography is based on the notion of distance. Where there is a spatial analysis, there is a distance measurement. However, the precondition for effective distance-based space is that the geographical systems have ... ...

    Abstract The traditional concept of space in geography is based on the notion of distance. Where there is a spatial analysis, there is a distance measurement. However, the precondition for effective distance-based space is that the geographical systems have characteristic scales. For a scale-free geographical system, the spatial structure cannot be validly described with pure distance, and thus the distance-based space is ineffective for geographical modelling. In the real geographical world, scale-free patterns and processes are everywhere. We need new notion of geographical space. Using the ideas from fractals and scaling relations, I propose a dimension-based concept of space for scale-free geographical analysis. If a geographical phenomenon bears characteristic scales, we can model it using distance measurement; if a geographical phenomenon has no characteristic scale, we will describe it using fractal dimension, which is based on the scaling relations between distance variable and the corresponding measurements. In short, geographical space fall into two types: scaleful space and scale-free space. This study shows a new way of spatial modeling and quantitative analyses for the geographical systems without characteristic scale.

    Comment: 22 pages, 7 tables
    Schlagwörter Physics - Physics and Society
    Thema/Rubrik (Code) 910
    Erscheinungsdatum 2020-02-04
    Erscheinungsland us
    Dokumenttyp Buch ; Online
    Datenquelle BASE - Bielefeld Academic Search Engine (Lebenswissenschaftliche Auswahl)

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  10. Buch ; Online: Exploring the Level of Urbanization Based on Zipf's Scaling Exponent

    Chen, Yanguang

    2020  

    Abstract: 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 ... ...

    Abstract 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.

    Comment: 29 pages, 2 figures, 8 tables
    Schlagwörter Physics - Physics and Society
    Thema/Rubrik (Code) 612
    Erscheinungsdatum 2020-05-24
    Erscheinungsland us
    Dokumenttyp Buch ; Online
    Datenquelle BASE - Bielefeld Academic Search Engine (Lebenswissenschaftliche Auswahl)

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